optimal_multiple_tte: Optimal phase II/III drug development planning for programs...

In Sterniii3/drugdevelopR: Utility-Based Optimal Phase II/III Drug Development Planning

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

Description

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

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).

Value

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

OP

probability that one endpoint is significant

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 date of the optimization procedure.

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)
## Not run: progressr::handlers(global = TRUE)
# Optimize

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
 

Sterniii3/drugdevelopR documentation built on Jan. 26, 2024, 6:17 a.m.