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

Benoit, Julia S.; Chan, Wenyaw; Luo, Sheng; Doody, Rachelle S.

doi:10.1002/sim.6861

Cited by 10 publications

(7 citation statements)

References 23 publications

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“…Identifiability of this model follows from [1]. However, real applications have a different form for the entries of the transition matrix, see for example [2,4]. Here we are interested in how identifiability can be investigated in such cases.…”

Section: Example 3: Longitudinal Hmmmentioning

confidence: 99%

Parameter redundancy and identifiability in hidden Markov models

Cole

2019

METRON

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Hidden Markov models are a flexible class of models that can be used to describe time series data which depends on an unobservable Markov process. As with any complex model, it is not always obvious whether all the parameters are identifiable, or if the model is parameter redundant; that is, the model can be reparameterised in terms of a smaller number of parameters. This paper considers different methods for detecting parameter redundancy and identifiability in hidden Markov models. We examine both numerical methods and methods that involve symbolic algebra. These symbolic methods require a unique representation of a model, known as an exhaustive summary. We provide an exhaustive summary for hidden Markov models and show how it can be used to investigate identifiability.

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Section: Example 3: Longitudinal Hmmmentioning

confidence: 99%

Parameter redundancy and identifiability in hidden Markov models

Cole

2019

METRON

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“…Additionally, the previous value of time-varying covariates could be used to assess transitions, however, longer lags in covariate patterns would violate the Markovian assumption. Lastly, initial state probabilities may be treated as nuisance parameters when inference is focused on transitions, similar to our setting (Benoit et al, 2016), assumed to be subject-specific, or specified to depend on baseline covariates (Zhou et al, 2020). We assume similar initial state probabilities, π 1 , across all subjects, In our simulation study below, we demonstrate the model’s insensitivity to this assumption on variable selection performance for transitions and emissions.…”

Section: Methodsmentioning

confidence: 99%

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

Liang¹,

Koslovsky²,

Hébert³

et al. 2023

Psychological Methods

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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.

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“…In the proposed joint model, problems of identifiability and estimability of parameters may occur due to the presence of a CTMC. As noted in Benoit et al , a CTMC model may be non‐identifiable (i.e., two or more set of parameters could result in a very close likelihood) when outcomes are recorded at prespecified times. This is because the sojourn time and state of change for a subject are not fully recorded; that is, their Markov chain observations do not record the exact duration of the sojourn time.…”

Section: Methodsmentioning

confidence: 99%

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

Rubin

Chan

Yamal

et al. 2017

Statistics in Medicine

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Summary 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.

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

Cited by 10 publications

References 23 publications

Parameter redundancy and identifiability in hidden Markov models

Parameter redundancy and identifiability in hidden Markov models

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

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

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