Handling Underlying Discrete Variables with Mixed Hidden Markov Models in NONMEM
Elodie L. Plan (1), Joakim Nyberg (1), Robert J. Bauer (2), Mats O. Karlsson (1)
(1) Pharmacometrics Research Group, Department of Pharmaceutical Biosciences, Uppsala University, Sweden; (2) Pharmacometrics, R&D, ICON Development Solutions, MD, USA
Objectives: Concomitant infection impact on CD4 counts or rescue medication effect on pain score are examples of covariate relationships often not modeled due to missing information, potentially causing bias in drug effect estimation. Besides, modeling of latent variables that represent the underlying disease has become an interest, leading to attractive drug effect characterization.
Mixed Hidden Markov models (MHMM), capable of handling Markov chains of unobserved states, have been proposed [1] and require challenging maximum likelihood estimation (MLE) computation summing over all previous conditions. The objectives of this work were to explore various MHMM implementations in NONMEM and to expand on the investigation of the benefits of this methodology.
Methods: MHMM methodology was implemented in NONMEM 7.3 with an initial stationary distribution and a scaling of the forward probabilities. A subroutine involving the Viterbi algorithm was used to evaluate the most likely hidden states chain during post-hoc analysis.
First, the model (a 2-state MHMM governing Poisson-based distributions) was applied to real clinical trial records (the 12-week screening phase of a study on 551 epileptic patients [2]). Then, 1000 copies of a hypothetical trial (60 HIV+ patients randomized to placebo or treatment with 60 observations each) were simulated and re-estimated with different models and MLE methods. Finally, an extension to a multivariate (MV) MHMM was developed (2 theoretical types of COPD records -1 measurement, 1 patient reported outcome- linked to presence or absence of relapse).
Results: The estimation of transition probabilities between hidden states associated with random effects was successful in all cases. While EM-based methods and Laplace provided similar estimates, EM-based methods were more consistent in reaching maximum likelihood with poorer initial estimates and Laplace, however, was faster.
Fitting a MHMM instead of a non-Markovian Poisson model to the simulated HIV trials led to a considerable OFV drop, a more accurate and precise drug effect estimate, and an improved power to detect drug effect.
Retrieving the effect of a hypothetical COPD drug on the hidden transition to relapse was possible with a MV-MHMM whereas it was not detectable when analyzing the observed variables with an open continuous model.
Conclusions: MHMM, here implemented in NONMEM, offer possibilities of better understanding and modeling of underlying data in numerous applications.
References:
[1] Delattre M, et al. Analysis of Exposure–response of CI-945 in Patients with Epilepsy: Application of Novel Mixed Hidden Markov Modeling Methodology. JPKPD (2012)
[2] Trocóniz IF, et al. Modelling overdispersion and Markovian features in count data. JPKPD (2009)
