Optimal phase II/III drug development planning with time-to-event endpoint

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.

Usage

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
)

Format

data.frame containing the optimization results (see Value)

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 $.
K: constraint on the costs of the program, default: Inf, e.g. no constraint
N: constraint on the total expected sample size of the program, default: Inf, e.g. no constraint
S: constraint on the expected probability of a successful program, default: -Inf, e.g. no constraint
steps1: lower boundary for effect size category "small" in HR scale, default: 1
stepm1: lower boundary for effect size category "medium" in HR scale = upper boundary for effect size category "small" in HR scale, default: 0.95
stepl1: lower boundary for effect size category "large" in HR scale = upper boundary for effect size category "medium" in HR scale, default: 0.85
b1: expected gain for effect size category "small"
b2: expected gain for effect size category "medium"
b3: expected gain for effect size category "large"
gamma: to model different populations in phase II and III choose gamma != 0, default: 0
fixed: choose if true treatment effects are fixed or random, if TRUE hr1 is used as a fixed effect and hr2 is ignored
skipII: choose if skipping phase II is an option, default: FALSE; if TRUE, the program calculates the expected utility for the case when phase II is skipped and compares it to the situation when phase II is not skipped. The results are then returned as a two-row data frame, res[1, ] being the results when including phase II and res[2, ] when skipping phase II. res[2, ] has an additional parameter, res[2, ]$median_prior_HR, which is the assumed hazards ratio used for planning the phase III study when the phase II is skipped. It is calculated as the exponential function of the median of the prior function.
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:

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
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.

References

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.

Examples

# Activate progress bar (optional)
if (FALSE) { # \dontrun{
progressr::handlers(global = TRUE)
} # }
# Optimize
# \donttest{
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 
#> Optimization result:
#>  Utility: 75.8
#>  Sample size:
#>    phase II: 122, phase III: 210, total: 332
#>  Expected number of events:
#>    phase II: 85, phase III: 147, total: 232
#>  Assumed event rate:
#>    phase II: 0.7, phase III: 0.7
#>  Probability to go to phase III: 0.46
#>  Total cost:
#>    phase II: 192, phase III: 278, 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: 0.24
#>  Joint probability of success and observed effect of size ... in phase III:
#>    small: 0.05, medium: 0.09, large: 0.11
#>  Significance level: 0.025
#>  Targeted power: 0.9
#>  Decision rule threshold: 0.8 [HRgo] 
#>  Parameters of the prior distribution: 
#>    hr1: 0.69,  hr2: 0.88, id1: 210, id2: 420, w: 0.3
#>  Treatment effect offset between phase II and III: 0 [gamma] 
# }