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2003
   Verona, Italy

Case Study in the Use of Bayesian Hierarchical Modeling and Simulation for Design and Analysis of a Clinical Trial

William R. Gillespie

Pharsight Corporation, 800 W. El Camino Real, Suite 200, Mountain View, CA 94040 USA

Objective: The objective of the work presented here is to optimize the design and analysis of a Phase II proof-of-concept (PoC) trial of a potentially disease-modifying drug for treatment of a slowly progressive illness. The trial design and analysis are to be optimized with respect to the quality of the PoC decision given limited prior information and consequent high uncertainty about the drug’s effects. This is a case study illustrating the use of Bayesian principles and methods that provide a coherent framework for quantifying that uncertainty and for making inferences in its presence.

Methods: Bayesian methods are used consistently throughout a model-based approach. In particular they are used for model development, trial simulation and trial analysis. A hierarchical model is used to describe disease progression and efficacy response to drug treatment. The model is fit to prior longitudinal data using a MCMC method (WinBUGS). The resulting samples from the joint posterior distribution of the model parameters quantify the correlated uncertainties in those parameters. For the trial simulations uncertainty in the model parameters is considered by resampling from the posterior samples. Three approaches to trial analysis for PoC decision-making are applied to the simulated trial results: a conventional frequentist analysis of endpoint data (ANCOVA) vs Bayesian hierarchical modeling of longitudinal data with or without the use of prior data.

Results: The selected model describes the time course of log(efficacy score) as a linear decline over time. The effect of dose is modeled as a proportional change in the slope of that decline. Log(score) at the ith observation time in the jth patient is modeled as:

log(scoreij) ~ N(aj+bjtonset,s2)

aj = a0j+qsexImale+qage(age-55)

bj = b0j+qdrugDose

(a0j,b0j) ~ MVN((qa,qb),W)

where tonset is the time from disease onset. Relatively diffuse priors were used for the parameters.

The performance of each trial design is measured by the probability of reaching the correct PoC decision, i.e., go for a “winner” drug and no-go for a “loser” drug. The working definition of a “winner” drug treatment for this disease is one that results in at least a 25% reduction in the population mean rate of decline of the efficacy score. For each simulated trial the “true” population mean drug effect is calculated from the model parameters (sampled from the previously estimated posteriors) used for the trial simulation and the drug is categorized as “winner” or “loser”. The simulated trial is then analyzed and a go/no-go outcome is assigned. The idea is to choose a trial design and a go/no-go decision method that minimizes Pr(loser|go) (approximates probability of a Phase III or marketing failure) and Pr(stop|winner) (probability of a lost opportunity). A key conclusion is that the quality of the PoC decision for this drug and disease is markedly improved (relative to a conventional endpoint analysis) by using Bayesian modeling of the longitudinal trial data combined with relevant prior data.



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