Optimal phase II/III drug development planning where several phase III trials are performed for time-to-event endpoints

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.

Usage

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
)

Arguments

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 hr1 in terms of number of events
id2: amount of information for hr2 in terms of number of events
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. 1 - beta is the power for calculation of the number of events for phase III by Schoenfeld's formula (Schoenfeld 1981)
xi2: assumed event rate for phase II, used for calculating the sample size of phase II via n2 = d2/xi2
xi3: event rate for phase III, used for calculating the sample size of phase III in analogy to xi2
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 case
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

Value

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

Strategy: Strategy: "number of trials to be conducted in order to achieve the goal of the case"
u: maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value
HRgo: optimal threshold value for the decision rule to go to phase III
d2: optimal total number of events for phase II
d3: total expected number of events for phase III; rounded to next natural number
d: total expected number of events in the program; d = d2 + d3
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 (lower boundary in HR scale is set to 1, as proposed by IQWiG (2016))
sProg2: 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))
sProg3: 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))
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.

Effect sizes

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.

References

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.

Examples

# Activate progress bar (optional)
if (FALSE) progressr::handlers(global = TRUE) # \dontrun{}
# Optimize
# \donttest{
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
#> Optimization result with 1 significant trial(s) needed, strategy 1:
#>  Utility: 859.71
#>  Sample size:
#>    phase II: 144, phase III: 446, total: 590
#>  Expected number of events:
#>    phase II: 100, phase III: 312, total: 412
#>  Assumed event rate:
#>    phase II: 0.7, phase III: 0.7
#>  Probability to go to phase III: 0.85
#>  Total cost:
#>    phase II: 208, phase III: 574, cost constraint: Inf
#>  Fixed cost:
#>    phase II: 100, phase III: 150
#>  Variable cost per patient:
#>    phase II: 0.75, phase III: 1
#>  Effect size categories (expected gains):
#>   small: 1 (1000), medium: 0.95 (2000), large: 0.85 (3000)
#>  Success probability: 0.67
#>  Joint probability of success and observed effect of size ... in phase III:
#>    small: 0.07, medium: 0.21, large: 0.38
#>  Significance level: 0.025
#>  Targeted power: 0.9
#>  Decision rule threshold: 0.85 [HRgo] 
#>  Assumed true effect: 0.69 [hr] 
#>  Treatment effect offset between phase II and III: 0 [gamma] 
#> 
#> Optimization result with 1 significant trial(s) needed, strategy 2:
#>  Utility: 714.39
#>  Sample size:
#>    phase II: 144, phase III: 628, total: 772
#>  Expected number of events:
#>    phase II: 100, phase III: 440, total: 540
#>  Assumed event rate:
#>    phase II: 0.7, phase III: 0.7
#>  Probability to go to phase III: 0.77
#>  Total cost:
#>    phase II: 208, phase III: 859, cost constraint: Inf
#>  Fixed cost:
#>    phase II: 100, phase III: 150
#>  Variable cost per patient:
#>    phase II: 0.75, phase III: 1
#>  Effect size categories (expected gains):
#>   small: 1 (1000), medium: 0.95 (2000), large: 0.85 (3000)
#>  Success probability: 0.68
#>  Joint probability of success and observed effect of size ... in phase III:
#>    small: 0.05, medium: 0.18, large: 0.46
#>  Significance level: 0.025
#>  Targeted power: 0.9
#>  Decision rule threshold: 0.8 [HRgo] 
#>  Assumed true effect: 0.69 [hr] 
#>  Treatment effect offset between phase II and III: 0 [gamma] 
#> 
# }