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Optimal phase II/III drug development planning for programs with multiple time-to-event endpoints

Source: R/optimal_multiple_tte.R
optimal_multiple_tte.Rd

The function optimal_multiple_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 (Preussler et. al, 2019) in a two-arm trial with two time-to-event endpoints.

Usage

optimal_multiple_tte(
  hr1,
  hr2,
  id1,
  id2,
  n2min,
  n2max,
  stepn2,
  hrgomin,
  hrgomax,
  stephrgo,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  b11,
  b21,
  b31,
  b12,
  b22,
  b32,
  steps1 = 1,
  stepm1 = 0.95,
  stepl1 = 0.85,
  rho,
  fixed = TRUE,
  num_cl = 1
)

Arguments

hr1

assumed true treatment effect on HR scale for endpoint 1 (e.g. OS)

hr2

assumed true treatment effect on HR scale for endpoint 2 (e.g. PFS)

id1

amount of information for hr1 in terms of number of events

id2

amount of information for hr2 in terms of number of events

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 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

b11

expected gain for effect size category "small" if endpoint 1 is significant (and endpoint 2 may or may not be significant)

b21

expected gain for effect size category "medium" if endpoint 1 is significant (and endpoint 2 may or may not be significant)

b31

expected gain for effect size category "large" if endpoint 1 is significant (and endpoint 2 may or may not be significant)

b12

expected gain for effect size category "small" if endpoint 1 is not significant, but endpoint 2 is

b22

expected gain for effect size category "medium"if endpoint 1 is not significant, but endpoint 2 is

b32

expected gain for effect size category "large" if endpoint 1 is not significant, but endpoint 2 is

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

rho

correlation between the two endpoints

fixed

assumed fixed treatment effect

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

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.

Details

In this setting, the drug development program is defined to be successful if it proceeds from phase II to phase III and at least one endpoint shows a statistically significant treatment effect in phase III. For example, this situation is found in oncology trials, where overall survival (OS) and progression-free survival (PFS) are the two endpoints of interest.

The gain of a successful program may differ according to the importance of the endpoint that is significant. If endpoint 1 is significant (no matter whether endpoint 2 is significant or not), then the gains b11, b21 and b31 will be used for calculation of the utility. If only endpoint 2 is significant, then b12, b22 and b32 will be used. This also matches the oncology example, where OS (i.e. endpoint 1) implicates larger expected gains than PFS alone (i.e. endpoint 2).

Fast computing is enabled by parallel programming.

Monte Carlo simulations are applied for calculating utility, event count and other operating characteristics in this setting. Hence, the results are affected by random uncertainty. The extent of uncertainty is discussed in (Kieser et al. 2018).

References

Kieser, M., Kirchner, M. Dölger, E., Götte, H. (2018).Optimal planning of phase II/III programs for clinical trials with multiple endpoints, Pharm Stat. 2018 Sep; 17(5):437-457.

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{
set.seed(123) # This function relies on Monte Carlo integration
optimal_multiple_tte(hr1 = 0.75,
  hr2 = 0.80, id1 = 210, id2 = 420,          # define assumed true HRs
  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
  b11 = 1000, b21 = 2000, b31 = 3000,
  b12 = 1000, b22 = 1500, b32 = 2000,        # define expected benefits (both scenarios)
  rho = 0.6, fixed = TRUE,                   # correlation and treatment effect
  num_cl = 1)                                # number of cores for parallelized computing
#> Optimization result:
#>  Utility: 171.6
#>  Sample size:
#>    phase II: 90, phase III: 301, total: 391
#>  Probability to go to phase III: 0.79
#>  Total cost:
#>    phase II: 168, phase III: 420, 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:
#>   small: 1 medium: 0.95 large: 0.85
#>  Expected gains if endpoint 1 is significant:
#>   small: 1000 medium: 2000 large: 3000
#>  Expected gains if only endpoint 2 is significant:
#>   small: 1000 medium: 1500 large: 2000
#>  Success probability: 0.43
#>  Joint probability of success and observed effect of size ... in phase III:
#>    medium: 0.23, large: 0.09
#>  Probability of endpoint 1 being significant in phase III: 0.61
#>  Significance level: 0.025
#>  Targeted power: 0.9
#>  Decision rule threshold: 0.85 [HRgo] 
#>  Assumed true effects [HR]: 
#>    endpoint 1: 0.75,  endpoint2 2: 0.8
#>  Correlation between endpoints: 0.6
 # }