Analysis of transtheoretical model of health behavioral changes in a nutrition intervention study—a continuous time Markov chain model with Bayesian approach

Abstract

Summary Continuous time Markov chain (CTMC) models are often used to study the progression of chronic diseases in medical research, but rarely applied to studies of the process of behavioral change. In studies of interventions to modify behaviors, a widely used psychosocial model is based on the transtheoretical model (TTM) that often has more than three states (representing stages of change) and conceptually permits all possible instantaneous transitions. Very little attention is given to the study of the relationships between a CTMC model and associated covariates under the framework of TTM. We developed a Bayesian approach to evaluate the covariate effects on a CTMC model through a log-linear regression link. A simulation study of this approach showed that model parameters were accurately and precisely estimated. We analyzed an existing data set on stages of change in dietary intake from the Next Step Trial using the proposed method and the generalized multinomial logit model (GMLM). We found that the GMLM was not suitable for these data since it ignores the unbalanced data structure and temporal correlation between successive measurements. Our analysis not only confirms that the nutrition intervention was effective, but also provides information on how the intervention affected the transitions among the stages of change. We found that, compared to the control group, subjects in the intervention group, on average, spent substantively less time in the precontemplation stage and were more/less likely to move from an unhealthy/healthy state to a healthy/unhealthy state.

Bayesian Variable Selection for Multistate Markov Models with Interval-censored Data in an Ecological Momentary Assessment Study of Smoking Cessation

“…As a result, assessments are sometimes missing, unequally spaced, and the exact time of transition between states is unknown (i.e., transition times are interval‐censored). For traditional longitudinal studies, this type of data structure is commonly analyzed using multistate, continuous‐time Markov models (MSMs) (Kalbfleisch and Lawless, ; Kay, ; Marshall and Jones, ; Saint‐Pierre et al., ; Jones et al., ; Pan et al., ; Ma et al., ). MSMs can offer insights into behavioral processes (Saint‐Pierre et al., ).…”

Continuous time Markov chain approaches for analyzing transtheoretical models of health behavioral change: A case study and comparison of model estimations

“…When the data are not balanced, neither of these approaches are suitable, and complex statistical models might be necessary 10 . There is a large body of literature that supports the TTM; however, mathematical approaches to quantify these transitions between states have not been sufficiently studied 9,11 .…”

“…In principle, this approach is applicable to any general CTMC model, but it fails when repeated eigenvalues exist. In contrast, the analytical form of the likelihood function is not required for Bayesian approaches, and the likelihood can be numerically calculated, for example, by solving ordinal differential equations 11,17,18,19 . Though both the maximum likelihood (ML) method and the Bayesian approach have been widely applied to address different biological questions, their relative performances for general CTMC models have not been empirically examined.…”

“…10 There is a large body of literature that supports the TTM; however, mathematical approaches to quantify these transitions between states have not been sufficiently studied. 9,11 In CTMC models, the transition probabilities are calculated as PðtÞ ¼ e Qt , where Q is the intensity/infinitesimal matrix and t is the time between two observed states. The likelihood function of a general CTMC model is complex and the calculation of the probabilities of PðtÞ involve solving a matrix exponential, which can be mathematically difficult.…”

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

“…Li and Chan developed a likelihood technique to estimate the transition rates of a three‐state CTMC with a binary covariate, thus providing comparisons of transition probabilities between states for two groups. The aforementioned likelihood technique was later extended to include multiple covariates, and also a practical interpretation of the process with covariates was provided . This research focuses on a possibly misclassified ternary recurrent outcome observed at irregular and varying time intervals among each individual.…”