Neurological Dose Level Model: Simulation & Optimization

1. Outline • Model fitting in WinBUGS • Choosing next dose • Pre-trial simulations

2. Model fitting: NDLM • Observation equation • response Yi is neurological score at 13 weeks • biis baseline neurological score • subject i at dose Zj • Yi - bi = j+ ij = 1,…,J; i = 1,…,Ii ~ i.i.d. N(0, 2)

3. sampling precision samplingdistribution θ is changefrom baseline specify prior vague, half-Normal prior on σ Observation equation: WinBUGS model{ for (i in 1:I){ Y[i] ~ dnorm(mu[i], sigma2inv) mu[i] <- baseline[i] + theta[d[i]] } sigma2inv <- 1 / (sigma * sigma) sigma ~ dnorm(0,0.1)I(0,) }

4. Locally around z = Zj a straight line with level qj and slope dj Parameters (qj , dj ) change between doses by adding a (small) evolution noise NDLM Evolution Variance = Smoother

5. Model fitting: NDLM • Evolution (system) equation where ωj and ej ~ i.i.d. N(0, Wj 2)

6. vague prior on placebo leveland slope θ dependson previous θ and δ randomwalk evolution variance of θ, δ is W * σ2 uniform prior on W, fraction of sampling variance Evolution equation:WinBUGS theta[1] ~ dnorm(mu.theta0, prec.theta0) delta[1] ~ dnorm(mu.delta0, prec.delta0) for(j in 2:J){ theta[j] ~ dnorm(mu.theta[j], prec.theta[j]) mu.theta[j] <- theta[j-1] + delta[j-1] delta[j] ~ dnorm(delta[j-1], prec.delta[j]) prec.theta[j] <- 1 / (W * sigma * sigma) prec.delta[j] <- 1 / (W * sigma * sigma) } W ~ dunif(0.001,1)

7. Choosing next dose • Select utility function • -V(response at ED95) • -V(ED95) • -det(VCOV(ED95, response at ED95) • Randomisation rule • placebo or optimal dose • probability proportional to utility of each dose • placebo or doses at or ‘near’ optimal utility

8. Choosing next dose • Estimating utility of each dose • full MCMC estimation of utility posterior predictive distribution • simpler estimation of expected utility • predict an observed response at each dose • calculate ED95 expected value by importance sampling • hence for each dose get utility -V(ED95)

9. Estimating utility

10. Pre-trial simulations • During actual trial, efficient computing less important • Critical for pre-trial simulations • underlying dose response curve • settings of longitudinal model • choice of covariates • utility function • randomisation rule • compare to ‘standard’ designs

11. Pre-trial simulations • call WinBUGS using x command options noxwait xmin; x cd &bugsdir; x winbugs14.exe /PAR &scriptname;

12. Construct text filesfor analysis, WinBUGS script,WinBUGS data set SAS WinBUGS Run in WinBUGS Import MCMC samples,predicted observation Trial stoppingrule triggered? Stop trial,call report Y Randomiseanotherpatient N Estimate utility Simulating a trial

13. proportionallocatedeach dose utility dose-responsecurve estimate ED95posterior Pre-trial simulations

14. Summary • Adaptive design (NDLM) straightforward in WinBUGS • Generic software simplifies implementation and validation • Interaction with SAS permits wide scope of pre-trial simulations • …and ease of integration with in-house reporting systems in industry

15. Acknowledgements • UK Medical Research Council • Pfizer Global Research & Development:Andy Grieve, Margaret Jones, Mike Smith, Mike Krams • Tessella: Tom Parke • Duke University: Peter Müller, Don Berry