Comparison of a maximum likelihood versus a full bayesian method to jointly model individual with summary level data
N.H. Prins (1), F. Jonsson (1), S. Haughie (2), P. Johnson (2), S.W. Martin (2)
(1) Pharsight, a Certara company, St. Louis, MO, USA.
Objectives: In a different presentation at this meeting we have described a model based meta-analysis combining individual and summary-level International Prostate Symptom Score (IPSS) data from benign prostatic hyperplasia (BPH) patients [1]. To jointly model these different data sources, a multi-level random effects approach was performed using the maximum likelihood estimation (MLE) nonlinear mixed effects regression package ‘nlme' in SPLUS. In order to investigate the validity and usefulness of the MLE approach, the data were re-analyzed employing Full Bayesian Estimation (FBE) using WinBUGS. The distributions of the parameters and the model predictions were compared.
Methods : The structure and inferences from the IPSS model is detailed in [1]. The probability density function of the exact same structural components, the multi-level random effects as well as the residual error model from the MLE model was transferred to WinBUGS and posterior distributions were then obtained using FBE. The quasi-posterior parameter distribution of the MLE regression were obtained by sampling from the variance-covariance matrix of fixed and random effects. The corresponding parameter distributions as well as the predicted IPSS dose response curve of a selected compound (UK-369,003) relative to tamsulosin 0.4 mg of the MLE and FBE approaches were compared.
Results: The FBE approach required a full day of computation, whereas the MLE model took ~2 min to converge. The shape of the posterior parameter distributions (FBE) were reminiscent of normal in most cases, with only occasional tailing. By default, the MLE parameter distributions are normal. The location of most parameter distributions was very similar across methods. When FBE was compared to MLE, the derived relative IPSS dose response curve was marginally shifted to the right without loss in maximum effect. This was due to slightly higher efficacy being estimated for tamsulosin using FBE, while the UK-369,003 parameters were superimposable using the 2 methods.
Conclusion: The MLE approach provides a pragmatic, useful and statistically sound method to jointly model individual and trial statistic data. As the computation time is substantially longer with the FBE method, it may be less suitable for pragmatic modeling work. But as FBE is statistically superior to MLE, we propose that the MLE method can be used as model-building tool, where the final model run(s) could be evaluated using FBE.
References:
[1] Use of model based meta-analysis combining patient-level with summary-level data using multilevel random effects to provide a quantitative assessment of the clinical efficacy (IPSS) profile and competitive positioning of a PDE5 inhibitor (UK369,003) for the treatment of benign prostatic hyperplasia (BPH). N.H. Prins, M. Green, S. Haughie, P. Johnson, S. W. Martin. PAGE 2009