Parametric and Nonparametric Population Modeling: a brief Summary Roger Jelliffe, M.D. USC Lab of Applied Pharmacokinetics 12/1/2018 USC LAPK

InTER-Individual Variability The variability between subjects in a population. Usually a single number (SD, CV%) in parametric population models But there may be specific subpopulation groups eg, fast, slow metabolizers, etc. How describe all this with one number? What will you DO with it? 12/1/2018 USC LAPK

InTRA-Individual Variability The variability within an individual subject. Assay error pattern, plus Errors in Recording times of samples Errors in Dosage Amounts given Errors in Recording Dosage times Structural Model Mis-specification Unrecognized changes in parameter values during data analysis. How describe all this with one number? How describe interoccasional variability only with one number? What will you DO with these numbers? 12/1/2018 USC LAPK

Bottom line for research or for TDM Don’t wait for steady state Don’t wait for distribution after the dose Start TDM with 1st dose Use D-opt principles 12/1/2018 USC LAPK

Parametric Population Models: IT2B, NONMEM, etc Assume shape (normal, lognormal) of param distribs. (Describe params parametrically) Get the param param values = param means, SD’s, covariances, etc. Get F from intermixed IV+PO dosage Get SEM’s, some confidence limits, signif tests. Separate “Inter -” from “Intra -” Individual from assay Variability But, usually get only summary single values for parameter distributions. And also, they are not consistent. 12/1/2018 USC LAPK

Summary Parametric Population Models Single point parameter estimates only. Only one (1) model. Cannot discover unsuspected subpopulations Cannot predict precision of goal achievement Most currently available ones not consistent. Can estimate Parameter ranges 12/1/2018 USC LAPK

A Parametric Population Model Joint Density 12/1/2018 USC LAPK

800 Normally distributed (K,V) points, correlation = +0.6 Non parametric methods prodcue discrete distrbutions. This plot is 800 biavariate normal distribution with a 0.6 positive correlation – V is a volume of dist,, K an elimination rate constant, from a large series of simulations of a single compartment model. 12/1/2018 USC LAPK

A Population Model, made by Breugel

What is the IDEAL Pop Model? The correct structural PK/PD Model. The collection of each subject’s exactly known parameter values for that model. Therefore, multiple individual models, one for each subject. Usual statistical summaries can also be obtained, but usually will lose info. How best approach this ideal? NP! 12/1/2018 USC LAPK

An NPML Population Model, made by Mallet 12/1/2018 USC LAPK

800 normal points give 70 NPAG support points Here the area of the red circles found by the NP method NPAG, our current production algorithm, are proportional to the probability of the support points at their centers 12/1/2018 USC LAPK

Nonparametric Population Models (1) Get the entire ML distribution, a DiscreteJoint Density: one param set per subject, + its prob. Shape of distribution not determined by some equation, only by the data itself. Multiple indiv models, up to one per subject. Can discover, locate, unsuspected subpopulations. Get F from intermixed IV+PO dosage. 12/1/2018 USC LAPK

Nonparametric Population Models (2) The multiple models permit multiple predictions. Can predict precision of goal achievement by a dosage regimen. Behavior is consistent. Use IIV +/or assay SD, stated ranges. 12/1/2018 USC LAPK

12/1/2018 USC LAPK