A continuous -time Markov chain approach for trinomial-outcome longitudinal data: An extension for multiple covariates

The methods of analysis for three-category-outcome longitudinal data vary. Some analyses use polytomous logistic regression; others use the ordered nature of the outcome data to create new variables where binary logistic regression is utilized. We have examined a continuous-time Markov chain approach for trinomial-outcome longitudinal data. This technique is unique in that it allows researchers to examine the time to transition across stages. The primary assumption of a Markov chain is that the probability of the future outcome depends only on the current outcome and not on past outcomes. Previous research on continuous-time Markov models was utilized to express and estimate the relationship of a longitudinal trinomial-outcome with independent covariates through transitional probabilities. An empirical study was conducted to evaluate the estimators and this new technique was applied to the Project HOME dataset. For the empirical study, 996 out of 3643 simulations (27.34%) had their maximum likelihood estimate (MLE) reach convergence with a relative tolerance convergence of 0.0001. The empirical study showed that the mean estimators appear to represent the true values fairly accurately. For all mean parameter estimates, except one, the difference between the mean and the true value was less than 0.09. The technique was then applied to the Project HOME dataset. Project HOME was a population-based randomized longitudinal trial that tested interventions to increase screening mammography using the Transtheoretical model, which includes sequential stages of change (e.g. precontemplation, contemplation, and action). It was determined that Project HOME participants in the precontemplation stage at baseline were more likely to progress to contemplation (probability 60%) than to action (40% probability), those participants in the contemplation stage were more likely to regress to precontemplation (68%) than to progress to action (32%), and participants in the action stage were fairly equally likely to regress to either contemplation (53%) or precontemplation (47%). Whites had a slightly larger probability of progressing or regressing into another stage than minorities. For both covariate comparisons, white to minority and intervention to control group, the ratio of mean time to change for the contemplation stage was greater than that for the action stage, which in turn was greater than that for the precontemplation stage. While, this Markovian technique may seem complex, the information it provides—the probability of the next movement and the time to change rate through the covariates—is impossible to attain from any other method. In the analyses of Project HOME data, the additional information provides a clearer understanding of the stage transition and of the impact on subgroups that could be used in targeting future interventions