Implementation and Evaluation of the SAEM Algorithm for Longitudinal Ordered Categorical Data with an Illustration in Pharmacokinetics–Pharmacodynamics

Analysis of longitudinal ordered categorical efficacy or safety data in clinical trials using mixed models is increasingly performed. However, algorithms available for maximum likelihood estimation using an approximation of the likelihood integral, including LAPLACE approach, may give rise to biased parameter estimates. The SAEM algorithm is an efficient and powerful tool in the analysis of continuous/count mixed models. The aim of this study was to implement and investigate the performance of the SAEM algorithm for longitudinal categorical data. The SAEM algorithm is extended for parameter estimation in ordered categorical mixed models together with an estimation of the Fisher information matrix and the likelihood. We used Monte Carlo simulations using previously published scenarios evaluated with NONMEM. Accuracy and precision in parameter estimation and standard error estimates were assessed in terms of relative bias and root mean square error. This algorithm was illustrated on the simultaneous analysis of pharmacokinetic and discretized efficacy data obtained after a single dose of warfarin in healthy volunteers. The new SAEM algorithm is implemented in MONOLIX 3.1 for discrete mixed models. The analyses show that for parameter estimation, the relative bias is low for both fixed effects and variance components in all models studied. Estimated and empirical standard errors are similar. The warfarin example illustrates how simple and rapid it is to analyze simultaneously continuous and discrete data with MONOLIX 3.1. The SAEM algorithm is extended for analysis of longitudinal categorical data. It provides accurate estimates parameters and standard errors. The estimation is fast and stable

Importance of Shrinkage in Empirical Bayes Estimates for Diagnostics: Problems and Solutions

Empirical Bayes (“post hoc”) estimates (EBEs) of ηs provide modelers with diagnostics: the EBEs themselves, individual prediction (IPRED), and residual errors (individual weighted residual (IWRES)). When data are uninformative at the individual level, the EBE distribution will shrink towards zero (η-shrinkage, quantified as 1-SD(ηEBE)/ω), IPREDs towards the corresponding observations, and IWRES towards zero (ε-shrinkage, quantified as 1-SD(IWRES)). These diagnostics are widely used in pharmacokinetic (PK) pharmacodynamic (PD) modeling; we investigate here their usefulness in the presence of shrinkage. Datasets were simulated from a range of PK PD models, EBEs estimated in non-linear mixed effects modeling based on the true or a misspecified model, and desired diagnostics evaluated both qualitatively and quantitatively. Identified consequences of η-shrinkage on EBE-based model diagnostics include non-normal and/or asymmetric distribution of EBEs with their mean values (“ETABAR”) significantly different from zero, even for a correctly specified model; EBE–EBE correlations and covariate relationships may be masked, falsely induced, or the shape of the true relationship distorted. Consequences of ε-shrinkage included low power of IPRED and IWRES to diagnose structural and residual error model misspecification, respectively. EBE-based diagnostics should be interpreted with caution whenever substantial η- or ε-shrinkage exists (usually greater than 20% to 30%). Reporting the magnitude of η- and ε-shrinkage will facilitate the informed use and interpretation of EBE-based diagnostics