######################################################################### # # This R Program simulates operating characteristics for the design of # WFdesign* # # *Wages NA, Fadul CE (2019). Adaptive dose finding based on safety # and feasibility in early-phase clinical trials of # adoptive cell immunotherapy. Clinical Trials, in review. # ######################################################################### ###install required R packages library(Iso) library(nnet) ###Load the function 'WFdesign' WFdesign<-function(truth,fprob,a0,b0,q.skel,aplus,tul,ell,Mmax,Nmax,start,put,puf){ ### run a trial ndose = length(truth); #number of combos y=n=z=M=dose.select=ptox.hat=peff.hat=p.infeasible=rep(0,ndose); jstar = start; #current dose level stopf=stops=untx=0; #indicate if trial stops early i=1 A=q.skel*aplus B=aplus-A while(i <= Mmax) { L=runif(1) fdoses=which(fprob>L) Y=ifelse(length(fdoses)==0,0,max(fdoses)) if(Y==0){untx=untx+1} z[fdoses]=z[fdoses]+1 M=M+1 for(j in 1:ndose){ p.infeasible[j] = pbeta(ell, z[j] + A[j], M[j] - z[j] + B[j]); } if(p.infeasible[1]> puf){ stopf=1 break } if(Y>0){ curr=min(jstar,Y) y[curr] = y[curr] + rbinom(1,1,truth[curr]); n[curr] = n[curr] + 1; tried=which(n>0) if(1 - pbeta(tul, y[1] + a0, n[1] - y[1] + b0) > put){ stops=1 break } if(length(tried) tul, (1-0.5)*(pipost-tul), 0.5*(tul-pipost)) T=lossvec==min(lossvec) poss=which(T) if(sum(T)==1){ sugglev=poss } else { if(all(pipost[poss]>tul)){ sugglev=min(poss) } else { sugglev=max(poss) } } if(pipost[sugglev]=Nmax){ stops=0 break } i=i+1 } if(stops==0 & stopf==0){ fmtd=min(max(fset),jstar) dose.select[fmtd]=dose.select[fmtd]+1; } return(list(dose.select=dose.select,tox.data=y,pt.allocation=n,stopf=stopf,stops=stops,unt=untx)) } ##########'WFdesign' end here ###Load the function 'WFdesign.sim' WFdesign.sim<-function(ntrial,truth,fprob,a0,b0,q.skel,aplus,tul,ell,Mmax,Nmax,start,put,puf){ ndose=length(truth) nuntx=rep(0,ntrial) dose.select<-y<-z<-n<-naf<-matrix(nrow=ntrial,ncol=ndose) nstopf=nstops=0 for(i in 1:ntrial){ result<-WFdesign(truth,fprob,a0,b0,q.skel,aplus,tul,ell,Mmax,Nmax,start,put,puf) dose.select[i,]=result\$dose.select y[i,]=result\$tox.data n[i,]=result\$pt.allocation #z[i,]=result\$feas.data #naf[i,]=result\$feas.eval nuntx[i]=result\$unt nstopf=nstopf+result\$stopf nstops=nstops+result\$stops } cat("True tox probability:\n"); cat(round(truth,3), sep="\t", "\n"); cat("True feas probability:\n"); cat(round(fprob,3), sep="\t", "\n"); cat("FMTD selection percentage:\n"); cat(formatC(colMeans(dose.select)*100, digits=1, format="f"), sep="\t", "\n"); cat("Average nmber of DLTs:\n"); cat(formatC(colMeans(y), digits=1, format="f"), sep="\t", "\n"); cat("Average number of patients infused:\n"); cat(formatC(colMeans(n), digits=1, format="f"), sep="\t", "\n"); #cat("number feasible: ", formatC(colMeans(z), digits=1, format="f"), sep="\t", "\n"); #cat("number evaluated feasibility: ", formatC(colMeans(M), digits=1, format="f"), sep="\t", "\n"); cat("Average number of patients not treated:\n"); cat(formatC(mean(nuntx), digits=1, format="f"), sep="\t", "\n"); cat("percentage of stop (safety):\n"); cat(nstops/ntrial*100, "\n"); cat("percentage of stop (feasibility):\n"); cat(nstopf/ntrial*100, "\n"); } ##########'WFdesign.sim' end here ##Comparison to Thall et al. (2001) t1<-c(0.10,0.30,0.50,0.70,0.80) f1<-c(0.99,0.95,0.90,0.75,0.50) t2<-c(0.10,0.30,0.50,0.70,0.80) f2<-c(0.90,0.75,0.50,0.25,0.05) t3<-c(0.05,0.10,0.30,0.50,0.60) f3<-c(0.25,0.10,0.05,0.02,0.01) t4<-c(0.01,0.05,0.07,0.10,0.30) f4<-c(0.99,0.95,0.90,0.75,0.50) t5<-c(0.50,0.60,0.70,0.75,0.80) f5<-c(0.90,0.75,0.50,0.25,0.05) tul=0.3 ##target toxicity rate ell=0.5 ##minimum infusibility threshold Nmax=24 ##maximum number evaluated for toxicity Mmax=48 ##maximum total sample size start=1 ##starting combination ntrial=10000 ##number of simulated trials put=0.7 ##upper probability cutoff for safety puf=0.7 ##upper probability cutoff for feasibility q.skel<-c(0.90,0.85,0.80,0.75,0.70) ##prior means for infusibility probabilities aplus=rep(0,length(q.skel)) ##prior sample size at each dose level ###calculate prior for toxicity x<-2*tul mu<-tul u<-0.95 f<-function(b){ pbeta(x,mu*b/(1-mu),b)-u } b0<-uniroot(f,c(0.0001,100))\$root a0<-mu*b0/(1-mu) round(c(a0,b0),2) ###calculate prior for unfusibility for(i in 1:length(q.skel)){ x=q.skel[i]/2 mu=q.skel[i] f<-function(b){ 1-pbeta(x,mu*b/(1-mu),b)-0.95 } bF=uniroot(f,c(0.0001,100))\$root aF=mu*bF/(1-mu) aplus[i]=round(aF+bF,2) } ##simulate a single trial #WFdesign(truth,fprob,a0,b0,q.skel,aplus,tul,ell,Mmax,Nmax,start,put,puf) truth<-t2 ##true toxicity probability scenario fprob<-f2 ##true feasibility probability scenario WFdesign.sim(ntrial,truth,fprob,a0,b0,q.skel,aplus,tul,ell,Mmax,Nmax,start,put,puf) ##Application to the glioblastoma phase I trial d<-4 ###True toxicity probability scenarios r1<-c(0.01,0.04,0.07,0.12) r2<-c(0.04,0.07,0.12,0.25) r3<-c(0.07,0.12,0.25,0.36) r4<-c(0.12,0.25,0.36,0.50) r5<-c(0.25,0.36,0.50,0.65) r6<-c(0.50,0.65,0.79,0.85) ###True un-feasibility probability scenarios nf1<-rep(1,d) nf1<-c(0.99,0.97,0.95,0.90) nf2<-c(0.95,0.90,0.80,0.70) nf3<-c(0.90,0.85,0.68,0.60) nf4<-c(0.85,0.70,0.65,0.55) nf5<-c(0.65,0.55,0.45,0.35) tul=0.25 ##target toxicity rate ell=0.8 ##minimum infusibility threshold Nmax=24 ##max number of pts evaluated for toxicity Mmax=30 ##max total sample size start=1 ##starting combination ntrial=1000 ##number of simulated trials put=0.9 ##upper probability cutoff for safety puf=0.7 ##upper probability cutoff for feasibility q.skel<-c(0.90,0.85,0.80,0.75) ##prior means for infusibility probabilities aplus=rep(0,length(q.skel)) ##prior sample size at each dose level ###calculate prior for unfusibility for(i in 1:length(q.skel)){ x=q.skel[i]/2 mu=q.skel[i] f<-function(b){ 1-pbeta(x,mu*b/(1-mu),b)-0.95 } bF=uniroot(f,c(0.0001,100))\$root aF=mu*bF/(1-mu) aplus[i]=round(aF+bF,2) } ###calculate prior for toxicity x<-2*tul mu<-tul u<-0.95 f<-function(b){ pbeta(x,mu*b/(1-mu),b)-u } b0<-uniroot(f,c(0.0001,100))\$root a0<-mu*b0/(1-mu) round(c(a0,b0),2) ##simulate a single trial #WFdesign(truth,fprob,a0,b0,q.skel,aplus,tul,ell,Mmax,Nmax,start,put,puf) truth<-r1 ##true toxicity probability scenario fprob<-nf1 ##true feasibility probability scenario WFdesign.sim(ntrial,truth,fprob,a0,b0,q.skel,aplus,tul,ell,Mmax,Nmax,start,put,puf)