Novel GPU-based Parallelized Qausi-random Parametric Expectation-Maximization (QRPEM) Estimation Method for Population Data Analysis
Chee M Ng
Children Hospital of Philadelphia and School of Medicine, University of Pennsylvania, Philadelphia, PA
Objectives: GPU is a graphic processing unit with hundreds of processor cores on a single chip and can be programmed to perform many numerical operations simultaneously for complex data analysis. Parallel code exploiting GPU hardware may yield results equivalent to many traditional CPUs at a fraction of the cost and consume much less energy. At the present time, three of the top five supercomputers of the world are based on GPU-computing technology [1]. Monte-Carlo parametric expectation-maximization method (MCPEM in NONMEM 7 and S-ADAPT) is an exact likelihood estimation method that is well-suited for parallel computing because the most computational intensive Expectation (E)-step of the algorithm can be analyzed independently [2]. Recently, a quasi-random (QR) sampling technique has been shown to be more efficient than a traditional sampling method in evaluating multidimensional integrals during the E-step of the PEM method [3]. In this study, first and novel GPU-based QRPEM method (GPU-QRPEM) was developed for population data analysis.
Methods: A GPU-QRPEM was developed in a single laptop computer equipped with an INTEL Core i7-920 processor and a NVIDIA Quadro FX3800M video graphic card that contained 128 stream processors. The QR samples were generated using Sobol sequences with Owen scrambling technique [4]. A one-compartment IV bolus PK model was used to simulate population data in assessing the performance of GPU-QPREM and QRPEM method developed for a single CPU (CPU-QRPEM).
Results: The GPU-QRPEM consistently achieved model convergence faster than the CPU-QRPEM and has a better scaling relationship between converging times and number of random samples (Nmc) used to compute the E-step of the algorithm. By increasing the Nmc from 1000 to 20000, the mean converging times increased from 2.87 to 38.1 min for CPU-QRPEM, but only from 0.539 to 1.93 min for GPU-QRPEM. GPU-QRPEM was about 20-folds faster in achieving model convergence when Nmc of 20000 was used. The precision and bias of the final model parameters were comparable for both methods.
Conclusions: To my best knowledge, this is the first GPU-based parallelized QRPEM estimation algorithm developed for population data analysis. Innovative, GPU-oriented approaches to modify existing estimation algorithms can lead to vast speed-up, and critically, enable data analysis and model development that presently cannot be performed due to limitations in traditional computational environment.
References:
[1] http://developer.nvidia.com/object/gpucomputing.html
[2] C.M. Ng, R. Bauer. The use of beowulf cluster to accelerate the performance of monte-carlo parametric expectation maximization (MCPEM) algorithm in analyzing complex population pharmacokinetic/pharmacodynamic/efficacy data. Clin Pharmacol Ther 2006;79(2):P54
[3] R.H. Leary. Quasi-Monte Carlo EM Methods for NLME analysis. PAGE 19. 2010
[4] A.B. Owen. Scrambling Sobol' and Niederreiter-Xing points. J of Complexity 1998;14:466-89
