Multinomial Logistic Functions in Markov Chain Models of Sleep Architecture: Internal and External Validation and Covariate Analysis

Abstract

Abstract. Mixed-effect Markov chain models have been recently proposed to characterize the time course of transition probabilities between sleep stages in insomniac patients. The most recent one, based on multinomial logistic functions, was used as a base to develop a final model combining the strengths of the existing ones. This final model was validated on placebo data applying also new diagnostic methods and then used for the inclusion of potential age, gender, and BMI effects. Internal validation was performed through simplified posterior predictive check (sPPC), visual predictive check (VPC) for categorical data, and new visual methods based on stochastic simulation and estimation and called visual estimation check (VEC). External validation mainly relied on the evaluation of the objective function value and sPPC. Covariate effects were identified through stepwise covariate modeling within NONMEM VI. New model features were introduced in the model, providing significant sPPC improvements. Outcomes from VPC, VEC, and external validation were generally very good. Age, gender, and BMI were found to be statistically significant covariates, but their inclusion did not improve substantially the model's predictive performance. In summary, an improved model for sleep internal architecture has been developed and suitably validated in insomniac patients treated with placebo. Thereafter, covariate effects have been included into the final model.

Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model

“…Therefore, additional design variables that could be optimized to provide more robust designs, including covariates (smoking or alcohol habits, weight, and gender) that have demonstrated pronounced effect in sleep patterns 19,34,35 or additional cross-over arms, can be examined without overtly increasing the runtimes. For example, the high uncertainty for the theoretical dose effect parameters D 50 (TP1) in the 'From awake' sub-model and D 50 (TP3) in the 'From asleep' sub-model could be merely a consequence of the limit of the number of crossovers explored, and the impact of additional cross-over arms could be explored with modest increase in runtime.…”

“…In addition to the possible improvements mentioned above to provide more robust trial designs in phase-advance sleep studies, optimal design could be expanded to non-homogeneous, discrete sleep multinomial Markov-chain models 18,19 . For this type of model, the sleep stages evaluated are partitioned into five different sleep states: awake, sleep stage 1, sleep stage 2, slow wave sleep and REM sleep employing a temporal dependence of transition probabilities via piecewise linear functions.…”

“…More expansive nonlinear mixed-effects models have previously been developed to estimate the transition probabilities to different sleep states [15][16][17][18][19] ; however, for this work, phase advanced sleep data were dichotomized (awake and asleep) to form the framework to investigate D-optimality for non-homogeneous (over time) discrete responses.…”

“…The NLMEMs created to describe the sleep architecture for this type of polysomnography (PSG) data are partitioned into separate, smaller models (sub-models) based on the previous sleep state (Markov-chain) and estimate the transition probabilities to different sleep states [15][16][17][18][19] . To account for non-homogeneity over time, temporal dependence is implemented using piecewise linear functions.…”

A Markov Chain Model to Evaluate the Effect of CYP3A5 and ABCB1 Polymorphisms on Adverse Events Associated with Tacrolimus in Pediatric Renal Transplantation

“…In other words, the probability of a certain state to occur in the following time interval is only dependent on the state in the current time interval. Markov models have been broadly applied in clinical studies (21)(22)(23). The adverse event data for the development of Markov chain model was from the pediatric renal transplant study.…”