drugdevelopR (version 1.0.2)

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

Description

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
)

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.

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

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)
# 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
# }