max_FI {GSED}

Maximum Fisher information

Description

max_FI is used to estimate maximum Fisher information based on two power criteria. - The first criterion consider the maxmimum Fisher information such that there is a pre-defined power to declare efficacy in the entire population for a given vector of parameters representing treatment effetcs in each subgroup. - The second criterion consider the maxmimum Fisher information such that there is a pre-defined power to declare efficacy in at least one subgroup for a given vector of parameters representing treatment effetcs in each subgroup.

Usage

max_FI(K_stages, N_subsets, f, ratio_Delta_star_d1, l, u, type_outcome, param_theta, 
pow, ordering, increasing_theta=FALSE, seed=42, n_trials, rule, updateProgress=NULL)

Arguments

K_stages

Integer indicating the number of stages in the design.

N_subsets

Integer representing the number of possible subgroups.

f

Vector containing the prevalence rates of each subgroup. Must be of length N_subsets.

ratio_Delta_star_d1

Vector containing the ratio between the (observed Fisher) information increments at each stage >1 with the (observed Fisher) information at stage 1. Must be of length K_stages-1.

l

Vector containing the lower boundaries for stagewise decisions. Must be of length K_stages.

u

Vector containing the upper boundaries for stagewise decisions. Must be of length K_stages.

type_outcome

A string containing the type of outcome, either "survival", "binary", or "continuous".

param_theta

Vector of parameters representing treatment effects in each subgroup. Must satisfy the properties detailed in Magnusson and Turnbull's article (reparametrization can be needed).

pow

Value representing the desired power.

ordering

Boolean indicating if the subgroups (theta) are ordered.

increasing_theta

Boolean indicating if greater values of theta parameters represent better treatment effects. The default value is set at FALSE.

seed

Interger representing the seed. The default value is set at 42.

n_trials

Integer indicating the number of trials to simulate.

rule

Integer with value either 1 or 2 for power criteria detailed in description section (1 for entire population, 2 for at least one subgroup).

updateProgress

(for Rshiny application)

Value

A value representing the maximum Fisher information is returned.

Author(s)

Marie-Karelle Riviere-Jourdan [e-mail]

References

Baldur P. Magnusson and Bruce W. Turnbull. Group sequential enrichment design incorporating subgroup selection. Statistics in Medicine, 2013. <doi:10.1002/sim.5738>

Examples

theta_assumption = list(matrix(c(0.4,0.6,0.4,0.6,0.4,0.6),nrow=2,ncol=3))

#For testing purpose only, larger number of simulations required (see in comments below)
max_FI(K_stages=2, N_subsets=3, f=c(0.6,0.2,0.2), ratio_Delta_star_d1=c(1), l=c(0.7962, 2.5204), 
u=c(2.7625, 2.5204), type_outcome="binary", param_theta=theta_assumption, pow=0.9, 
ordering=FALSE, increasing_theta=FALSE, seed=140691, n_trials=3, rule=1)
       
#max_FI(K_stages=2, N_subsets=3, f=c(0.6,0.2,0.2), ratio_Delta_star_d1=c(1), l=c(0.7962, 2.5204), 
#u=c(2.7625, 2.5204), type_outcome="binary", param_theta=theta_assumption, pow=0.9, 
#ordering=FALSE, increasing_theta=FALSE, seed=140691, n_trials=10000000, rule=1)

#max_FI(K_stages=2, N_subsets=3, f=c(0.6,0.2,0.2), ratio_Delta_star_d1=c(1), l=c(0.7962, 2.5204), 
#u=c(2.7625, 2.5204), type_outcome="binary", param_theta=theta_assumption, pow=0.9,
#ordering=FALSE, increasing_theta=FALSE, seed=140691, n_trials=10000000, rule=2)