Parallel Bayesian Methodology for Population Analysis
Ihab G. Girgis, Tom Schaible, Partha Nandy, Filip De Ridder, Jeffrey Mathers, and Surya Mohanty
Johnson & Johnson Pharmaceutical Research & Development
Introduction: Present processors are fast and powerful to run most of the statistical computations within reasonable CPU time. However, when using sophisticated models and large datasets some simulations may require days to compute. Parallel computing could be a very efficient approach to test and compute different scenarios and explore diverse suite of physiological and statistical models in robust and time efficient way. Nevertheless implementing parallel computation is not trivial.
Objectives: The aim of this work is to present a novel computational tool to expedite population pharmacokinetics analysis (PK) and perform modeling and simulation using fully parallel Bayesian approach through Markov chain Monte Carlo (MCMC) technique. This tool can be applied to perform population pharmacodynamics (PD) and population PK/PD analysis as well. The proposed computational capability could be efficiently used for executing parallel analysis, such as, model building and selection, covariates searching, convergence testing, and initial-value independence check, as shown in Figures 1 and 2.
Since Bayesian computation could be subdivided into components that would be done independently, this tool provides a unique opportunity for executing a single model in parallel on large number of independent processors and then collect and merge each processor's statistical output to obtain the final model estimates, as shown in Figure 3.
This tool uses WinBUGS to fit a wide range of complex differential and closed-form models with a high degree of flexibility capable of handling multiple levels of uncertainty (variability), missing data, and time discontinuities.
Methods: A web application, GridBUGS, was built and tested to execute WinBUGS 1.4[1], with the WBDiff addon[2], on Johnson & Johnson's grid[3], which enables using hundreds of high-end dedicated machines, with processing power that exceeds 1200 Gflops.
The web interface was built using a Java based client framework that provides a rich graphical user interface. The interface provides many useful utilities for submitting Bayesian models with multiple input files such as script generation, input editing, automatic input checking, execution concurrency, and chain randomization. Additionally, it provides tools for monitoring and retrieving submitted models, such as customizable downloads, early result retrieval, and auto-refreshing tables. We illustrate the implementation of this tool by analyzing a PK dataset and comparing the results with the estimates obtained through the NONMEM software.
Study Case and Results: A PK dataset was simulated using three-compartment closed form model with infusion input for different doses. A log-normal error model was assumed and both inter-individual and intra-individual variabilities were considered. Differential equations describing the three-compartment model were then used to fit the above data using both GridBUGS and NONMEM (FO method). A very good agreement was observed between the two results.
Conclusions: GridBUGS is a useful tool for model development that provides researchers with vast flexibility to expedite, explore and subsequently incorporate diverse statistical objectives in model building. This web-based application could be implemented both in parallel and serial methodologies to execute both differential and closed-form models. Although, expediting the computation is dependent on many factors, such as, nature of the model, size of the dataset, number of burn-in iterations, and number of the required iterations for convergence, for the present study case, an exponential reduction in run time was achieved as number of nodes increases. As shown in Figure 11, the optimum number of nodes (processors) for our study case was between three to six processors. Using three processes has resulted in 64% reduction in run time while using six processors resulted in 78% reduction. The asymptote value of run time reduction is around 80%.
References:
[1] http://www.mrc-bsu.cam.ac.uk/bugs/
[2] http://www.winbugs-development.org.uk/wbdiff.html
[3] http://www.ud.com/products/gridmp.php
[4] Mu S, Ludden TM. Estimation of population pharmacokinetic parameters in the presence of noncompliance. J Pharmacokinetics Pharmacodynamics 2003; 30: 53-81
