optimal_binary: Optimal phase II/III drug development planning with binary endpoint

Description

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.

Usage

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
)

Value

The output of the function is a data.frame object containing the optimization results:

RRgo: optimal threshold value for the decision rule to go to phase III
n2: total sample size for phase II; rounded to the next even natural number
n3: total sample size for phase III; rounded to the next even natural number
n: total sample size in the program; n = n2 + n3
K: 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)
pgo: probability to go to phase III
sProg: probability of a successful program
sProg1: probability of a successful program with "small" treatment effect in phase III
sProg2: probability of a successful program with "medium" treatment effect in phase III
sProg3: probability of a successful program with "large" treatment effect in phase III
K2: expected costs for phase II
K3: 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.

Arguments

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 p11 in terms of sample size, see here for details
in2: amount of information for p12 in terms of sample size, see here for details
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. 1 - beta is the power for calculation of the number of events 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 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 gamma != 0, default: 0, see here for details
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, res[1, ] being the results when including phase II and res[2, ] when skipping phase II. res[2, ] has an additional parameter, res[2, ]$median_prior_RR, which is the assumed effect size used for planning the phase III study when the phase II is skipped.
num_cl: number of clusters used for parallel computing, default: 1

References

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.

Examples

Run this code

# Activate progress bar (optional)
if (FALSE) {
progressr::handlers(global = TRUE)
}
# Optimize
# \donttest{
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
  # }