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

2. Model fitting: NDLM Observation equation –response Y i is neurological score at 13 weeks –b i is baseline neurological score –subject i at dose Z j Y i - b i = j + i j = 1,…,J; i = 1,…,I i ~ i.i.d. N(0, 2 )

3. 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,) } sampling distribution θ is change from baseline vague, half-Normal prior on σ specify prior sampling precision

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

5. Model fitting: NDLM Evolution (system) equation where ω j and e j ~ i.i.d. N(0, W j 2 )

6. 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) uniform prior on W, fraction of sampling variance vague prior on placebo level and slope random walk evolution variance of θ, δ is W * σ 2 θ depends on previous θ and δ

7. Choosing next dose Select utility function -V(response at ED 95 ) -V(ED 95 ) -det(VCOV(ED 95, response at ED 95 ) 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 ED 95 expected value by importance sampling –hence for each dose get utility -V(ED 95 )

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. Simulating a trial Construct text files for analysis, WinBUGS script, WinBUGS data set Run in WinBUGS Import MCMC samples, predicted observation Trial stopping rule triggered? Stop trial, call report Y Estimate utility Randomise another patient N WinBUGS SAS

13. Pre-trial simulations utility ED 95 posterior proportion allocated each dose dose-response curve estimate

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