The AAPS Journal

, Volume 13, Issue 1, pp 44–53 | Cite as

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

  • Radojka M. SavicEmail author
  • France Mentré
  • Marc Lavielle
Research Article


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.

Key words

categorical data mixed models MONOLIX proportional odds model SAEM 



Radojka Savic was financially supported by a postdoctoral grant from the Swedish Academy of Pharmaceutical Sciences (Apotekarsocieteten). We thank the MONOLIX team, Hector Mesa, and Kaelig Chatel for their help with implementation of the algorithm in the MONOLIX software. We also thank two anonymous reviewers for their valuable comments on the manuscript.


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Copyright information

© American Association of Pharmaceutical Scientists 2010

Authors and Affiliations

  • Radojka M. Savic
    • 1
    Email author
  • France Mentré
    • 1
  • Marc Lavielle
    • 2
  1. 1.UMR 738INSERM–Université Paris DiderotParisFrance
  2. 2.INRIA Saclay & Department of MathematicsUniversity Paris 11OrsayFrance

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