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Optimal phase II/III drug development planning for multi-arm programs with time-to-event endpoint

Source: R/optimal_multiarm.R
optimal_multiarm.Rd

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.

Usage

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
)

Arguments

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. 1 - beta is the (any-pair) power for calculation of the number of events for phase III

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: 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"

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

Value

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

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

sProg2

probability of a successful program with two arms in phase III

sProg3

probability of a successful program with three arms 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

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.

Examples

# Activate progress bar (optional)
if (FALSE) progressr::handlers(global = TRUE) # \dontrun{}
# Optimize
# \donttest{
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 
#> Optimization result:
#>  Utility: 56.47
#>  Sample size:
#>    phase II: 90, phase III: 420, total: 510
#>  Probability to go to phase III: 0.77
#>  Total cost:
#>    phase II: 168, phase III: 535, 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: 0.37
#>  Success probability for a trial with:
#>    two arms in phase III: 0.37, three arms in phase III: 0
#>  Significance level: 0.025
#>  Targeted power: 0.9
#>  Decision rule threshold: 0.85 [HRgo] 
#>  Assumed true effects [HR]: 
#>    treatment 1: 0.75,  treatment 2: 0.8
#>  Control arm event rate: 0.6
  # }