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• W148838336 abstract "We extended our nonparametric EM (NPEM) PC software to include nonlinear systems, incorporating a differential equation (DE) solver and parallelization. The user either draws the model with the BOXES program or enters the DE's on the PC, and runs another PC program to enter instructions for the SDSC Cray T3E, and to specify subject data files. The user then uses SSH to access the Cray, gets the files from his local FTP node, compiles the DE source code, and runs the program. Speedup is 24-fold for 32 nodes. Using 8 nodes, a 5-parameter Michaelis-Menten model of pipericillin, using 80,000 grid points, took 1/2 hr. The user FTP's the result files to his PC and examines them with local software and plots. INTRODUCTION AND OVERVIEW Pharmacokinetic population analysis is used to quantify the intersubject variability in pharmacokinetic studies. It is a necessary tool in model and noise parameters. The parameters are random variables with a common but unknown population distribution. Population analysis is the estimation of this population distribution based on the population data. There are basically two approaches: parametric and nonparametric. In the parametric approach, the shape of the population distribution is assumed to be known except for the unknown population parameter values (e.g., normal with unknown means and covariances). The NONMEM system of Beal and Sheiner (1) is an example. In the nonparametric approach, no such parametric assumptions about the form of the population parameter distributions are made. The entire distribution is estimated from the population data. It allows for non-normal and multimodal distributions such as occur, for example, in a population of fast and slow acetylators. This approach was developed by Mallet (3). A variation based on the nonparametric EM (NPEM) algorithm was developed by Schumitzky (4). Both approaches use two methods for the optimal estimates and their variability: maximum likelihood and Bayesian. The Here we describe a Monte Carlo simulation study of the algorithm. We consider a one compartment model with bolus input applied to a population of 20 simulated subjects. The model for the ith subject is given by: yi = [ 20*exp( -Ki*tj )/Vi ] (1 + ej ); j=1,..,M, where Ki = elimination rate constant Vi = volume of distribution M = # of measurements per subject tj = time of the jth measurement, ej = noise for jth measurement. It is assumed that the {ej } are independent and ej~N(0, 0.04) where the notation x ~ N( m, s ) means that the of x is normal with mean = m and standard deviation = s. In the Monte Carlo simulation, the random vectors (Ki,Vi)} are independent and identically distributed as a mixture of two normals so Ki and Vi are independent and Vi~N( 2.0, 0..2 ), and Ki ~0.5 N( 0.5, 0.05 )+ 0.5 * N(1.5, 0.15 ). The true probability of (K, V) is graphed in Figure 1. Note that in Figures 1-5, the x-axis corresponds to K; the y-axis corresponds to V. Figure 2, in which most of the mass is situated where in the true there is no mass at all. Fig. 2. Normal of a random vector with same mean and covariance as (K,V). Two cases are considered: 5 and 2 levels per subject. Figure 3 shows the smoothed estimated for the 5 levels case. Figure 4 shows the smoothed estimated (K, V) for the 2 levels case. There is not much deterioration from the loss of measurements. The densities are actually discrete. Fig. 4. Smooth estimated discrete of (K, V), 2 levels / subject Figure 5 shows the similarly smoothed density supported uniformly on the 20 actual points (Ki,Vi) used in the Monte Carlo simulation. It resembles Figures 3 and 4. Fig. 5. Smooth empirical discrete of (K, V), 20 subjects Thus the algorithm can discover previously unsuspected subpopulations of patients, while parametric methods cannot, without further help and further information. The Big NPEM now implemented on the SDSC Cray T3E has the following procedure for performing the analysis. STEP 1. Run BOXES on the PC. Output=PROG.FOR, a Fortran file containing source code defining the model, or type in the Fortran source code. The structural model is shown in Figure 6 below. V1 = Vol R1 = Input Rate" @default.
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• W148838336 date "1998-01-01" @default.
• W148838336 modified "2023-09-27" @default.
• W148838336 title "NONLINEAR PARAMETRIC AND NONPARAMETRIC POPULATION PHARMACOKINETIC MODELING ON A SUPERCOMPUTER" @default.
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