optimal_multiple_normal: 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 normally distributed endpoints

Description

The function optimal_multiple_normal 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 two-arm trials with two normally distributed endpoints and one control group (Preussler et. al, 2019).

Usage

optimal_multiple_normal(
  Delta1,
  Delta2,
  in1,
  in2,
  sigma1,
  sigma2,
  n2min,
  n2max,
  stepn2,
  kappamin,
  kappamax,
  stepkappa,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 0,
  stepm1 = 0.5,
  stepl1 = 0.8,
  b1,
  b2,
  b3,
  rho,
  fixed,
  relaxed = FALSE,
  num_cl = 1
)

Arguments

Delta1	assumed true treatment effect for endpoint 1 measured as the difference in means
Delta2	assumed true treatment effect for endpoint 2 measured as the difference in means
in1	amount of information for Delta1 in terms of number of events
in2	amount of information for Delta2 in terms of number of events
sigma1	variance of endpoint 1
sigma2	variance of endpoint 2
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
kappamin	minimal threshold value kappa for the go/no-go decision rule
kappamax	maximal threshold value kappa for the go/no-go decision rule
stepkappa	step size for the optimization over the threshold value kappa
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 sample size 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
steps1	lower boundary for effect size category "small", default: 0
stepm1	lower boundary for effect size category "medium" = upper boundary for effect size category "small" default: 0.5
stepl1	lower boundary for effect size category "large" = upper boundary for effect size category "medium", default: 0.8
b1	expected gain for effect size category "small" in 10^5 $
b2	expected gain for effect size category "medium" in 10^5 $
b3	expected gain for effect size category "large" in 10^5 $
rho	correlation between the two endpoints
fixed	assumed fixed treatment effect
relaxed	relaxed or strict decision rule
num_cl	number of clusters used for parallel computing, default: 1

Details

For this setting, the drug development program is defined to be successful if it proceeds from phase II to phase III and all endpoints show a statistically significant treatment effect in phase III. For example, this situation is found in Alzheimer’s disease trials, where a drug should show significant results in improving cognition (cognitive endpoint) as well as in improving activities of daily living (functional endpoint).

The effect size categories small, medium and large are applied to both endpoints. In order to define an overall effect size from the two individual effect sizes, the function implements two different combination rules:

• A strict rule (relaxed = FALSE) assigning a large overall effect in case both endpoints show an effect of large size, a small overall effect in case that at least one of the endpoints shows a small effect, and a medium overall effect otherwise, and

• A relaxed rule (relaxed = TRUE) assigning a large overall effect if at least one of the endpoints shows a large effect, a small effect if both endpoints show a small effect, and a medium overall effect otherwise.

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.

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

Kappa

optimal threshold value for the decision rule to go to phase III

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

Meinhard Kieser, Marietta Kirchner, Eva Dölger, Heiko Götte (2018). Optimal planning of phase II/III programs for clinical trials with multiple endpoints

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_normal(Delta1 = 0.75,
  Delta2 = 0.80, in1=300, in2=600,                   # define assumed true HRs
  sigma1 = 8, sigma2= 12,                            # variances for both endpoints
  n2min = 30, n2max = 90, stepn2 = 10,               # define optimization set for n2
  kappamin = 0.05, kappamax = 0.2, stepkappa = 0.05, # define optimization set for HRgo
  alpha = 0.025, beta = 0.1,                         # planning parameters
  c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,           # fixed/variable costs: phase II/III
  K = Inf, N = Inf, S = -Inf,                        # set constraints
  steps1 = 0,                                        # define lower boundary for "small"
  stepm1 = 0.5,                                      # "medium"
  stepl1 = 0.8,                                      # and "large" effect size categories
  b1 = 1000, b2 = 2000, b3 = 3000,                   # define expected benefit
  rho = 0.5, relaxed = TRUE,                         # strict or relaxed rule
  fixed = TRUE,                                      # treatment effect
  num_cl = 1)                                        # parallelized computing
  

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