M. Neely, T. Tatarinova, J. Bartroff, M. van Guilder, W. Yamada, D. Bayard, R. Jelliffe, A. Schumitzky
Laboratory of Applied Pharmacokinetics, University of Southern California, Los Angeles, CA, USA
Objectives: Compared with most parametric population modeling methods, our non-parametric (NP) expectation maximization (EM) algorithm calculates exact, rather than approximate likelihoods, and it easily discovers unexpected sub-populations and outliers. However, NPEM cannot calculate credibility intervals around parameter estimates. Therefore, we tested our novel NP Bayesian (NPB) algorithm, derived from [1], that uses stick-breaking to construct a Dirichlet prior (DP) and combines the best of parametric and NP methods.
Methods: We took dosing and weight data from 35 infants enrolled in an IV zidovudine PK study as a template to simulate new observations (obs) after a short IV infusion into one compartment. We set elimination (KE) as a bimodal distribution, with means of 0.5 and 1.0 1/h and weights of 0.3 and 0.7. Volume (V) was unimodal, with a mean of 2.0 L/kg. The SD for each distribution was a CV% of 25%. Noise, ~N(mu=0,sigma=0.01), was added to simulated obs. Using the Pmetrics and rjags packages for R, plus the JAGS software [2], we compared simulated vs. predicted (pred) KE, V, and obs from our NPB and NP Adaptive Grid (NPAG) NPEM algorithms [3].
Results: The simulated (true) means (SD) of KE and V were 0.77 (0.27) and 2.03 (0.28). Obs ranged from <0.01 to 1.64 mg/L, calculated up to 8 hours after dosing, with 5–6 samples per subject. For NPB fitting, we used one MCMC chain, drawing every 10th posterior sample from iteration 10K to 10.5K. The optimal number of stick breaks (support points) for the DP was 17. The NPB weighted mean KE was 0.76 (95% credibility interval 0.73–0.79) with SD of 0.24 (0.20–0.32); weighted mean V was 1.98 (1.92–2.03) and SD was 0.30 (0.25–0.40). The NPAG weighted means (SD) of 23 support points for KE and V were 0.77 (0.27) and 2.03 (0.27). Obs vs. pred plots for both NPB and NPAG were nearly identical, with R^2 for population predictions of 0.81 and 0.81, slope 0.98 and 1.01, and intercept of 0.04 and 0.04, respectively. For posterior predictions, R^2 was 1.00, slope was 1.00, and intercept was 0.00 for both NPB and NPAG, and they each captured the bimodal distribution of KE in marginal plots. NPB parameter estimates were robust to changes in initial values, chain number, and obs noise.
Conclusions: Non-Parametric Bayesian population analysis is a novel and accurate method to estimate PK parameter values, discover subpopulations not specified a priori, and provide robust credibility intervals for all parameter estimates.
References:
[1] Sethuraman J. A constructive definition of Dirichlet priors. Statistica Sinica 1994; 4:639–650.
[2] The Pmetrics R package is available from http://www.lapk.org. The rjags R package can be downloaded from http://cran.r-project.org. JAGS can be accessed from http://mcmc-jags.sourceforge.net/.
[3] Schumitzky A. Nonparametric EM Algorithms for Estimating Prior Distributions. Applied Math and Computation 1991; 45:141–157.
Reference: PAGE 21 (2012) Abstr 2332 [www.page-meeting.org/?abstract=2332]
Poster: New Modelling Approaches