R codes to implement the multi-agent nonparametric overdose control design for dose finding in phase I drug-combination trials.
To enhance the robustness as well as safety of the design, we extend the non-parametric overdose control (NOC) design proposed by Lin and Yin (2016) to drug-combination trials. Under the Bayesian framework, the proposed multi-agent NOC (MANOC) design transforms dose finding into a model-selection problem in the model space composed with all paired dose combinations. In the MANOC design, the dose-toxicity relationship is modelled solely based on the partial information of the toxicity order. In addition, the posterior probability of each dose pair being the MTD combination is timely updated upon the availability of new information. To prevent patients from experiencing excessive toxicities, the dose combination assigned to each new cohort of patients is determined by minimizing an asymmetric loss function, such that overdosing is penalized to some extent. Our nonparametric model specification in conjunction with the conservative dose-assignment scheme guarantee the MANOC design to be safe and yet maintain competitive performance for identifying the MTD combination.
- ToxProb_Generate.R: containing a function
generate_p.sample.mat()for generating samples of the toxicity matrix p from its prior distribution. Details can be found in the Appendix of the paper.generate_p.sample.mat(ndose.A,ndose.B, NN, target, epi) - MTDSelection.R: containing a function
MTDSelection()for selecting a dose pair as the MTD combination.MTDSelection(y,n,target,p.sample.mat) - NextDoseComb.R: containing a function
get.next.manoc()for determining the next dose combination.get.next.manoc(y,n,target,p.sample.mat,delta,j_curr,k_curr,alpha,eta) - PosteriorProbability.R: containing a function
posteriorH()for calculating the posterior model probability for each dose combination.posteriorH(y,n,target,p.sample.mat) - Simulation.R: containing a function
simulation()for conducting simulation studies.simulation(simid, Tox_Prob_Mat, p.sample.mat, samplesize, cohortsize, target, alpha, delta, eta) - Summarize.R: containing a function
summarize()for summarizing the outputs produced by the functionsimulation().summarize(sim_Results,nsim,target)
- alpha: the prespecified feasible bound.
- cohortsize: the number of patients in each cohort.
- delta: a small increment on the posterior probabilities for the untried dose combinations.
- epi: A small positive value that defines the neighbourhood of the target toxicity probability.
- eta: the dose-switching cutoff.
- j_curr: the current dose level of drug A.
- k_curr: the current dose level of drug B.
- n: a matrix recording the number of patients treated at each dose combination.
- ndose.A: the total number of dose levels of drug A.
- ndose.B: the total number of dose levels of drug B.
- NN: the number of samples of p generated from its prior distribution.
- nsim: the number of trials simulated under each scenario.
- p.sample.mat: the samples of p simulated from its joint prior distribution using the function
generate_p.sample.mat(). - samplesize: the maximum number of patients to be enrolled.
- sim_Results: the simulation results produced by the function
simulation(). - simid: the seed of the random number generator.
- target: the target toxicity rate.
- Tox_Prob_Mat: a prespecified toxicity probability matrix in a senario of a simulation study.
- y: a matrix recording the number of toxicities at each dose combination.
We apply the MANOC design to the phase Ib trial with a combination of five doses of buparlisib and four doses of trametinib.
If ten cohorts of patients have been enrolled and the corresponding number of patients treated at each dose combination n and the corresponding number of toxicities y are
> n
Dose1 Dose2 Dose3 Dose4 Dose5
Dose4 0 0 0 3 0
Dose3 0 0 3 3 0
Dose2 0 3 0 9 3
Dose1 3 0 0 0 3
> y
Dose1 Dose2 Dose3 Dose4 Dose5
Dose4 0 0 0 2 0
Dose3 0 0 0 2 0
Dose2 0 0 0 1 2
Dose1 0 0 0 0 0Suppose the tenth cohort of patients is treated at the dose combination (1,5). To determine the dose combination at which the eleventh cohort of patients will be treated, we use the function get.next.manoc().
> rm(list=ls())
> setwd("/MANOC_master/")
> source("ToxProb_Generate.R")
> source("NextDoseComb.R")
>
> target <- 0.33
> epi <- 0.025
> delta <- 0.05
> NN <- 50000
>
> j_curr<-1
> k_curr<-5
>
> alpha<-0.35
> eta<-0.55
>
> n<-matrix(c(0,0,0,3, 0,0,3,0, 0,3,0,0, 3,3,9,0, 0,0,3,3),4,5)
> y<-matrix(c(0,0,0,0, 0,0,0,0, 0,0,0,0, 2,2,1,0, 0,0,2,0),4,5)
> ## Generate the matrices of p. ##
> p.sample.mat <- generate_p.sample.mat(ndose.A=nrow(n),ndose.B=ncol(n), NN=NN, target=target, epi=epi)
> get.next.manoc(y=y,n=n,target=target,delta=delta,p.sample.mat=p.sample.mat,j_curr=j_curr,k_curr=k_curr,alpha=alpha,eta=eta)
$next.dose
[1] 2 5That is, we assign the eleventh cohort of patients to dose combination (2,5).
Suppose at the end of trial, the number of patients treated at each dose combination n and the corresponding number of toxicities y are
> n
Dose1 Dose2 Dose3 Dose4 Dose5
Dose4 0 0 0 3 0
Dose3 0 0 3 3 0
Dose2 0 3 0 9 39
Dose1 3 0 0 0 3
> y
Dose1 Dose2 Dose3 Dose4 Dose5
Dose4 0 0 0 2 0
Dose3 0 0 0 2 0
Dose2 0 0 0 1 12
Dose1 0 0 0 0 0We can use the following codes to select the MTD combination.
> rm(list=ls())
>
> setwd("/MANOC_master/")
> source("ToxProb_Generate.R")
> source("MTDSelection.R")
>
> target <- 0.33
> epi <- 0.025
> NN <- 50000
>
> n<-matrix(c(0,0,0,3, 0,0,3,0, 0,3,0,0, 3,3,9,0, 0,0,39,3),4,5)
> y<-matrix(c(0,0,0,0, 0,0,0,0, 0,0,0,0, 2,2,1,0, 0,0,12,0),4,5)
>
> p.sample.mat <- generate_p.sample.mat(ndose.A=nrow(n),ndose.B=ncol(n), NN=NN, target=target, epi=epi)
> MTDSelection(y=y,n=n,target=target,p.sample.mat=p.sample.mat)The output including the posterior probability of each dose combination and the selected MTD pair are respectively given by
> MTDSelection(y=y,n=n,target=target,p.sample.mat=p.sample.mat)
$pos.model
Dose1 Dose2 Dose3 Dose4 Dose5
Dose4 0.01 0.05 0.15 0.06 0.00
Dose3 0.00 0.00 0.04 0.19 0.05
Dose2 0.00 0.00 0.00 0.02 0.42
Dose1 0.00 0.00 0.00 0.00 0.02
$MTD.sel
row col
[1,] 2 5Therefore, the dose pair (2,5) with the posterior probability 0.42 is selected as the MTD combination.
Suppose the toxicity probability for each combination of the dose levels is given by
> Tox_Prob_Mat
Dose1 Dose2 Dose3 Dose4 Dose5
Dose4 0.06 0.33 0.42 0.58 0.72
Dose3 0.03 0.15 0.24 0.38 0.53
Dose2 0.01 0.07 0.12 0.21 0.33
Dose1 0.01 0.03 0.06 0.10 0.18We simulate 1000 trials to obtain the operating characteristics of the MANOC design with the target toxicity probability phi=0.33 and the tuning parameters alpha=0.35, delta=0.05, eta=0.55, epi=0.025. The cohort size is three and the maximum number of patients is 66.
> rm(list=ls())
>
> setwd("/MANOC_master/")
> source("ToxProb_Generate.R")
> source("Simulation.R")
> source("Summarize.R")
>
> require(parallel)
>
> # A toxicity probability matrix.
> Tox_Prob_Mat <-
+ matrix(c(
+ 0.06,0.03,0.01,0.01,
+ 0.33,0.15,0.07,0.03,
+ 0.42,0.24,0.12,0.06,
+ 0.58,0.38,0.21,0.10,
+ 0.72,0.53,0.33,0.18
+ ),
+ nrow=4, ncol=5
+ )
>
> samplesize <- 66
> cohortsize <- 3
> target <- 0.33
> epi <- 0.025
> NN <- 50000
>
> alpha<-0.35
> delta<-0.05
> eta<-0.55
>
> nsim <- 1000
>
> ## Generate the matrices of p according to the prior distribution of each model. ##
> p.sample.mat <- generate_p.sample.mat(ndose.A=nrow(Tox_Prob_Mat),ndose.B=ncol(Tox_Prob_Mat), NN=NN, target=target, epi=epi)
>
> sim_Results<-mclapply(1:nsim, function(simid) simulation(simid=simid,Tox_Prob_Mat=Tox_Prob_Mat, p.sample.mat=p.sample.mat,samplesize=samplesize, cohortsize=cohortsize, target=target, alpha=alpha, delta=delta, eta=eta), mc.cores=1)We can use the function summarize() to obtain the operating characteristics of the MANOC design as a list.
> summarize(sim_Results=sim_Results,nsim=nsim,target=target)
$MTD_Sel
[1] 39.8
$MTD_Pts
[1] 22.2
$AI
[1] 70.6
$Over_Sel
[1] 27.6
$Over_Pts
[1] 22.0
$DLT
[1] 25.1
$summary.MTD.pctg
Dose1 Dose2 Dose3 Dose4 Dose5
Dose4 0.2 20.7 8.9 0.4 0.0
Dose3 0.0 0.7 12.5 18.0 0.3
Dose2 0.0 0.0 0.3 13.9 19.1
Dose1 0.0 0.0 0.0 0.4 4.6
$summary.patients.pctg
Dose1 Dose2 Dose3 Dose4 Dose5
Dose4 1.55 12.2 4.95 2.91 0.14
Dose3 0.29 3.64 16.6 13.1 0.86
Dose2 0.20 6.70 3.85 13.0 9.98
Dose1 4.73 0.09 0.17 1.11 3.92
$summary.dlt.pctg
Dose1 Dose2 Dose3 Dose4 Dose5
Dose4 0.08 3.59 2.07 1.69 0.11
Dose3 0.01 0.52 3.86 4.93 0.47
Dose2 0.00 0.49 0.50 2.80 2.98
Dose1 0.06 0.00 0.01 0.11 0.76
$Tox_Prob_Mat
Dose1 Dose2 Dose3 Dose4 Dose5
Dose4 0.06 0.33 0.42 0.58 0.72
Dose3 0.03 0.15 0.24 0.38 0.53
Dose2 0.01 0.07 0.12 0.21 0.33
Dose1 0.01 0.03 0.06 0.10 0.18The values returned by summarize() include
- AI: the accuracy index.
- MTD_Pts: the percentage of patients treated at the MTD combination(s).
- MTD_Sel: the correct selection percentage of the MTD combination(s).
- Over_Pts: the percentage of patients treated at the overtoxic dose combination(s).
- Over_Sel: the selection percentage of the overtoxic dose combination(s).
- summary.dlt.pctg: the number of toxicities observed at each dose combination.
- summary.MTD.pctg: the selection percentage at each dose combination.
- summary.patients.pctg: the number of patients treated at each dose combination.
Chi Kin Lam, Ruitao Lin and Guosheng Yin
Lam, C.K., Lin R. and Yin, G. (2017) ''Nonparametric overdose control for dose finding in drug-combination trial''.
Lin, R., and Yin, G. (2016). ''Nonparametric overdose control with late-onset toxicity in phase I clinical trials''. Biostatistics, in press. DOI: 10.1093/biostatistics/kxw038.