Handling underlying discrete variables with bivariate mixed hidden Markov models in NONMEM

A tutorial on pharmacometric Markov models

The Markov chain is a stochastic process in which the future value of a variable is conditionally independent of the past, given its present value. Data with Markovian features are characterized by: frequent observations relative to the expected changes in values, many consecutive same-category or similar-value observations at the individual level, and a positive correlation observed between the current and previous values for that variable. In drug development and clinical settings, the data available commonly present Markovian features and are increasingly often modeled using Markov elements or dedicated Markov models. This tutorial presents the main characteristics, evaluations, and applications of various Markov modeling approaches including the discrete-time Markov models (DTMM), continuous-time Markov models (CTMM), hidden Markov models, and item-response theory model with Markov sub-models. The tutorial has a specific emphasis on the use of DTMM and CTMM for modeling ordered-categorical data with Markovian features. Although the main body of this tutorial is written in a software-neutral manner, annotated NONMEM code for all key Markov models is included in the Supplementary Information.

Characterization of anti-drug antibody dynamics using a bivariate mixed hidden-markov model by nonlinear-mixed effects approach

Biological therapies may act as immunogenic triggers leading to the formation of anti-drug antibodies (ADAs). Population pharmacokinetic (PK) models can be used to characterize the relationship between ADA and drug disposition but often rely on the ADA bioassay results, which may not be sufficiently sensitive to inform on this characterization.In this work, a methodology that could help to further elucidate the underlying ADA production and impact on the drug disposition was explored. A mixed hidden-Markov model (MHMM) was developed to characterize the underlying (hidden) formation of ADA against the biologic, using certolizumab pegol (CZP), as a test drug. CZP is a PEGylated Fc free TNF-inhibitor used in the treatment of rheumatoid arthritis and other chronic inflammatory diseases.The bivariate MHMM used information from plasma drug concentrations and ADA measurements, from six clinical studies (n = 845), that were correlated through a bivariate Gaussian function to infer about two hidden states; production and no-production of ADA influencing PK. Estimation of inter-individual variability was not supported in this case. Parameters associated with the observed part of the model were reasonably well estimated while parameters associated with the hidden part were less precise. Individual state sequences obtained using a Viterbi algorithm suggested that the model was able to determine the start of ADA production for each individual, being a more assay-independent methodology than traditional population PK. The model serves as a basis for identification of covariates influencing the ADA formation, and thus has the potential to identify aspects that minimize its impact on PK and/or efficacy.

Go Multivariate: Recommendations on Bayesian Multilevel Hidden Markov Models with Categorical Data

The multilevel hidden Markov model (MHMM) is a promising method to investigate intense longitudinal data obtained within the social and behavioral sciences. The MHMM quantifies information on the latent dynamics of behavior over time. In addition, heterogeneity between individuals is accommodated with the inclusion of individual-specific random effects, facilitating the study of individual differences in dynamics. However, the performance of the MHMM has not been sufficiently explored. We performed an extensive simulation to assess the effect of the number of dependent variables (1-8), number of individuals (5-90), and number of observations per individual (100-1600) on the estimation performance of a Bayesian MHMM with categorical data including various levels of state distinctiveness and separation. We found that using multivariate data generally alleviates the sample size needed and improves the stability of the results. Moreover, including variables only consisting of random noise was generally not detrimental to model performance. Regarding the estimation of group-level parameters, the number of individuals and observations largely compensate for each other. However, only the former drives the estimation of between-individual variability. We conclude with guidelines on the sample size necessary based on the level of state distinctiveness and separation and study objectives of the researcher.

Revolutionizing Medicinal Chemistry: The Application of Artificial Intelligence (AI) in Early Drug Discovery

Artificial intelligence (AI) has permeated various sectors, including the pharmaceutical industry and research, where it has been utilized to efficiently identify new chemical entities with desirable properties. The application of AI algorithms to drug discovery presents both remarkable opportunities and challenges. This review article focuses on the transformative role of AI in medicinal chemistry. We delve into the applications of machine learning and deep learning techniques in drug screening and design, discussing their potential to expedite the early drug discovery process. In particular, we provide a comprehensive overview of the use of AI algorithms in predicting protein structures, drug-target interactions, and molecular properties such as drug toxicity. While AI has accelerated the drug discovery process, data quality issues and technological constraints remain challenges. Nonetheless, new relationships and methods have been unveiled, demonstrating AI's expanding potential in predicting and understanding drug interactions and properties. For its full potential to be realized, interdisciplinary collaboration is essential. This review underscores AI's growing influence on the future trajectory of medicinal chemistry and stresses the importance of ongoing synergies between computational and domain experts.

Evaluation of patient-reported severity of hand-foot syndrome under capecitabine using a Markov modeling approach

Purpose

The inclusion of the patient’s perspective has become increasingly important when reporting adverse events and may assist in management of toxicity. The relationship between drug exposure and toxicity can be quantified by combining Markov elements with pharmacometric models. A minimal continuous-time Markov model (mCTMM) was applied to patient-reported outcomes using hand–foot syndrome (HFS) induced by capecitabine anti-cancer therapy as an example.

Methods

Patient-reported HFS grades over time of 150 patients from two observational studies treated with oral capecitabine were analyzed using a mCTMM approach. Grading of HFS severity was based on the Common Terminology Criteria for Adverse Events. The model was evaluated by visual predictive checks (VPC). Furthermore, a simulation study of the probability of HFS severity over time was performed in which the standard dosing regimen and dose adjustments according to HFS severity were investigated.

Results

The VPC of the developed dose–toxicity model indicated an accurate description of HFS severity over time. Individual absolute daily dose was found to be a predictor for HFS. The simulation study demonstrated a reduction of severe HFS using the recommended dose adjustment strategy.

Conclusion

A minimal continuous-time Markov model was developed based on patient-reported severity of hand–foot syndrome under capecitabine. Thus, a modeling framework for patient-reported outcomes was created which may assist in the optimization of dosage regimens and adjustment strategies aiming at minimizing symptom burden during anti-cancer drug therapy.

Electronic supplementary material

The online version of this article (10.1007/s00280-020-04128-7) contains supplementary material, which is available to authorized users.