| Title: | Utility-Based Optimal Phase II/III Drug Development Planning |
|---|---|
| Description: | Plan optimal sample size allocation and go/no-go decision rules for phase II/III drug development programs with time-to-event, binary or normally distributed endpoints when assuming fixed treatment effects or a prior distribution for the treatment effect, using methods from Kirchner et al. (2016) <doi:10.1002/sim.6624> and Preussler (2020). Optimal is in the sense of maximal expected utility, where the utility is a function taking into account the expected cost and benefit of the program. It is possible to extend to more complex settings with bias correction (Preussler S et al. (2020) <doi:10.1186/s12874-020-01093-w>), multiple phase III trials (Preussler et al. (2019) <doi:10.1002/bimj.201700241>), multi-arm trials (Preussler et al. (2019) <doi:10.1080/19466315.2019.1702092>), and multiple endpoints (Kieser et al. (2018) <doi:10.1002/pst.1861>). |
| Authors: | Stella Erdmann [aut], Johannes Cepicka [aut], Marietta Kirchner
[aut], Meinhard Kieser [aut], Lukas D. Sauer [aut, cre]
|
| Maintainer: | Lukas D. Sauer <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 1.0.2 |
| Built: | 2025-02-13 06:15:54 UTC |
| Source: | https://github.com/sterniii3/drugdevelopr |
The function optimal_bias of the drugdevelopR package enables planning of phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules including methods for discounting of phase II results for time-to-event endpoints (Preussler et. al, 2020).
The discounting may be necessary as programs that proceed to phase III can be overoptimistic about the treatment effect (i.e. they are biased).
The assumed true treatment effects can be assumed fixed (planning is then also possible via user friendly R Shiny App: bias) or modelled by a prior distribution.
The R Shiny application prior visualizes the prior distributions used in this package.
Fast computing is enabled by parallel programming.
optimal_bias( w, hr1, hr2, id1, id2, d2min, d2max, stepd2, hrgomin, hrgomax, stephrgo, adj = "both", lambdamin = NULL, lambdamax = NULL, steplambda = NULL, alphaCImin = NULL, alphaCImax = NULL, stepalphaCI = NULL, alpha, beta, xi2, xi3, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, b1, b2, b3, fixed = FALSE, num_cl = 1 )optimal_bias( w, hr1, hr2, id1, id2, d2min, d2max, stepd2, hrgomin, hrgomax, stephrgo, adj = "both", lambdamin = NULL, lambdamax = NULL, steplambda = NULL, alphaCImin = NULL, alphaCImax = NULL, stepalphaCI = NULL, alpha, beta, xi2, xi3, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, b1, b2, b3, fixed = FALSE, num_cl = 1 )
w |
weight for mixture prior distribution |
hr1 |
first assumed true treatment effect on HR scale for prior distribution, see the vignette on priors as well as the Shiny app for more details concerning the definition of a prior distribution. |
hr2 |
second assumed true treatment effect on HR scale for prior distribution |
id1 |
amount of information for |
id2 |
amount of information for |
d2min |
minimal number of events for phase II |
d2max |
maximal number of events for phase II |
stepd2 |
stepsize for the optimization over |
hrgomin |
minimal threshold value for the go/no-go decision rule |
hrgomax |
maximal threshold value for the go/no-go decision rule |
stephrgo |
stepsize for the optimization over HRgo |
adj |
choose type of adjustment: |
lambdamin |
minimal multiplicative adjustment parameter lambda (i.e. use estimate with a retention factor) |
lambdamax |
maximal multiplicative adjustment parameter lambda (i.e. use estimate with a retention factor) |
steplambda |
stepsize for the adjustment parameter lambda |
alphaCImin |
minimal additive adjustment parameter alphaCI (i.e. adjust the lower bound of the one-sided confidence interval) |
alphaCImax |
maximal additive adjustment parameter alphaCI (i.e. adjust the lower bound of the one-sided confidence interval) |
stepalphaCI |
stepsize for alphaCI |
alpha |
one-sided significance level |
beta |
1-beta power for calculation of the number of events for phase III by Schoenfeld (1981) formula |
xi2 |
event rate for phase II |
xi3 |
event rate for phase III |
c2 |
variable per-patient cost for phase II in 10^5 $ |
c3 |
variable per-patient cost for phase III in 10^5 $ |
c02 |
fixed cost for phase II in 10^5 $ |
c03 |
fixed cost for phase III in 10^5 $ |
K |
constraint on the costs of the program, default: Inf, e.g. no constraint |
N |
constraint on the total expected sample size of the program, default: Inf, e.g., no constraint |
S |
constraint on the expected probability of a successful program, default: -Inf, e.g., no constraint |
steps1 |
lower boundary for effect size category "small" in HR scale, default: 1 |
stepm1 |
lower boundary for effect size category "medium" in HR scale = upper boundary for effect size category "small" in HR scale, default: 0.95 |
stepl1 |
lower boundary for effect size category "large" in HR scale = upper boundary for effect size category "medium" in HR scale, default: 0.85 |
b1 |
expected gain for effect size category "small" in 10^5 $ |
b2 |
expected gain for effect size category "medium" in 10^5 $ |
b3 |
expected gain for effect size category "large" in 10^5 $ |
fixed |
choose if true treatment effects are fixed or random, if TRUE hr1 is used as fixed effect |
num_cl |
number of clusters used for parallel computing, default: 1 |
The output of the function is a data.frame object containing the optimization results:
Type of adjustment: "multipl." (multiplicative adjustment of effect size), "add." (additive adjustment of effect size), "multipl2." (multiplicative adjustment of effect size and threshold), "add2." (additive adjustment of effect size and threshold)
optimal adjustment parameter (lambda or alphaCI according to Method)
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
optimal total number of events for phase II
total expected number of events for phase III; rounded to next natural number
total expected number of events in the program; d = d2 + d3
total sample size for phase II; rounded to the next even natural number
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)
probability to go to phase III
probability of a successful program
probability of a successful program with "small" treatment effect in phase III
probability of a successful program with "medium" treatment effect in phase III
probability of a successful program with "large" treatment effect in phase III
expected costs for phase II
expected costs for phase III
and further input parameters. Taking cat(comment()) of the
data frame lists the used optimization sequences, start and
finish time of the optimization procedure. The attribute
attr(,"trace") returns the utility values of all parameter
combinations visited during optimization.
IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, last access 15.05.19.
Preussler, S., Kirchner, M., Goette, H., Kieser, M. (2020). Optimal designs for phase II/III drug development programs including methods for discounting of phase II results. Submitted to peer-review journal.
Schoenfeld, D. (1981). The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika, 68(1), 316-319.
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) ## End(Not run) # Optimize optimal_bias(w = 0.3, # define parameters for prior hr1 = 0.69, hr2 = 0.88, id1 = 210, id2 = 420, # (https://web.imbi.uni-heidelberg.de/prior/) d2min = 20, d2max = 100, stepd2 = 5, # define optimization set for d2 hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05, # define optimization set for HRgo adj = "both", # choose type of adjustment lambdamin = 0.2, lambdamax = 1, steplambda = 0.05, # define optimization set for lambda alphaCImin = 0.025, alphaCImax = 0.5, stepalphaCI = 0.025, # define optimization set for alphaCI alpha = 0.025, beta = 0.1, xi2 = 0.7, xi3 = 0.7, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # define expected benefits fixed = FALSE, # true treatment effects are fixed/random num_cl = 1) # number of coresfor parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) ## End(Not run) # Optimize optimal_bias(w = 0.3, # define parameters for prior hr1 = 0.69, hr2 = 0.88, id1 = 210, id2 = 420, # (https://web.imbi.uni-heidelberg.de/prior/) d2min = 20, d2max = 100, stepd2 = 5, # define optimization set for d2 hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05, # define optimization set for HRgo adj = "both", # choose type of adjustment lambdamin = 0.2, lambdamax = 1, steplambda = 0.05, # define optimization set for lambda alphaCImin = 0.025, alphaCImax = 0.5, stepalphaCI = 0.025, # define optimization set for alphaCI alpha = 0.025, beta = 0.1, xi2 = 0.7, xi3 = 0.7, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # define expected benefits fixed = FALSE, # true treatment effects are fixed/random num_cl = 1) # number of coresfor parallelized computing
The function optimal_bias_binary of the drugdevelopR package enables planning of phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules including methods for discounting of phase II results for binary endpoints (Preussler et. al, 2020).
The discounting may be necessary as programs that proceed to phase III can be overoptimistic about the treatment effect (i.e. they are biased).
The assumed true treatment effects can be assumed fixed or modelled by a prior distribution.
The R Shiny application prior visualizes the prior distributions used in this package.
Fast computing is enabled by parallel programming.
optimal_bias_binary( w, p0, p11, p12, in1, in2, n2min, n2max, stepn2, rrgomin, rrgomax, steprrgo, adj = "both", lambdamin = NULL, lambdamax = NULL, steplambda = NULL, alphaCImin = NULL, alphaCImax = NULL, stepalphaCI = NULL, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, b1, b2, b3, fixed = FALSE, num_cl = 1 )optimal_bias_binary( w, p0, p11, p12, in1, in2, n2min, n2max, stepn2, rrgomin, rrgomax, steprrgo, adj = "both", lambdamin = NULL, lambdamax = NULL, steplambda = NULL, alphaCImin = NULL, alphaCImax = NULL, stepalphaCI = NULL, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, b1, b2, b3, fixed = FALSE, num_cl = 1 )
w |
weight for mixture prior distribution |
p0 |
assumed true rate of control group, see here for details |
p11 |
assumed true rate of treatment group, see here for details |
p12 |
assumed true rate of treatment group, see here for details |
in1 |
amount of information for |
in2 |
amount of information for |
n2min |
minimal total sample size for phase II; must be an even number |
n2max |
maximal total sample size for phase II, must be an even number |
stepn2 |
step size for the optimization over n2; must be an even number |
rrgomin |
minimal threshold value for the go/no-go decision rule |
rrgomax |
maximal threshold value for the go/no-go decision rule |
steprrgo |
step size for the optimization over RRgo |
adj |
choose type of adjustment: |
lambdamin |
minimal multiplicative adjustment parameter lambda (i.e. use estimate with a retention factor) |
lambdamax |
maximal multiplicative adjustment parameter lambda (i.e. use estimate with a retention factor) |
steplambda |
stepsize for the adjustment parameter lambda |
alphaCImin |
minimal additive adjustment parameter alphaCI (i.e. adjust the lower bound of the one-sided confidence interval) |
alphaCImax |
maximal additive adjustment parameter alphaCI (i.e. adjust the lower bound of the one-sided confidence interval) |
stepalphaCI |
stepsize for alphaCI |
alpha |
one-sided significance level |
beta |
type II error rate; i.e. |
c2 |
variable per-patient cost for phase II in 10^5 $ |
c3 |
variable per-patient cost for phase III in 10^5 $ |
c02 |
fixed cost for phase II in 10^5 $ |
c03 |
fixed cost for phase III in 10^5 $ |
K |
constraint on the costs of the program, default: Inf, e.g. no constraint |
N |
constraint on the total expected sample size of the program, default: Inf, e.g. no constraint |
S |
constraint on the expected probability of a successful program, default: -Inf, e.g. no constraint |
steps1 |
lower boundary for effect size category "small" in RR scale, default: 1 |
stepm1 |
lower boundary for effect size category "medium" in RR scale = upper boundary for effect size category "small" in RR scale, default: 0.95 |
stepl1 |
lower boundary for effect size category "large" in RR scale = upper boundary for effect size category "medium" in RR scale, default: 0.85 |
b1 |
expected gain for effect size category "small" |
b2 |
expected gain for effect size category "medium" |
b3 |
expected gain for effect size category "large" |
fixed |
choose if true treatment effects are fixed or random, if TRUE p11 is used as fixed effect for p1 |
num_cl |
number of clusters used for parallel computing, default: 1 |
The output of the function is a data.frame object containing the optimization results:
Type of adjustment: "multipl." (multiplicative adjustment of effect size), "add." (additive adjustment of effect size), "multipl2." (multiplicative adjustment of effect size and threshold), "add2." (additive adjustment of effect size and threshold)
optimal adjustment parameter (lambda or alphaCI according to Method)
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
total sample size for phase II; rounded to the next even natural number
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)
probability to go to phase III
probability of a successful program
probability of a successful program with "small" treatment effect in phase III
probability of a successful program with "medium" treatment effect in phase III
probability of a successful program with "large" treatment effect in phase III
expected costs for phase II
expected costs for phase III
and further input parameters. Taking cat(comment()) of the
data frame lists the used optimization sequences, start and
finish time of the optimization procedure. The attribute
attr(,"trace") returns the utility values of all parameter
combinations visited during optimization.
IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_bias_binary(w = 0.3, # define parameters for prior p0 = 0.6, p11 = 0.3, p12 = 0.5, in1 = 30, in2 = 60, # (https://web.imbi.uni-heidelberg.de/prior/) n2min = 20, n2max = 100, stepn2 = 10, # define optimization set for n2 rrgomin = 0.7, rrgomax = 0.9, steprrgo = 0.05, # define optimization set for RRgo adj = "both", # choose type of adjustment alpha = 0.025, beta = 0.1, # drug development planning parameters lambdamin = 0.2, lambdamax = 1, steplambda = 0.05, # define optimization set for lambda alphaCImin = 0.025, alphaCImax = 0.5, stepalphaCI = 0.025, # define optimization set for alphaCI c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed and variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # define expected benefits fixed = TRUE, # true treatment effects are fixed/random num_cl = 1) # number of cores for parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_bias_binary(w = 0.3, # define parameters for prior p0 = 0.6, p11 = 0.3, p12 = 0.5, in1 = 30, in2 = 60, # (https://web.imbi.uni-heidelberg.de/prior/) n2min = 20, n2max = 100, stepn2 = 10, # define optimization set for n2 rrgomin = 0.7, rrgomax = 0.9, steprrgo = 0.05, # define optimization set for RRgo adj = "both", # choose type of adjustment alpha = 0.025, beta = 0.1, # drug development planning parameters lambdamin = 0.2, lambdamax = 1, steplambda = 0.05, # define optimization set for lambda alphaCImin = 0.025, alphaCImax = 0.5, stepalphaCI = 0.025, # define optimization set for alphaCI c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed and variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # define expected benefits fixed = TRUE, # true treatment effects are fixed/random num_cl = 1) # number of cores for parallelized computing
The function optimal_bias_normal of the drugdevelopR package enables planning of phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules including methods for discounting of phase II results for normally distributed endpoints (Preussler et. al, 2020).
The discounting may be necessary as programs that proceed to phase III can be overoptimistic about the treatment effect (i.e. they are biased).
The assumed true treatment effects can be assumed fixed or modelled by a prior distribution.
The R Shiny application prior visualizes the prior distributions used in this package.
Fast computing is enabled by parallel programming.
optimal_bias_normal( w, Delta1, Delta2, in1, in2, a, b, n2min, n2max, stepn2, kappamin, kappamax, stepkappa, adj = "both", lambdamin = NULL, lambdamax = NULL, steplambda = NULL, alphaCImin = NULL, alphaCImax = NULL, stepalphaCI = NULL, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 0, stepm1 = 0.5, stepl1 = 0.8, b1, b2, b3, fixed = FALSE, num_cl = 1 )optimal_bias_normal( w, Delta1, Delta2, in1, in2, a, b, n2min, n2max, stepn2, kappamin, kappamax, stepkappa, adj = "both", lambdamin = NULL, lambdamax = NULL, steplambda = NULL, alphaCImin = NULL, alphaCImax = NULL, stepalphaCI = NULL, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 0, stepm1 = 0.5, stepl1 = 0.8, b1, b2, b3, fixed = FALSE, num_cl = 1 )
w |
weight for mixture prior distribution |
Delta1 |
assumed true prior treatment effect measured as the standardized difference in means, see here for details |
Delta2 |
assumed true prior treatment effect measured as the standardized difference in means, see here for details |
in1 |
amount of information for |
in2 |
amount of information for |
a |
lower boundary for the truncation of the prior distribution |
b |
upper boundary for the truncation of the prior distribution |
n2min |
minimal total sample size for phase II; must be an even number |
n2max |
maximal total sample size for phase II, must be an even number |
stepn2 |
step size for the optimization over n2; must be an even number |
kappamin |
minimal threshold value kappa for the go/no-go decision rule |
kappamax |
maximal threshold value kappa for the go/no-go decision rule |
stepkappa |
step size for the optimization over the threshold value kappa |
adj |
choose type of adjustment: |
lambdamin |
minimal multiplicative adjustment parameter lambda (i.e. use estimate with a retention factor) |
lambdamax |
maximal multiplicative adjustment parameter lambda (i.e. use estimate with a retention factor) |
steplambda |
stepsize for the adjustment parameter lambda |
alphaCImin |
minimal additive adjustment parameter alphaCI (i.e. adjust the lower bound of the one-sided confidence interval) |
alphaCImax |
maximal additive adjustment parameter alphaCI (i.e. adjust the lower bound of the one-sided confidence interval) |
stepalphaCI |
stepsize for alphaCI |
alpha |
one-sided significance level |
beta |
type II error rate; i.e. |
c2 |
variable per-patient cost for phase II in 10^5 $ |
c3 |
variable per-patient cost for phase III in 10^5 $ |
c02 |
fixed cost for phase II in 10^5 $ |
c03 |
fixed cost for phase III in 10^5 $ |
K |
constraint on the costs of the program, default: Inf, e.g. no constraint |
N |
constraint on the total expected sample size of the program, default: Inf, e.g. no constraint |
S |
constraint on the expected probability of a successful program, default: -Inf, e.g. no constraint |
steps1 |
lower boundary for effect size category "small", default: 0 |
stepm1 |
lower boundary for effect size category "medium" = upper boundary for effect size category "small" default: 0.5 |
stepl1 |
lower boundary for effect size category "large" = upper boundary for effect size category "medium", default: 0.8 |
b1 |
expected gain for effect size category "small" in 10^5 $ |
b2 |
expected gain for effect size category "medium" in 10^5 $ |
b3 |
expected gain for effect size category "large" in 10^5 $ |
fixed |
choose if true treatment effects are fixed or following a prior distribution, if TRUE |
num_cl |
number of clusters used for parallel computing, default: 1 |
The output of the function is a data.frame object containing the optimization results:
Type of adjustment: "multipl." (multiplicative adjustment of effect size), "add." (additive adjustment of effect size), "multipl2." (multiplicative adjustment of effect size and threshold), "add2." (additive adjustment of effect size and threshold)
optimal adjustment parameter (lambda or alphaCI according to Method)
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
total sample size for phase II; rounded to the next even natural number
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)
probability to go to phase III
probability of a successful program
probability of a successful program with "small" treatment effect in phase III
probability of a successful program with "medium" treatment effect in phase III
probability of a successful program with "large" treatment effect in phase III
expected costs for phase II
expected costs for phase III
and further input parameters. Taking cat(comment()) of the
data frame lists the used optimization sequences, start and
finish time of the optimization procedure. The attribute
attr(,"trace") returns the utility values of all parameter
combinations visited during optimization.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences.
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_bias_normal(w=0.3, # define parameters for prior Delta1 = 0.375, Delta2 = 0.625, in1=300, in2=600, # (https://web.imbi.uni-heidelberg.de/prior/) a = 0.25, b = 0.75, n2min = 20, n2max = 100, stepn2 = 10, # define optimization set for n2 kappamin = 0.02, kappamax = 0.2, stepkappa = 0.02, # define optimization set for kappa adj = "both", # choose type of adjustment lambdamin = 0.2, lambdamax = 1, steplambda = 0.05, # define optimization set for lambda alphaCImin = 0.025, alphaCImax = 0.5, stepalphaCI = 0.025, # define optimization set for alphaCI alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.675, c3 = 0.72, c02 = 15, c03 = 20, # fixed and variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 0, # define lower boundary for "small" stepm1 = 0.5, # "medium" stepl1 = 0.8, # and "large" effect size categories b1 = 3000, b2 = 8000, b3 = 10000, # define expected benefits fixed = TRUE, # true treatment effects are fixed/random num_cl = 1) # number of coresfor parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_bias_normal(w=0.3, # define parameters for prior Delta1 = 0.375, Delta2 = 0.625, in1=300, in2=600, # (https://web.imbi.uni-heidelberg.de/prior/) a = 0.25, b = 0.75, n2min = 20, n2max = 100, stepn2 = 10, # define optimization set for n2 kappamin = 0.02, kappamax = 0.2, stepkappa = 0.02, # define optimization set for kappa adj = "both", # choose type of adjustment lambdamin = 0.2, lambdamax = 1, steplambda = 0.05, # define optimization set for lambda alphaCImin = 0.025, alphaCImax = 0.5, stepalphaCI = 0.025, # define optimization set for alphaCI alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.675, c3 = 0.72, c02 = 15, c03 = 20, # fixed and variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 0, # define lower boundary for "small" stepm1 = 0.5, # "medium" stepl1 = 0.8, # and "large" effect size categories b1 = 3000, b2 = 8000, b3 = 10000, # define expected benefits fixed = TRUE, # true treatment effects are fixed/random num_cl = 1) # number of coresfor parallelized computing
The optimal_binary function of the drugdevelopR package enables
planning of phase II/III drug development programs with optimal sample size
allocation and go/no-go decision rules for binary endpoints. In this case,
the treatment effect is measured by the risk ratio (RR). The assumed true
treatment effects can be assumed to be fixed or modelled by a prior
distribution. The R Shiny application
prior visualizes the prior
distributions used in this package. Fast computing is enabled by parallel
programming.
optimal_binary( w, p0, p11, p12, in1, in2, n2min, n2max, stepn2, rrgomin, rrgomax, steprrgo, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, b1, b2, b3, gamma = 0, fixed = FALSE, skipII = FALSE, num_cl = 1 )optimal_binary( w, p0, p11, p12, in1, in2, n2min, n2max, stepn2, rrgomin, rrgomax, steprrgo, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, b1, b2, b3, gamma = 0, fixed = FALSE, skipII = FALSE, num_cl = 1 )
w |
weight for mixture prior distribution |
p0 |
assumed true rate of control group, see here for details |
p11 |
assumed true rate of treatment group, see here for details |
p12 |
assumed true rate of treatment group, see here for details |
in1 |
amount of information for |
in2 |
amount of information for |
n2min |
minimal total sample size for phase II; must be an even number |
n2max |
maximal total sample size for phase II, must be an even number |
stepn2 |
step size for the optimization over n2; must be an even number |
rrgomin |
minimal threshold value for the go/no-go decision rule |
rrgomax |
maximal threshold value for the go/no-go decision rule |
steprrgo |
step size for the optimization over RRgo |
alpha |
one-sided significance level |
beta |
type II error rate; i.e. |
c2 |
variable per-patient cost for phase II in 10^5 $ |
c3 |
variable per-patient cost for phase III in 10^5 $ |
c02 |
fixed cost for phase II in 10^5 $ |
c03 |
fixed cost for phase III in 10^5 $ |
K |
constraint on the costs of the program, default: Inf, e.g. no constraint |
N |
constraint on the total expected sample size of the program, default: Inf, e.g. no constraint |
S |
constraint on the expected probability of a successful program, default: -Inf, e.g. no constraint |
steps1 |
lower boundary for effect size category "small" in RR scale, default: 1 |
stepm1 |
lower boundary for effect size category "medium" in RR scale = upper boundary for effect size category "small" in RR scale, default: 0.95 |
stepl1 |
lower boundary for effect size category "large" in RR scale = upper boundary for effect size category "medium" in RR scale, default: 0.85 |
b1 |
expected gain for effect size category "small" |
b2 |
expected gain for effect size category "medium" |
b3 |
expected gain for effect size category "large" |
gamma |
to model different populations in phase II and III choose |
fixed |
choose if true treatment effects are fixed or random, if TRUE p11 is used as fixed effect for p1 |
skipII |
skipII choose if skipping phase II is an option, default: FALSE;
if TRUE, the program calculates the expected utility for the case when phase
II is skipped and compares it to the situation when phase II is not skipped.
The results are then returned as a two-row data frame, |
num_cl |
number of clusters used for parallel computing, default: 1 |
The output of the function is a data.frame object containing the optimization results:
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
total sample size for phase II; rounded to the next even natural number
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)
probability to go to phase III
probability of a successful program
probability of a successful program with "small" treatment effect in phase III
probability of a successful program with "medium" treatment effect in phase III
probability of a successful program with "large" treatment effect in phase III
expected costs for phase II
expected costs for phase III
and further input parameters. Taking cat(comment()) of the
data frame lists the used optimization sequences, start and
finish time of the optimization procedure. The attribute
attr(,"trace") returns the utility values of all parameter
combinations visited during optimization.
IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, last access 15.05.19.
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) ## End(Not run) # Optimize optimal_binary(w = 0.3, # define parameters for prior p0 = 0.6, p11 = 0.3, p12 = 0.5, in1 = 30, in2 = 60, # (https://web.imbi.uni-heidelberg.de/prior/) n2min = 20, n2max = 100, stepn2 = 4, # define optimization set for n2 rrgomin = 0.7, rrgomax = 0.9, steprrgo = 0.05, # define optimization set for RRgo alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed and variable costs for phase II/III, K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" treatment effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # define expected benefits gamma = 0, # population structures in phase II/III fixed = FALSE, # true treatment effects are fixed/random skipII = FALSE, # choose if skipping phase II is an option num_cl = 2) # number of cores for parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) ## End(Not run) # Optimize optimal_binary(w = 0.3, # define parameters for prior p0 = 0.6, p11 = 0.3, p12 = 0.5, in1 = 30, in2 = 60, # (https://web.imbi.uni-heidelberg.de/prior/) n2min = 20, n2max = 100, stepn2 = 4, # define optimization set for n2 rrgomin = 0.7, rrgomax = 0.9, steprrgo = 0.05, # define optimization set for RRgo alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed and variable costs for phase II/III, K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" treatment effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # define expected benefits gamma = 0, # population structures in phase II/III fixed = FALSE, # true treatment effects are fixed/random skipII = FALSE, # choose if skipping phase II is an option num_cl = 2) # number of cores for parallelized computing
The function optimal_multiarm of the drugdevelopR package
enables planning of multi-arm phase II/III drug development programs with
optimal sample size allocation and go/no-go decision rules
(Preussler et. al, 2019) for time-to-event endpoints. So far, only three-arm
trials with two treatments and one control are supported. The assumed true
treatment effects are assumed fixed (planning is also possible via
user-friendly R Shiny App:
multiarm). Fast
computing is enabled by parallel programming.
optimal_multiarm( hr1, hr2, ec, n2min, n2max, stepn2, hrgomin, hrgomax, stephrgo, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, b1, b2, b3, strategy, num_cl = 1 )optimal_multiarm( hr1, hr2, ec, n2min, n2max, stepn2, hrgomin, hrgomax, stephrgo, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, b1, b2, b3, strategy, num_cl = 1 )
hr1 |
assumed true treatment effect on HR scale for treatment 1 |
hr2 |
assumed true treatment effect on HR scale for treatment 2 |
ec |
control arm event rate for phase II and III |
n2min |
minimal total sample size in phase II, must be divisible by 3 |
n2max |
maximal total sample size in phase II, must be divisible by 3 |
stepn2 |
stepsize for the optimization over n2, must be divisible by 3 |
hrgomin |
minimal threshold value for the go/no-go decision rule |
hrgomax |
maximal threshold value for the go/no-go decision rule |
stephrgo |
step size for the optimization over HRgo |
alpha |
one-sided significance level/family-wise error rate |
beta |
type-II error rate for any pair, i.e. |
c2 |
variable per-patient cost for phase II |
c3 |
variable per-patient cost for phase III |
c02 |
fixed cost for phase II |
c03 |
fixed cost for phase III |
K |
constraint on the costs of the program, default: |
N |
constraint on the total expected sample size of the program, default: |
S |
constraint on the expected probability of a successful program, default: |
steps1 |
lower boundary for effect size category "small" in HR scale, default: 1 |
stepm1 |
lower boundary for effect size category "medium" in HR scale = upper boundary for effect size category "small" in HR scale, default: 0.95 |
stepl1 |
lower boundary for effect size category "large" in HR scale = upper boundary for effect size category "medium" in HR scale, default: 0.85 |
b1 |
expected gain for effect size category "small" |
b2 |
expected gain for effect size category "medium" |
b3 |
expected gain for effect size category "large" |
strategy |
choose strategy: 1 (only the best promising candidate), 2 (all promising candidates) or 3 (both strategies) |
num_cl |
number of clusters used for parallel computing, default: 1 |
The output of the function is a data.frame object containing the optimization results:
Strategy, 1: "only best promising" or 2: "all promising"
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
optimal total number of events for phase II
total expected number of events for phase III; rounded to next natural number
total expected number of events in the program; d = d2 + d3
total sample size for phase II; rounded to the next even natural number
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)
probability to go to phase III
probability of a successful program
probability of a successful program with two arms in phase III
probability of a successful program with three arms in phase III
expected costs for phase II
expected costs for phase III
and further input parameters. Taking cat(comment()) of the
data frame lists the used optimization sequences, start and
finish time of the optimization procedure. The attribute
attr(,"trace") returns the utility values of all parameter
combinations visited during optimization.
Preussler, S., Kirchner, M., Goette, H., Kieser, M. (2019). Optimal Designs for Multi-Arm Phase II/III Drug Development Programs. Submitted to peer-review journal.
IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_multiarm(hr1 = 0.75, hr2 = 0.80, # define assumed true HRs ec = 0.6, # control arm event rate n2min = 30, n2max = 90, stepn2 = 6, # define optimization set for n2 hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05, # define optimization set for HRgo alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # define expected benefit strategy = 1, # choose strategy: 1, 2 or 3 num_cl = 1) # number of cores for parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_multiarm(hr1 = 0.75, hr2 = 0.80, # define assumed true HRs ec = 0.6, # control arm event rate n2min = 30, n2max = 90, stepn2 = 6, # define optimization set for n2 hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05, # define optimization set for HRgo alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # define expected benefit strategy = 1, # choose strategy: 1, 2 or 3 num_cl = 1) # number of cores for parallelized computing
The optimal_multiarm_binary function enables planning of
multi-arm phase II/III drug
development programs with optimal sample size allocation and go/no-go
decision rules. For binary endpoints the treatment effect is measured by the
risk ratio (RR). So far, only three-arm trials with two treatments and one
control are supported. The assumed true treatment effects can be assumed fixed
or modelled by a prior distribution. The R Shiny application
prior visualizes the prior
distributions used in this package. Fast computing is enabled by parallel
programming.
optimal_multiarm_binary( p0, p11, p12, n2min, n2max, stepn2, rrgomin, rrgomax, steprrgo, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, b1, b2, b3, strategy, num_cl = 1 )optimal_multiarm_binary( p0, p11, p12, n2min, n2max, stepn2, rrgomin, rrgomax, steprrgo, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, b1, b2, b3, strategy, num_cl = 1 )
p0 |
assumed true rate of the control group |
p11 |
assumed true rate of the treatment arm 1 |
p12 |
assumed true rate of treatment arm 2 |
n2min |
minimal total sample size in phase II, must be divisible by 3 |
n2max |
maximal total sample size in phase II, must be divisible by 3 |
stepn2 |
stepsize for the optimization over n2, must be divisible by 3 |
rrgomin |
minimal threshold value for the go/no-go decision rule |
rrgomax |
maximal threshold value for the go/no-go decision rule |
steprrgo |
step size for the optimization over RRgo |
alpha |
one-sided significance level/family-wise error rate |
beta |
type-II error rate for any pair, i.e. |
c2 |
variable per-patient cost for phase II |
c3 |
variable per-patient cost for phase III |
c02 |
fixed cost for phase II |
c03 |
fixed cost for phase III |
K |
constraint on the costs of the program, default: |
N |
constraint on the total expected sample size of the program, default: |
S |
constraint on the expected probability of a successful program, default: |
steps1 |
lower boundary for effect size category "small" in RR scale, default: 1 |
stepm1 |
lower boundary for effect size category "medium" in RR scale = upper boundary for effect size category "small" in RR scale, default: 0.95 |
stepl1 |
lower boundary for effect size category "large" in RR scale = upper boundary for effect size category "medium" in RR scale, default: 0.85 |
b1 |
expected gain for effect size category "small" |
b2 |
expected gain for effect size category "medium" |
b3 |
expected gain for effect size category "large" |
strategy |
choose strategy: 1 (only the best promising candidate), 2 (all promising candidates) or 3 (both strategies) |
num_cl |
number of clusters used for parallel computing, default: 1 |
The output of the function is a data.frame object containing the optimization results:
Strategy, 1: "only best promising" or 2: "all promising"
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
total sample size for phase II; rounded to the next even natural number
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)
probability to go to phase III
probability of a successful program
probability of a successful program with two arms in phase III
probability of a successful program with three arms in phase III
expected costs for phase II
expected costs for phase III
and further input parameters. Taking cat(comment()) of the
data frame lists the used optimization sequences, start and
finish time of the optimization procedure. The attribute
attr(,"trace") returns the utility values of all parameter
combinations visited during optimization.
IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_multiarm_binary( p0 = 0.6, p11 = 0.3, p12 = 0.5, n2min = 20, n2max = 100, stepn2 = 4, # define optimization set for n2 rrgomin = 0.7, rrgomax = 0.9, steprrgo = 0.05, # define optimization set for RRgo alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # define expected benefits strategy = 1, num_cl = 1) # number of cores for parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_multiarm_binary( p0 = 0.6, p11 = 0.3, p12 = 0.5, n2min = 20, n2max = 100, stepn2 = 4, # define optimization set for n2 rrgomin = 0.7, rrgomax = 0.9, steprrgo = 0.05, # define optimization set for RRgo alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # define expected benefits strategy = 1, num_cl = 1) # number of cores for parallelized computing
The optimal_multiarm_normal function enables planning of
multi-arm phase II/III drug development programs with optimal sample size
allocation and go/no-go decision rules. For normally distributed endpoints,
the treatment effect is measured by the standardized difference in means
(Delta). So far, only three-arm trials with two treatments and one control
are supported. The assumed true treatment effects can be assumed fixed or
modelled by a prior distribution. The R Shiny application
prior visualizes the
prior distributions used in this package. Fast computing is enabled by
parallel programming.
optimal_multiarm_normal( Delta1, Delta2, n2min, n2max, stepn2, kappamin, kappamax, stepkappa, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 0, stepm1 = 0.5, stepl1 = 0.8, b1, b2, b3, strategy, num_cl = 1 )optimal_multiarm_normal( Delta1, Delta2, n2min, n2max, stepn2, kappamin, kappamax, stepkappa, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 0, stepm1 = 0.5, stepl1 = 0.8, b1, b2, b3, strategy, num_cl = 1 )
Delta1 |
assumed true treatment effect as the standardized difference in means for treatment arm 1 |
Delta2 |
assumed true treatment effect as the standardized difference in means for treatment arm 2 |
n2min |
minimal total sample size in phase II, must be divisible by 3 |
n2max |
maximal total sample size in phase II, must be divisible by 3 |
stepn2 |
stepsize for the optimization over n2, must be divisible by 3 |
kappamin |
minimal threshold value kappa for the go/no-go decision rule |
kappamax |
maximal threshold value kappa for the go/no-go decision rule |
stepkappa |
step size for the optimization over the threshold value kappa |
alpha |
one-sided significance level/family-wise error rate |
beta |
type-II error rate for any pair, i.e. |
c2 |
variable per-patient cost for phase II |
c3 |
variable per-patient cost for phase III |
c02 |
fixed cost for phase II |
c03 |
fixed cost for phase III |
K |
constraint on the costs of the program, default: |
N |
constraint on the total expected sample size of the program, default: |
S |
constraint on the expected probability of a successful program, default: |
steps1 |
lower boundary for effect size category "small", default: 0 |
stepm1 |
lower boundary for effect size category "medium" = upper boundary for effect size category "small" default: 0.5 |
stepl1 |
lower boundary for effect size category "large" = upper boundary for effect size category "medium", default: 0.8 |
b1 |
expected gain for effect size category "small" |
b2 |
expected gain for effect size category "medium" |
b3 |
expected gain for effect size category "large" |
strategy |
choose strategy: 1 (only the best promising candidate), 2 (all promising candidates) or 3 (both strategies) |
num_cl |
number of clusters used for parallel computing, default: 1 |
The output of the function is a data.frame object containing the optimization results:
Strategy, 1: "only best promising" or 2: "all promising"
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
total sample size for phase II; rounded to the next even natural number
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)
probability to go to phase III
probability of a successful program
probability of a successful program with two arms in phase III
probability of a successful program with three arms in phase III
expected costs for phase II
expected costs for phase III
and further input parameters. Taking cat(comment()) of the
data frame lists the used optimization sequences, start and
finish time of the optimization procedure. The attribute
attr(,"trace") returns the utility values of all parameter
combinations visited during optimization.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences.
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_multiarm_normal(Delta1 = 0.375, Delta2 = 0.625, n2min = 20, n2max = 100, stepn2 = 4, # define optimization set for n2 kappamin = 0.02, kappamax = 0.2, stepkappa = 0.02, # define optimization set for kappa alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.675, c3 = 0.72, c02 = 15, c03 = 20, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 0, # define lower boundary for "small" stepm1 = 0.5, # "medium" stepl1 = 0.8, # and "large" effect size categories b1 = 3000, b2 = 8000, b3 = 10000, # define expected benefits strategy = 1, num_cl = 1) # number of cores for parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_multiarm_normal(Delta1 = 0.375, Delta2 = 0.625, n2min = 20, n2max = 100, stepn2 = 4, # define optimization set for n2 kappamin = 0.02, kappamax = 0.2, stepkappa = 0.02, # define optimization set for kappa alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.675, c3 = 0.72, c02 = 15, c03 = 20, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 0, # define lower boundary for "small" stepm1 = 0.5, # "medium" stepl1 = 0.8, # and "large" effect size categories b1 = 3000, b2 = 8000, b3 = 10000, # define expected benefits strategy = 1, num_cl = 1) # number of cores for parallelized computing
The function optimal_multiple_normal of the drugdevelopR
package enables planning of phase II/III drug development programs with
optimal sample size allocation and go/no-go decision rules for two-arm
trials with two normally distributed endpoints and one control group
(Preussler et. al, 2019).
optimal_multiple_normal( Delta1, Delta2, in1, in2, sigma1, sigma2, n2min, n2max, stepn2, kappamin, kappamax, stepkappa, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 0, stepm1 = 0.5, stepl1 = 0.8, b1, b2, b3, rho, fixed, relaxed = FALSE, num_cl = 1 )optimal_multiple_normal( Delta1, Delta2, in1, in2, sigma1, sigma2, n2min, n2max, stepn2, kappamin, kappamax, stepkappa, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 0, stepm1 = 0.5, stepl1 = 0.8, b1, b2, b3, rho, fixed, relaxed = FALSE, num_cl = 1 )
Delta1 |
assumed true treatment effect for endpoint 1 measured as the difference in means |
Delta2 |
assumed true treatment effect for endpoint 2 measured as the difference in means |
in1 |
amount of information for Delta1 in terms of number of events |
in2 |
amount of information for Delta2 in terms of number of events |
sigma1 |
variance of endpoint 1 |
sigma2 |
variance of endpoint 2 |
n2min |
minimal total sample size in phase II, must be divisible by 3 |
n2max |
maximal total sample size in phase II, must be divisible by 3 |
stepn2 |
stepsize for the optimization over n2, must be divisible by 3 |
kappamin |
minimal threshold value kappa for the go/no-go decision rule |
kappamax |
maximal threshold value kappa for the go/no-go decision rule |
stepkappa |
step size for the optimization over the threshold value kappa |
alpha |
one-sided significance level/family-wise error rate |
beta |
type-II error rate for any pair, i.e. |
c2 |
variable per-patient cost for phase II in 10^5 $ |
c3 |
variable per-patient cost for phase III in 10^5 $ |
c02 |
fixed cost for phase II in 10^5 $ |
c03 |
fixed cost for phase III in 10^5 $ |
K |
constraint on the costs of the program, default: Inf, e.g. no constraint |
N |
constraint on the total expected sample size of the program, default: Inf, e.g. no constraint |
S |
constraint on the expected probability of a successful program, default: -Inf, e.g. no constraint |
steps1 |
lower boundary for effect size category "small", default: 0 |
stepm1 |
lower boundary for effect size category "medium" = upper boundary for effect size category "small" default: 0.5 |
stepl1 |
lower boundary for effect size category "large" = upper boundary for effect size category "medium", default: 0.8 |
b1 |
expected gain for effect size category "small" in 10^5 $ |
b2 |
expected gain for effect size category "medium" in 10^5 $ |
b3 |
expected gain for effect size category "large" in 10^5 $ |
rho |
correlation between the two endpoints |
fixed |
assumed fixed treatment effect |
relaxed |
relaxed or strict decision rule |
num_cl |
number of clusters used for parallel computing, default: 1 |
For this setting, the drug development program is defined to be successful if it proceeds from phase II to phase III and all endpoints show a statistically significant treatment effect in phase III. For example, this situation is found in Alzheimer’s disease trials, where a drug should show significant results in improving cognition (cognitive endpoint) as well as in improving activities of daily living (functional endpoint).
The effect size categories small, medium and large are applied to both endpoints. In order to define an overall effect size from the two individual effect sizes, the function implements two different combination rules:
A strict rule (relaxed = FALSE) assigning a large overall effect in case
both endpoints show an effect of large size, a small overall effect in
case that at least one of the endpoints shows a small effect, and a medium
overall effect otherwise, and
A relaxed rule (relaxed = TRUE) assigning a large overall effect if at
least one of the endpoints shows a large effect, a small effect if both
endpoints show a small effect, and a medium overall effect otherwise.
Fast computing is enabled by parallel programming.
Monte Carlo simulations are applied for calculating utility, event count and other operating characteristics in this setting. Hence, the results are affected by random uncertainty.
The output of the function is a data.frame object containing the optimization results:
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
total sample size for phase II; rounded to the next even natural number
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)
probability to go to phase III
probability of a successful program
probability of a successful program with "small" treatment effect in phase III
probability of a successful program with "medium" treatment effect in phase III
probability of a successful program with "large" treatment effect in phase III
expected costs for phase II
expected costs for phase III
and further input parameters. Taking cat(comment()) of the
data frame lists the used optimization sequences, start and
finish time of the optimization procedure. The attribute
attr(,"trace") returns the utility values of all parameter
combinations visited during optimization.
Meinhard Kieser, Marietta Kirchner, Eva Dölger, Heiko Götte (2018). Optimal planning of phase II/III programs for clinical trials with multiple endpoints
IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize set.seed(123) # This function relies on Monte Carlo integration optimal_multiple_normal(Delta1 = 0.75, Delta2 = 0.80, in1=300, in2=600, # define assumed true HRs sigma1 = 8, sigma2= 12, # variances for both endpoints n2min = 30, n2max = 90, stepn2 = 10, # define optimization set for n2 kappamin = 0.05, kappamax = 0.2, stepkappa = 0.05, # define optimization set for HRgo alpha = 0.025, beta = 0.1, # planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed/variable costs: phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 0, # define lower boundary for "small" stepm1 = 0.5, # "medium" stepl1 = 0.8, # and "large" effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # define expected benefit rho = 0.5, relaxed = TRUE, # strict or relaxed rule fixed = TRUE, # treatment effect num_cl = 1) # parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize set.seed(123) # This function relies on Monte Carlo integration optimal_multiple_normal(Delta1 = 0.75, Delta2 = 0.80, in1=300, in2=600, # define assumed true HRs sigma1 = 8, sigma2= 12, # variances for both endpoints n2min = 30, n2max = 90, stepn2 = 10, # define optimization set for n2 kappamin = 0.05, kappamax = 0.2, stepkappa = 0.05, # define optimization set for HRgo alpha = 0.025, beta = 0.1, # planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed/variable costs: phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 0, # define lower boundary for "small" stepm1 = 0.5, # "medium" stepl1 = 0.8, # and "large" effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # define expected benefit rho = 0.5, relaxed = TRUE, # strict or relaxed rule fixed = TRUE, # treatment effect num_cl = 1) # parallelized computing
The function optimal_multiple_tte of the drugdevelopR package
enables planning of phase II/III drug development programs with optimal
sample size allocation and go/no-go decision rules (Preussler et. al, 2019)
in a two-arm trial with two time-to-event endpoints.
optimal_multiple_tte( hr1, hr2, id1, id2, n2min, n2max, stepn2, hrgomin, hrgomax, stephrgo, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, b11, b21, b31, b12, b22, b32, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, rho, fixed = TRUE, num_cl = 1 )optimal_multiple_tte( hr1, hr2, id1, id2, n2min, n2max, stepn2, hrgomin, hrgomax, stephrgo, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, b11, b21, b31, b12, b22, b32, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, rho, fixed = TRUE, num_cl = 1 )
hr1 |
assumed true treatment effect on HR scale for endpoint 1 (e.g. OS) |
hr2 |
assumed true treatment effect on HR scale for endpoint 2 (e.g. PFS) |
id1 |
amount of information for hr1 in terms of number of events |
id2 |
amount of information for hr2 in terms of number of events |
n2min |
minimal total sample size in phase II, must be divisible by 3 |
n2max |
maximal total sample size in phase II, must be divisible by 3 |
stepn2 |
stepsize for the optimization over n2, must be divisible by 3 |
hrgomin |
minimal threshold value for the go/no-go decision rule |
hrgomax |
maximal threshold value for the go/no-go decision rule |
stephrgo |
step size for the optimization over HRgo |
alpha |
one-sided significance level/family-wise error rate |
beta |
type-II error rate for any pair, i.e. |
c2 |
variable per-patient cost for phase II in 10^5 $. |
c3 |
variable per-patient cost for phase III in 10^5 $. |
c02 |
fixed cost for phase II in 10^5 $. |
c03 |
fixed cost for phase III in 10^5 $. |
K |
constraint on the costs of the program, default: Inf, e.g. no constraint |
N |
constraint on the total expected sample size of the program, default: Inf, e.g. no constraint |
S |
constraint on the expected probability of a successful program, default: -Inf, e.g. no constraint |
b11 |
expected gain for effect size category |
b21 |
expected gain for effect size category |
b31 |
expected gain for effect size category |
b12 |
expected gain for effect size category |
b22 |
expected gain for effect size category |
b32 |
expected gain for effect size category |
steps1 |
lower boundary for effect size category "small" in HR scale, default: 1 |
stepm1 |
lower boundary for effect size category "medium" in HR scale = upper boundary for effect size category "small" in HR scale, default: 0.95 |
stepl1 |
lower boundary for effect size category "large" in HR scale = upper boundary for effect size category "medium" in HR scale, default: 0.85 |
rho |
correlation between the two endpoints |
fixed |
assumed fixed treatment effect |
num_cl |
number of clusters used for parallel computing, default: 1 |
In this setting, the drug development program is defined to be successful if it proceeds from phase II to phase III and at least one endpoint shows a statistically significant treatment effect in phase III. For example, this situation is found in oncology trials, where overall survival (OS) and progression-free survival (PFS) are the two endpoints of interest.
The gain of a successful program may differ according to the importance of
the endpoint that is significant. If endpoint 1 is significant (no matter
whether endpoint 2 is significant or not), then the gains b11, b21
and b31 will be used for calculation of the utility. If only endpoint 2
is significant, then b12, b22 and b32 will be used. This
also matches the oncology example, where OS (i.e. endpoint 1) implicates
larger expected gains than PFS alone (i.e. endpoint 2).
Fast computing is enabled by parallel programming.
Monte Carlo simulations are applied for calculating utility, event count and other operating characteristics in this setting. Hence, the results are affected by random uncertainty. The extent of uncertainty is discussed in (Kieser et al. 2018).
The output of the function is a data.frame object containing the optimization results:
probability that one endpoint is significant
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
optimal total number of events for phase II
total expected number of events for phase III; rounded to next natural number
total expected number of events in the program; d = d2 + d3
total sample size for phase II; rounded to the next even natural number
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)
probability to go to phase III
probability of a successful program
probability of a successful program with "small" treatment effect in phase III
probability of a successful program with "medium" treatment effect in phase III
probability of a successful program with "large" treatment effect in phase III
expected costs for phase II
expected costs for phase III
and further input parameters. Taking cat(comment()) of the
data frame lists the used optimization sequences, start and
finish time of the optimization procedure. The attribute
attr(,"trace") returns the utility values of all parameter
combinations visited during optimization.
Kieser, M., Kirchner, M. Dölger, E., Götte, H. (2018).Optimal planning of phase II/III programs for clinical trials with multiple endpoints, Pharm Stat. 2018 Sep; 17(5):437-457.
Preussler, S., Kirchner, M., Goette, H., Kieser, M. (2019). Optimal Designs for Multi-Arm Phase II/III Drug Development Programs. Submitted to peer-review journal.
IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize set.seed(123) # This function relies on Monte Carlo integration optimal_multiple_tte(hr1 = 0.75, hr2 = 0.80, id1 = 210, id2 = 420, # define assumed true HRs n2min = 30, n2max = 90, stepn2 = 6, # define optimization set for n2 hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05, # define optimization set for HRgo alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" effect size categories b11 = 1000, b21 = 2000, b31 = 3000, b12 = 1000, b22 = 1500, b32 = 2000, # define expected benefits (both scenarios) rho = 0.6, fixed = TRUE, # correlation and treatment effect num_cl = 1) # number of cores for parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize set.seed(123) # This function relies on Monte Carlo integration optimal_multiple_tte(hr1 = 0.75, hr2 = 0.80, id1 = 210, id2 = 420, # define assumed true HRs n2min = 30, n2max = 90, stepn2 = 6, # define optimization set for n2 hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05, # define optimization set for HRgo alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" effect size categories b11 = 1000, b21 = 2000, b31 = 3000, b12 = 1000, b22 = 1500, b32 = 2000, # define expected benefits (both scenarios) rho = 0.6, fixed = TRUE, # correlation and treatment effect num_cl = 1) # number of cores for parallelized computing
The function optimal_multitrial of the drugdevelopR package enables planning of phase II/III drug development programs with time-to-event endpoints for programs with several phase III trials (Preussler et. al, 2019).
Its main output values are the optimal sample size allocation and optimal go/no-go decision rules.
The assumed true treatment effects can be assumed to be fixed (planning is then also possible via user friendly R Shiny App: multitrial) or can be modelled by a prior distribution.
The R Shiny application prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.
optimal_multitrial( w, hr1, hr2, id1, id2, d2min, d2max, stepd2, hrgomin, hrgomax, stephrgo, alpha, beta, xi2, xi3, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, b1, b2, b3, case, strategy = TRUE, fixed = FALSE, num_cl = 1 )optimal_multitrial( w, hr1, hr2, id1, id2, d2min, d2max, stepd2, hrgomin, hrgomax, stephrgo, alpha, beta, xi2, xi3, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, b1, b2, b3, case, strategy = TRUE, fixed = FALSE, num_cl = 1 )
w |
weight for mixture prior distribution, see this Shiny application for the choice of weights |
hr1 |
first assumed true treatment effect on HR scale for prior distribution |
hr2 |
second assumed true treatment effect on HR scale for prior distribution |
id1 |
amount of information for |
id2 |
amount of information for |
d2min |
minimal number of events for phase II |
d2max |
maximal number of events for phase II |
stepd2 |
step size for the optimization over d2 |
hrgomin |
minimal threshold value for the go/no-go decision rule |
hrgomax |
maximal threshold value for the go/no-go decision rule |
stephrgo |
step size for the optimization over HRgo |
alpha |
one-sided significance level |
beta |
type II error rate; i.e. |
xi2 |
assumed event rate for phase II, used for calculating the sample size of phase II via |
xi3 |
event rate for phase III, used for calculating the sample size of phase III in analogy to |
c2 |
variable per-patient cost for phase II in 10^5 $. |
c3 |
variable per-patient cost for phase III in 10^5 $. |
c02 |
fixed cost for phase II in 10^5 $. |
c03 |
fixed cost for phase III in 10^5 $. |
K |
constraint on the costs of the program, default: Inf, e.g. no constraint |
N |
constraint on the total expected sample size of the program, default: Inf, e.g. no constraint |
S |
constraint on the expected probability of a successful program, default: -Inf, e.g. no constraint |
b1 |
expected gain for effect size category "small" |
b2 |
expected gain for effect size category "medium" |
b3 |
expected gain for effect size category "large" |
case |
choose case: "at least 1, 2 or 3 significant trials needed for approval" |
strategy |
choose strategy: "conduct 1, 2, 3 or 4 trials in order to achieve the case's goal"; TRUE calculates all strategies of the selected |
fixed |
choose if true treatment effects are fixed or random, if TRUE hr1 is used as a fixed effect and hr2 is ignored |
num_cl |
number of clusters used for parallel computing, default: 1 |
The output of the function is a data.frame object containing the optimization results:
Case: "number of significant trials needed"
Strategy: "number of trials to be conducted in order to achieve the goal of the case"
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
optimal total number of events for phase II
total expected number of events for phase III; rounded to next natural number
total expected number of events in the program; d = d2 + d3
total sample size for phase II; rounded to the next even natural number
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)
probability to go to phase III
probability of a successful program
probability of a successful program with "small" treatment effect in phase III (lower boundary in HR scale is set to 1, as proposed by IQWiG (2016))
probability of a successful program with "medium" treatment effect in phase III (lower boundary in HR scale is set to 0.95, as proposed by IQWiG (2016))
probability of a successful program with "large" treatment effect in phase III (lower boundary in HR scale is set to 0.85, as proposed by IQWiG (2016))
expected costs for phase II
expected costs for phase III
and further input parameters. Taking cat(comment()) of the
data frame lists the used optimization sequences, start and
finish time of the optimization procedure. The attribute
attr(,"trace") returns the utility values of all parameter
combinations visited during optimization.
In other settings, the definition of "small", "medium" and "large" effect
sizes can be user-specified using the input parameters steps1, stepm1 and
stepl1. Due to the complexity of the multitrial setting, this feature is
not included for this setting. Instead, the effect sizes were set to
to predefined values as explained under sProg1, sProg2 and sProg3 in the
Value section.
IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.
Preussler, S., Kieser, M., and Kirchner, M. (2019). Optimal sample size allocation and go/no-go decision rules for phase II/III programs where several phase III trials are performed. Biometrical Journal, 61(2), 357-378.
Schoenfeld, D. (1981). The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika, 68(1), 316-319.
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_multitrial(w = 0.3, # define parameters for prior hr1 = 0.69, hr2 = 0.88, id1 = 210, id2 = 420, # (https://web.imbi.uni-heidelberg.de/prior/) d2min = 20, d2max = 100, stepd2 = 5, # define optimization set for d2 hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05, # define optimization set for HRgo alpha = 0.025, beta = 0.1, xi2 = 0.7, xi3 = 0.7, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed and variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints b1 = 1000, b2 = 2000, b3 = 3000, # expected benefit for each effect size case = 1, strategy = TRUE, # chose Case and Strategy fixed = TRUE, # true treatment effects are fixed/random num_cl = 1) # number of cores for parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_multitrial(w = 0.3, # define parameters for prior hr1 = 0.69, hr2 = 0.88, id1 = 210, id2 = 420, # (https://web.imbi.uni-heidelberg.de/prior/) d2min = 20, d2max = 100, stepd2 = 5, # define optimization set for d2 hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05, # define optimization set for HRgo alpha = 0.025, beta = 0.1, xi2 = 0.7, xi3 = 0.7, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed and variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints b1 = 1000, b2 = 2000, b3 = 3000, # expected benefit for each effect size case = 1, strategy = TRUE, # chose Case and Strategy fixed = TRUE, # true treatment effects are fixed/random num_cl = 1) # number of cores for parallelized computing
The optimal_multitrial_binary function enables planning of phase II/III
drug development programs with several phase III trials for the same
binary endpoint. The main output values are optimal sample size allocation
and go/no-go decision rules. For binary endpoints, the treatment effect is
measured by the risk ratio (RR).
optimal_multitrial_binary( w, p0, p11, p12, in1, in2, n2min, n2max, stepn2, rrgomin, rrgomax, steprrgo, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, b1, b2, b3, case, strategy = TRUE, fixed = FALSE, num_cl = 1 )optimal_multitrial_binary( w, p0, p11, p12, in1, in2, n2min, n2max, stepn2, rrgomin, rrgomax, steprrgo, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, b1, b2, b3, case, strategy = TRUE, fixed = FALSE, num_cl = 1 )
w |
weight for mixture prior distribution |
p0 |
assumed true rate of control group, see here for details |
p11 |
assumed true rate of treatment group, see here for details |
p12 |
assumed true rate of treatment group, see here for details |
in1 |
amount of information for |
in2 |
amount of information for |
n2min |
minimal total sample size for phase II; must be an even number |
n2max |
maximal total sample size for phase II, must be an even number |
stepn2 |
step size for the optimization over n2; must be an even number |
rrgomin |
minimal threshold value for the go/no-go decision rule |
rrgomax |
maximal threshold value for the go/no-go decision rule |
steprrgo |
step size for the optimization over RRgo |
alpha |
one-sided significance level |
beta |
type II error rate; i.e. |
c2 |
variable per-patient cost for phase II in 10^5 $ |
c3 |
variable per-patient cost for phase III in 10^5 $ |
c02 |
fixed cost for phase II in 10^5 $ |
c03 |
fixed cost for phase III in 10^5 $ |
K |
constraint on the costs of the program, default: Inf, e.g. no constraint |
N |
constraint on the total expected sample size of the program, default: Inf, e.g. no constraint |
S |
constraint on the expected probability of a successful program, default: -Inf, e.g. no constraint |
b1 |
expected gain for effect size category "small" |
b2 |
expected gain for effect size category "medium" |
b3 |
expected gain for effect size category "large" |
case |
choose case: "at least 1, 2 or 3 significant trials needed for approval" |
strategy |
choose strategy: "conduct 1, 2, 3 or 4 trials in order to achieve the case's goal"; TRUE calculates all strategies of the selected |
fixed |
choose if true treatment effects are fixed or random, if TRUE p11 is used as fixed effect for p1 |
num_cl |
number of clusters used for parallel computing, default: 1 |
The assumed true treatment effects can be assumed fixed or modelled by a prior distribution. The R Shiny application prior visualizes the prior distributions used in this package.
Fast computing is enabled by parallel programming.
The output of the function is a data.frame object containing the optimization results:
Case: "number of significant trials needed"
Strategy: "number of trials to be conducted in order to achieve the goal of the case"
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
total sample size for phase II; rounded to the next even natural number
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)
probability to go to phase III
probability of a successful program
probability of a successful program with "small" treatment effect in phase III (lower boundary in HR scale is set to 1, as proposed by IQWiG (2016))
probability of a successful program with "medium" treatment effect in phase III (lower boundary in HR scale is set to 0.95, as proposed by IQWiG (2016))
probability of a successful program with "large" treatment effect in phase III (lower boundary in HR scale is set to 0.85, as proposed by IQWiG (2016))
expected costs for phase II
expected costs for phase III
and further input parameters. Taking cat(comment()) of the
data frame lists the used optimization sequences, start and
finish time of the optimization procedure. The attribute
attr(,"trace") returns the utility values of all parameter
combinations visited during optimization.
In other settings, the definition of "small", "medium" and "large" effect
sizes can be user-specified using the input parameters steps1, stepm1 and
stepl1. Due to the complexity of the multitrial setting, this feature is
not included for this setting. Instead, the effect sizes were set to
to predefined values as explained under sProg1, sProg2 and sProg3 in the
Value section.
IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_multitrial_binary(w = 0.3, # define parameters for prior p0 = 0.6, p11 = 0.3, p12 = 0.5, in1 = 30, in2 = 60, # (https://web.imbi.uni-heidelberg.de/prior/) n2min = 20, n2max = 100, stepn2 = 4, # define optimization set for n2 rrgomin = 0.7, rrgomax = 0.9, steprrgo = 0.05, # define optimization set for RRgo alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed and variable costs for phase II/III, K = Inf, N = Inf, S = -Inf, # set constraints b1 = 1000, b2 = 2000, b3 = 3000, # expected benefit for a each effect size case = 1, strategy = TRUE, # chose Case and Strategy fixed = TRUE, # true treatment effects are fixed/random num_cl = 1) # number of cores for parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_multitrial_binary(w = 0.3, # define parameters for prior p0 = 0.6, p11 = 0.3, p12 = 0.5, in1 = 30, in2 = 60, # (https://web.imbi.uni-heidelberg.de/prior/) n2min = 20, n2max = 100, stepn2 = 4, # define optimization set for n2 rrgomin = 0.7, rrgomax = 0.9, steprrgo = 0.05, # define optimization set for RRgo alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed and variable costs for phase II/III, K = Inf, N = Inf, S = -Inf, # set constraints b1 = 1000, b2 = 2000, b3 = 3000, # expected benefit for a each effect size case = 1, strategy = TRUE, # chose Case and Strategy fixed = TRUE, # true treatment effects are fixed/random num_cl = 1) # number of cores for parallelized computing
The optimal_multitrial_normal function enables planning of phase II/III
drug development programs with several phase III trials for
the same normally distributed endpoint. Its main output values are optimal
sample size allocation and go/no-go decision rules. For normally distributed
endpoints, the treatment effect is measured by the standardized difference in
means (Delta). The assumed true treatment effects can be assumed fixed or
modelled by a prior distribution.
optimal_multitrial_normal( w, Delta1, Delta2, in1, in2, a, b, n2min, n2max, stepn2, kappamin, kappamax, stepkappa, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, b1, b2, b3, case, strategy = TRUE, fixed = FALSE, num_cl = 1 )optimal_multitrial_normal( w, Delta1, Delta2, in1, in2, a, b, n2min, n2max, stepn2, kappamin, kappamax, stepkappa, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, b1, b2, b3, case, strategy = TRUE, fixed = FALSE, num_cl = 1 )
w |
weight for mixture prior distribution |
Delta1 |
assumed true prior treatment effect measured as the standardized difference in means, see here for details |
Delta2 |
assumed true prior treatment effect measured as the standardized difference in means, see here for details |
in1 |
amount of information for |
in2 |
amount of information for |
a |
lower boundary for the truncation of the prior distribution |
b |
upper boundary for the truncation of the prior distribution |
n2min |
minimal total sample size for phase II; must be an even number |
n2max |
maximal total sample size for phase II, must be an even number |
stepn2 |
step size for the optimization over n2; must be an even number |
kappamin |
minimal threshold value kappa for the go/no-go decision rule |
kappamax |
maximal threshold value kappa for the go/no-go decision rule |
stepkappa |
step size for the optimization over the threshold value kappa |
alpha |
one-sided significance level |
beta |
type II error rate; i.e. |
c2 |
variable per-patient cost for phase II in 10^5 $ |
c3 |
variable per-patient cost for phase III in 10^5 $ |
c02 |
fixed cost for phase II in 10^5 $ |
c03 |
fixed cost for phase III in 10^5 $ |
K |
constraint on the costs of the program, default: Inf, e.g. no constraint |
N |
constraint on the total expected sample size of the program, default: Inf, e.g. no constraint |
S |
constraint on the expected probability of a successful program, default: -Inf, e.g. no constraint |
b1 |
expected gain for effect size category "small" in 10^5 $ |
b2 |
expected gain for effect size category "medium" in 10^5 $ |
b3 |
expected gain for effect size category "large" in 10^5 $ |
case |
choose case: "at least 1, 2 or 3 significant trials needed for approval" |
strategy |
choose strategy: "conduct 1, 2, 3 or 4 trials in order to achieve the case's goal"; TRUE calculates all strategies of the selected |
fixed |
choose if true treatment effects are fixed or following a prior distribution, if TRUE |
num_cl |
number of clusters used for parallel computing, default: 1 |
The R Shiny application prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.
The output of the function is a data.frame object containing the optimization results:
Case: "number of significant trials needed"
Strategy: "number of trials to be conducted in order to achieve the goal of the case"
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
total sample size for phase II; rounded to the next even natural number
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)
probability to go to phase III
probability of a successful program
probability of a successful program with "small" treatment effect in phase III (lower boundary in HR scale is set to 0, as proposed by Cohen (1988))
probability of a successful program with "medium" treatment effect in phase III (lower boundary in HR scale is set to 0.5, as proposed Cohen (1988))
probability of a successful program with "large" treatment effect in phase III (lower boundary in HR scale is set to 0.8, as proposed Cohen (1988))
expected costs for phase II
expected costs for phase III
and further input parameters. Taking cat(comment()) of the
data frame lists the used optimization sequences, start and
finish time of the optimization procedure. The attribute
attr(,"trace") returns the utility values of all parameter
combinations visited during optimization.
In other settings, the definition of "small", "medium" and "large" effect
sizes can be user-specified using the input parameters steps1, stepm1 and
stepl1. Due to the complexity of the multitrial setting, this feature is
not included for this setting. Instead, the effect sizes were set to
to predefined values as explained under sProg1, sProg2 and sProg3 in the
Value section.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences.
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_multitrial_normal(w = 0.3, # define parameters for prior Delta1 = 0.375, Delta2 = 0.625, in1 = 300, in2 = 600, # (https://web.imbi.uni-heidelberg.de/prior/) a = 0.25, b = 0.75, n2min = 20, n2max = 100, stepn2 = 4, # define optimization set for n2 kappamin = 0.02, kappamax = 0.2, stepkappa = 0.02, # define optimization set for kappa alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.675, c3 = 0.72, c02 = 15, c03 = 20, # fixed and variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints b1 = 3000, b2 = 8000, b3 = 10000, # expected benefit for each effect size case = 1, strategy = TRUE, # chose Case and Strategy fixed = TRUE, # true treatment effects are fixed/random num_cl = 1) # number of cores for parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_multitrial_normal(w = 0.3, # define parameters for prior Delta1 = 0.375, Delta2 = 0.625, in1 = 300, in2 = 600, # (https://web.imbi.uni-heidelberg.de/prior/) a = 0.25, b = 0.75, n2min = 20, n2max = 100, stepn2 = 4, # define optimization set for n2 kappamin = 0.02, kappamax = 0.2, stepkappa = 0.02, # define optimization set for kappa alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.675, c3 = 0.72, c02 = 15, c03 = 20, # fixed and variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints b1 = 3000, b2 = 8000, b3 = 10000, # expected benefit for each effect size case = 1, strategy = TRUE, # chose Case and Strategy fixed = TRUE, # true treatment effects are fixed/random num_cl = 1) # number of cores for parallelized computing
The function optimal_normal of the drugdevelopR
package enables planning of phase II/III drug development programs with
optimal sample size allocation and go/no-go decision rules for normally
distributed endpoints. The treatment effect is measured by the standardized
difference in means. The assumed true treatment effects can be assumed to be
fixed or modelled by a prior distribution. The R Shiny application
prior visualizes the prior
distributions used in this package. Fast computing is enabled by parallel
programming.
optimal_normal( w, Delta1, Delta2, in1, in2, a, b, n2min, n2max, stepn2, kappamin, kappamax, stepkappa, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 0, stepm1 = 0.5, stepl1 = 0.8, b1, b2, b3, gamma = 0, fixed = FALSE, skipII = FALSE, num_cl = 1 )optimal_normal( w, Delta1, Delta2, in1, in2, a, b, n2min, n2max, stepn2, kappamin, kappamax, stepkappa, alpha, beta, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 0, stepm1 = 0.5, stepl1 = 0.8, b1, b2, b3, gamma = 0, fixed = FALSE, skipII = FALSE, num_cl = 1 )
w |
weight for mixture prior distribution |
Delta1 |
assumed true prior treatment effect measured as the standardized difference in means, see here for details |
Delta2 |
assumed true prior treatment effect measured as the standardized difference in means, see here for details |
in1 |
amount of information for |
in2 |
amount of information for |
a |
lower boundary for the truncation of the prior distribution |
b |
upper boundary for the truncation of the prior distribution |
n2min |
minimal total sample size for phase II; must be an even number |
n2max |
maximal total sample size for phase II, must be an even number |
stepn2 |
step size for the optimization over n2; must be an even number |
kappamin |
minimal threshold value kappa for the go/no-go decision rule |
kappamax |
maximal threshold value kappa for the go/no-go decision rule |
stepkappa |
step size for the optimization over the threshold value kappa |
alpha |
one-sided significance level |
beta |
type II error rate; i.e. |
c2 |
variable per-patient cost for phase II in 10^5 $ |
c3 |
variable per-patient cost for phase III in 10^5 $ |
c02 |
fixed cost for phase II in 10^5 $ |
c03 |
fixed cost for phase III in 10^5 $ |
K |
constraint on the costs of the program, default: Inf, e.g. no constraint |
N |
constraint on the total expected sample size of the program, default: Inf, e.g. no constraint |
S |
constraint on the expected probability of a successful program, default: -Inf, e.g. no constraint |
steps1 |
lower boundary for effect size category "small", default: 0 |
stepm1 |
lower boundary for effect size category "medium" = upper boundary for effect size category "small" default: 0.5 |
stepl1 |
lower boundary for effect size category "large" = upper boundary for effect size category "medium", default: 0.8 |
b1 |
expected gain for effect size category "small" in 10^5 $ |
b2 |
expected gain for effect size category "medium" in 10^5 $ |
b3 |
expected gain for effect size category "large" in 10^5 $ |
gamma |
to model different populations in phase II and III choose |
fixed |
choose if true treatment effects are fixed or following a prior distribution, if TRUE |
skipII |
choose if skipping phase II is an option, default: FALSE;
if TRUE, the program calculates the expected utility for the case when phase
II is skipped and compares it to the situation when phase II is not skipped.
The results are then returned as a two-row data frame, |
num_cl |
number of clusters used for parallel computing, default: 1 |
The output of the function optimal_normal is a data.frame containing the optimization results:
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
total sample size for phase II
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program
probability to go to phase III
probability of a successful program
probability of a successful program with "small" treatment effect in phase III
probability of a successful program with "medium" treatment effect in phase III
probability of a successful program with "large" treatment effect in phase III
expected costs for phase II
expected costs for phase III
and further input parameters.
Taking cat(comment()) of the data.frame object lists the used optimization
sequences, start and finish date of the optimization procedure. Taking
attr(,"trace") returns the utility values of all parameter combinations
visited during optimization
Cohen, J. (1988). Statistical power analysis for the behavioral sciences.
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_normal(w=0.3, # define parameters for prior Delta1 = 0.375, Delta2 = 0.625, in1=300, in2=600, # (https://web.imbi.uni-heidelberg.de/prior/) a = 0.25, b = 0.75, n2min = 20, n2max = 100, stepn2 = 4, # define optimization set for n2 kappamin = 0.02, kappamax = 0.2, stepkappa = 0.02, # define optimization set for kappa alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.675, c3 = 0.72, c02 = 15, c03 = 20, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 0, # define lower boundary for "small" stepm1 = 0.5, # "medium" stepl1 = 0.8, # and "large" effect size categories b1 = 3000, b2 = 8000, b3 = 10000, # benefit for each effect size category gamma = 0, # population structures in phase II/III fixed = FALSE, # true treatment effects are fixed/random skipII = FALSE, # skipping phase II num_cl = 1) # number of cores for parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) # Optimize optimal_normal(w=0.3, # define parameters for prior Delta1 = 0.375, Delta2 = 0.625, in1=300, in2=600, # (https://web.imbi.uni-heidelberg.de/prior/) a = 0.25, b = 0.75, n2min = 20, n2max = 100, stepn2 = 4, # define optimization set for n2 kappamin = 0.02, kappamax = 0.2, stepkappa = 0.02, # define optimization set for kappa alpha = 0.025, beta = 0.1, # drug development planning parameters c2 = 0.675, c3 = 0.72, c02 = 15, c03 = 20, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 0, # define lower boundary for "small" stepm1 = 0.5, # "medium" stepl1 = 0.8, # and "large" effect size categories b1 = 3000, b2 = 8000, b3 = 10000, # benefit for each effect size category gamma = 0, # population structures in phase II/III fixed = FALSE, # true treatment effects are fixed/random skipII = FALSE, # skipping phase II num_cl = 1) # number of cores for parallelized computing
The function optimal_tte of the drugdevelopR
package enables planning of phase II/III drug development programs with optimal
sample size allocation and go/no-go decision rules for time-to-event endpoints
(Kirchner et al., 2016). The assumed true treatment effects can be assumed to
be fixed or modelled by
a prior distribution. When assuming fixed true treatment effects, planning can
also be done with the user-friendly R Shiny app
basic.
The app prior visualizes
the prior distributions used in this package. Fast computing is enabled by
parallel programming.
optimal_tte( w, hr1, hr2, id1, id2, d2min, d2max, stepd2, hrgomin, hrgomax, stephrgo, alpha, beta, xi2, xi3, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, b1, b2, b3, gamma = 0, fixed = FALSE, skipII = FALSE, num_cl = 1 )optimal_tte( w, hr1, hr2, id1, id2, d2min, d2max, stepd2, hrgomin, hrgomax, stephrgo, alpha, beta, xi2, xi3, c2, c3, c02, c03, K = Inf, N = Inf, S = -Inf, steps1 = 1, stepm1 = 0.95, stepl1 = 0.85, b1, b2, b3, gamma = 0, fixed = FALSE, skipII = FALSE, num_cl = 1 )
w |
weight for mixture prior distribution, see this Shiny application for the choice of weights |
hr1 |
first assumed true treatment effect on HR scale for prior distribution |
hr2 |
second assumed true treatment effect on HR scale for prior distribution |
id1 |
amount of information for |
id2 |
amount of information for |
d2min |
minimal number of events for phase II |
d2max |
maximal number of events for phase II |
stepd2 |
step size for the optimization over d2 |
hrgomin |
minimal threshold value for the go/no-go decision rule |
hrgomax |
maximal threshold value for the go/no-go decision rule |
stephrgo |
step size for the optimization over HRgo |
alpha |
one-sided significance level |
beta |
type II error rate; i.e. |
xi2 |
assumed event rate for phase II, used for calculating the sample size of phase II via |
xi3 |
event rate for phase III, used for calculating the sample size of phase III in analogy to |
c2 |
variable per-patient cost for phase II in 10^5 $. |
c3 |
variable per-patient cost for phase III in 10^5 $. |
c02 |
fixed cost for phase II in 10^5 $. |
c03 |
fixed cost for phase III in 10^5 $. |
K |
constraint on the costs of the program, default: Inf, e.g. no constraint |
N |
constraint on the total expected sample size of the program, default: Inf, e.g. no constraint |
S |
constraint on the expected probability of a successful program, default: -Inf, e.g. no constraint |
steps1 |
lower boundary for effect size category "small" in HR scale, default: 1 |
stepm1 |
lower boundary for effect size category "medium" in HR scale = upper boundary for effect size category "small" in HR scale, default: 0.95 |
stepl1 |
lower boundary for effect size category "large" in HR scale = upper boundary for effect size category "medium" in HR scale, default: 0.85 |
b1 |
expected gain for effect size category "small" |
b2 |
expected gain for effect size category "medium" |
b3 |
expected gain for effect size category "large" |
gamma |
to model different populations in phase II and III choose |
fixed |
choose if true treatment effects are fixed or random, if TRUE hr1 is used as a fixed effect and hr2 is ignored |
skipII |
choose if skipping phase II is an option, default: FALSE;
if TRUE, the program calculates the expected utility for the case when phase
II is skipped and compares it to the situation when phase II is not skipped.
The results are then returned as a two-row data frame, |
num_cl |
number of clusters used for parallel computing, default: 1 |
data.frame containing the optimization results (see Value)
The output of the function is a data.frame object containing the optimization results:
maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
optimal threshold value for the decision rule to go to phase III
optimal total number of events for phase II
total expected number of events for phase III; rounded to next natural number
total expected number of events in the program; d = d2 + d3
total sample size for phase II; rounded to the next even natural number
total sample size for phase III; rounded to the next even natural number
total sample size in the program; n = n2 + n3
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)
probability to go to phase III
probability of a successful program
probability of a successful program with "small" treatment effect in phase III
probability of a successful program with "medium" treatment effect in phase III
probability of a successful program with "large" treatment effect in phase III
expected costs for phase II
expected costs for phase III
and further input parameters. Taking cat(comment()) of the
data frame lists the used optimization sequences, start and
finish time of the optimization procedure. The attribute
attr(,"trace") returns the utility values of all parameter
combinations visited during optimization.
Kirchner, M., Kieser, M., Goette, H., & Schueler, A. (2016). Utility-based optimization of phase II/III programs. Statistics in Medicine, 35(2), 305-316.
IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, last access 15.05.19.
Schoenfeld, D. (1981). The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika, 68(1), 316-319.
optimal_binary, optimal_normal, optimal_bias, optimal_multitrial and optimal_multiarm
# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) ## End(Not run) # Optimize optimal_tte(w = 0.3, # define parameters for prior hr1 = 0.69, hr2 = 0.88, id1 = 210, id2 = 420, # (https://web.imbi.uni-heidelberg.de/prior/) d2min = 20, d2max = 100, stepd2 = 5, # define optimization set for d2 hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05, # define optimization set for HRgo alpha = 0.025, beta = 0.1, xi2 = 0.7, xi3 = 0.7, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" treatment effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # expected benefit for each effect size category gamma = 0, # population structures in phase II/III fixed = FALSE, # true treatment effects are fixed/random skipII = FALSE, # skipping phase II num_cl = 1) # number of cores for parallelized computing# Activate progress bar (optional) ## Not run: progressr::handlers(global = TRUE) ## End(Not run) # Optimize optimal_tte(w = 0.3, # define parameters for prior hr1 = 0.69, hr2 = 0.88, id1 = 210, id2 = 420, # (https://web.imbi.uni-heidelberg.de/prior/) d2min = 20, d2max = 100, stepd2 = 5, # define optimization set for d2 hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05, # define optimization set for HRgo alpha = 0.025, beta = 0.1, xi2 = 0.7, xi3 = 0.7, # drug development planning parameters c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed/variable costs for phase II/III K = Inf, N = Inf, S = -Inf, # set constraints steps1 = 1, # define lower boundary for "small" stepm1 = 0.95, # "medium" stepl1 = 0.85, # and "large" treatment effect size categories b1 = 1000, b2 = 2000, b3 = 3000, # expected benefit for each effect size category gamma = 0, # population structures in phase II/III fixed = FALSE, # true treatment effects are fixed/random skipII = FALSE, # skipping phase II num_cl = 1) # number of cores for parallelized computing