A Bayesian Meta-Analysis of Longitudinal Data in Placebo Controlled Studies with Naproxen
Pfizer Global Research and Development, Sandwich, UK
Objectives: Understanding the response characteristics of a comparator will typically involve looking at external literature and any relevant previous studies run in-house. Often a suitable variance measure will be taken from a paper and put into a sample size formula. Less common however is a quantitative modelling approach to capture dose response, time course and other characteristics of these comparators.
On a simplistic level one can either adopt a ‘Classical' or ‘Bayesian' approach to carry out such a meta analysis. The former has tended to be the approach of choice but the tools to carry out Bayesian meta-modelling are readily available and there are a growing number of papers in the literature where such approaches have been taken.
A Bayesian approach has many advantages over a Classical one . These advantages include the ability to subjectively weight the evidence according to relevance and the ability to make direct probabilistic statements about measurements of interest from the resulting posterior distribution(s).
The aim here is to model a pain questionnaire endpoint for comparator drug naproxen and placebo from internal and external summary data using a Bayesian Evidence Synthesis approach. The resulting posterior distributions will allow direct probabilistic statements about parameters of interest such as the difference in effect between placebo and naproxen at different time points as well as making predictions for future studies.Methods: A Bayesian random effects non-linear hierarchical model was fitted to WOMAC pain score summary data across 15 osteoarthritis studies, ten of which were internal studies and 5 from a systematic literature search. All studies were placebo controlled with naproxen 500mg bid also investigated. The Emax model was designed to capture the relationship between WOMAC pain score versus time post start of dosing, allowing for different model parameters as appropriate for naproxen and placebo.
The resulting posterior distributions were used to look at the probability that a baseline adjusted naproxen versus placebo difference is greater than several pre-defined deltas of interest. Different forms of residual error were assessed, baseline was included as a covariate and between study variability was examined across the model parameters.
Results: Work ongoing.
Conclusions: Work ongoing.
 Sutton AJ, Abrams EJ. Bayesian methods in meta-analysis and evidence synthesis. Statistical Methods in Medical Research. 2001; 10 :277-303.