BEMPP: Bayesian efficacy monitoring of 1 binomial parameter

In IDDI-BE/PhII_Bayes: Bayesian tools for PhII clinical trial design

Description

Single arm Bayesian Efficacy Monitoring Via Predictive Probability (BEMPR) or Bayesian Efficacy Monitoring Via Posterior Probability (BEMPO)
The frequentist properties can be investigated for combinations of
1) Different sample sizes 2) Different true response rates # BEMPO interim futility stopping rule is P(Delta<=Delta_fut)>P_fut BEMPO interim efficacy stopping rule is P(Delta>Delta_eff)>=P_eff BEMPO final efficacy stopping rule is P(Delta>Delta_fin)>=P_fin

BEMPR interim futility stopping rule is PP<P_fut BEMPR interim efficacy stopping rule is PP>=P_eff BEMPR final efficacy stopping rule is P(Delta>Delta_fin)>=P_fin

Usage

BEMPP(
  N,
  p,
  design,
  interim_type,
  interim,
  cohortsize = NULL,
  interimstart = NULL,
  interimstop = NULL,
  Delta_fut = NULL,
  P_fut,
  Delta_eff = NULL,
  P_eff,
  Delta_fin,
  P_fin,
  Beta_dis,
  nsim
)

Arguments

N	sample size to investigate operating characteristics: can be a scalar or a vector
p	response rate to investigate operating characteristics: can be a scalar or a vector
design	choice between "BEMPR" (predictive probability) and "BEMPO" (posterior probability)
interim_type	choice between 3 character types: "perc", "cont" or "fix". Only one sequence at once can be investigated: 1) "perc": percentage(s) of information, e.g. c(0.5,0.75), specified as a vector via the 'interim' parameter 2) "fix": fixed number of patients, e.g. c(10,20), specified as a vector via the 'interim' parameter 3) "cont": continuous monitoring. Run-in without monitoring (e.g. first 10) is specified in the "interimstart" parameter. Run-out without monitoring (e.g. last 5) is specified in the "interimstop" parameter.
interim	This must be a vector, only to be specified when the parameter 'interim type' is "perc" or "fix" e.g. c(0.5,0.75) when 'interim type' is "perc", or e.g. c(10,20) when 'interim type' is "fix"
cohortsize	This must be a scalar, indicating the frequency of continuous monitoring. Only needs to be defined in case the parameter 'interim_type'="cont"
interimstart	This must be a scalar, specifying run-in without monitoring. Only needs to be defined in case the parameter 'interim_type'="cont". Default is 10
interimstop	This must be a scalar, specifying run-out without monitoring. Only needs to be defined in case the parameter 'interim_type'="cont". Default is 5.
Delta_fut	This may be a scalar or a vector. Must only be specified for BEMPO
P_fut	This may be a scalar or a vector
Delta_eff	This may be a scalar or a vector. Must only be specified for BEMPO
P_eff	This may be a scalar or a vector
Delta_fin	This must be a scalar
P_fin	This must be a scalar
Beta_dis	two parameters Beta(alpha,beta) of the prior Beta distribution
nsim	number of simulations

Value

a list of 3 data.frames: first with design parameters + operating characteristics ($param_simul) ,
one with futility decision rules ($Fut_rules), and one with efficacy decision rules ($Eff_rules)

• param_simul: dataframe with all input parameters + operating characteristics

• param_simul$scenario: combination of vector N and p

• param_simul$N: sample size for which frequentist properties simulated

• param_simul$p: binomial parameter (true proportion) for which frequentist properties simulated

• param_simul$param: string with all input parameters

• param_simul$N_interim: number of interim analyses (final analysis not included)

• param_simul$interim: string with number of patients per interim analysis

• param_simul$pow: proportion of simulations where H0 was rejected

• param_simul$eff_fin: proportion of simulations where H0 was rejected only at the final analysis

• param_simul$eff_stop: proportion of simulations where H0 was rejected at an interim analysis

• param_simul$fut: proportion of simulations where H0 was not rejected

• param_simul$eff_fin: proportion of simulations where decision of not rejecting H0 was at the final analysis

• param_simul$fut_stop: proportion of simulations where trial stopped for futility at an interim analysis

• param_simul$N_avg: average number of patients for simulated datasets

• param_simul$int_nrx: number of patients at x'th interim analysis

• param_simul$effx: proportion of simulations where trial stopped for efficacy at xth interim analysis

• param_simul$futx: proportion of simulations where trial stopped for futility at xth interim analysis

• param_simul$decision rules: for efficacy: if >=x: stop for efficacy; for futility: if <=x: stop for futility

• Fut_rules: dataframe with futility rules for each interim

• Fut_rules$n: number of patients at interim

• Fut_rules$x: number of successes at interim (Futility if observed successes <=x)

• Fut_rules$P_Bayes/Fut_rules$PP: actual posterior probability or PP at cutoff

• Eff_rules: dataframe with efficacy rules for each interim

• Eff_rules$n: number of patients at interim

• Eff_rules$x: number of successes at interim (Efficacy if observed successes >=x)

• Eff_rules$P_Bayes/Fut_rules$PP: actual posterior probability or PP at cutoff

References

Lee JJ, Liu DD.A predictive probability design for phase II cancer clinical trialsClinical Trials 2008; 5: 93–106

Examples

#Check versus https://biostatistics.mdanderson.org/shinyapps/BEMPO/
test1<-BEMPP(N=15,p=0.5, design="BEMPO", interim_type="fix",interim=c(5,10),Delta_fut=0.3,
 P_fut=0.7,Delta_eff=0.3,P_eff=0.9,Delta_fin=0.3,P_fin=0.8,Beta_dis=c(0.5,0.5),nsim=10)
test2<-BEMPP(N=15,p=0.5, design="BEMPO", interim_type="fix",interim=c(5,10),Delta_fut=0.3,
 P_fut=1  ,Delta_eff=0.3,P_eff=1  ,Delta_fin=0.3,P_fin=0.8,Beta_dis=c(0.5,0.5),nsim=10)
test3<-BEMPP(N=15,p=0.5, design="BEMPR", interim_type="fix",interim=c(5,10),P_fut=0.3,
 P_eff=0.9,Delta_fin=0.3,P_fin=0.7,Beta_dis=c(0.5,0.5),nsim=10)
test4<-BEMPP(N=15,p=0.5, design="BEMPR", interim_type="fix",interim=c(5,10),P_fut=0,P_eff=1,
 Delta_fin=0.3,P_fin=0.8,Beta_dis=c(0.5,0.5),nsim=10)

IDDI-BE/PhII_Bayes documentation built on May 19, 2021, 3:04 p.m.