A hidden Markov model approach to analyze longitudinal ternary outcomes when some observed states are possibly misclassified

Latent classification model for censored longitudinal binary outcome

Latent classification model is a class of statistical methods for identifying unobserved class membership among the study samples using some observed data. In this study, we proposed a latent classification model that takes a censored longitudinal binary outcome variable and uses its changing pattern over time to predict individuals' latent class membership. Assuming the time-dependent outcome variables follow a continuous-time Markov chain, the proposed method has two primary goals: (1) estimate the distribution of the latent classes and predict individuals' class membership, and (2) estimate the class-specific transition rates and rate ratios. To assess the model's performance, we conducted a simulation study and verified that our algorithm produces accurate model estimates (ie, small bias) with reasonable confidence intervals (ie, achieving approximately 95% coverage probability). Furthermore, we compared our model to four other existing latent class models and demonstrated that our approach yields higher prediction accuracies for latent classes. We applied our proposed method to analyze the COVID-19 data in Houston, Texas, US collected between January first 2021 and December 31st 2021. Early reports on the COVID-19 pandemic showed that the severity of a SARS-CoV-2 infection tends to vary greatly by cases. We found that while demographic characteristics explain some of the differences in individuals' experience with COVID-19, some unaccounted-for latent variables were associated with the disease.

Bayesian continuous-time hidden Markov models with covariate selection for intensive longitudinal data with measurement error

Intensive longitudinal data collected with ecological momentary assessment methods capture information on participants' behaviors, feelings, and environment in near real-time. While these methods can reduce recall biases typically present in survey data, they may still suffer from other biases commonly found in self-reported data (e.g., measurement error and social desirability bias). To accommodate potential biases, we develop a Bayesian hidden Markov model to simultaneously identify risk factors for subjects transitioning between discrete latent states as well as risk factors potentially associated with them misreporting their true behaviors. We use simulated data to demonstrate how ignoring potential measurement error can negatively affect variable selection performance and estimation accuracy. We apply our proposed model to smartphone-based ecological momentary assessment data collected within a randomized controlled trial that evaluated the impact of incentivizing abstinence from cigarette smoking among socioeconomically disadvantaged adults. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

A mixed hidden Markov model for multivariate monotone disease processes in the presence of measurement errors

Motivated by a longitudinal oral health study, the Signal-Tandmobiel® study, an inhomogeneous mixed hidden Markov model with continuous state-space is proposed to explain the caries disease process in children between 6 and 12 years of age. The binary caries experience outcomes are subject to misclassification. We modelled this misclassification process via a longitudinal latent continuous response subject to a measurement error process and showing a monotone behaviour. The baseline distributions of the unobservable continuous processes are defined as a function of the covariates through the specification of conditional distributions making use of the Markov property. In addition, random effects are considered to model the relationships among the multivariate responses. Our approach is in contrast with a previous approach working on the binary outcome scale. This method requires conditional independence of the possibly corrupted binary outcomes on the true binary outcomes. We assumed conditional independence on the latent scale, which is a weaker assumption than conditional independence on the binary scale. The aim of this article is therefore to show the properties of a model for a progressive longitudinal response with misclassification on the manifest scale but modelled on the latent scale. The model parameters are estimated in a Bayesian way using an efficient Markov chain Monte Carlo method. The model performance is shown through a simulation-based example, and the analysis of the motivating dataset is presented.

A Hidden Markov Model to Address Measurement Errors in Ordinal Response Scale and Non-Decreasing Process

A Bayesian approach was developed, tested, and applied to model ordinal response data in monotone non-decreasing processes with measurement errors. An inhomogeneous hidden Markov model with continuous state-space was considered to incorporate measurement errors in the categorical response at the same time that the non-decreasing patterns were kept. The computational difficulties were avoided by including latent variables that allowed implementing an efficient Markov chain Monte Carlo method. A simulation-based analysis was carried out to validate the approach, whereas the proposed approach was applied to analyze aortic aneurysm progression data.

Longitudinal Sensitivity of Alzheimer's Disease Severity Staging

Understanding Alzheimer's disease (AD) dynamics is essential in diagnosis and measuring progression for clinical decision-making; however, clinical instruments are imperfect at classifying true disease stages. This research evaluates sensitivity and determinants of AD stage changes longitudinally using current classifications of "mild," "moderate," and "severe" AD, using Mini-Mental State Examination (MMSE), Alzheimer's Disease Assessment Scale-Cognitive subscale (ADAS-Cog), and the Clinical Dementia Rating-Sum of Boxes (CDR-SB) thresholds. Age and pre-progression rate were significant determinants of AD progression using MMSE alone to stage AD, and pre-progression was found to impact disease progression with CDR-SB. Sensitivity of these instruments for identifying clinical stages of AD to correctly staging a "moderate" level of disease severity for outcomes MMSE, CDR-SB, and ADAS-Cog was 92%, 78%, and 92%, respectively. This research derives longitudinal sensitivity of clinical instruments used to stage AD useful for clinical decision-making. The MMSE and ADAS-Cog provided adequate sensitivity to classify AD stages.

A joint logistic regression and covariate-adjusted continuous-time Markov chain model

The use of longitudinal measurements to predict a categorical outcome is an increasingly common goal in research studies. Joint models are commonly used to describe two or more models simultaneously by considering the correlated nature of their outcomes and the random error present in the longitudinal measurements. However, there is limited research on joint models with longitudinal predictors and categorical cross-sectional outcomes. Perhaps the most challenging task is how to model the longitudinal predictor process such that it represents the true biological mechanism that dictates the association with the categorical response. We propose a joint logistic regression and Markov chain model to describe a binary cross-sectional response, where the unobserved transition rates of a two-state continuous-time Markov chain are included as covariates. We use the method of maximum likelihood to estimate the parameters of our model. In a simulation study, coverage probabilities of about 95%, standard deviations close to standard errors, and low biases for the parameter values show that our estimation method is adequate. We apply the proposed joint model to a dataset of patients with traumatic brain injury to describe and predict a 6-month outcome based on physiological data collected post-injury and admission characteristics. Our analysis indicates that the information provided by physiological changes over time may help improve prediction of long-term functional status of these severely ill subjects. Copyright © 2017 John Wiley & Sons, Ltd.