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Many chronic medical conditions can be meaningfully characterized in terms of a two-state stochastic process. Here we consider the problem in which subjects make transitions among two such states in continuous time but are only observed at discrete, irregularly spaced time points that are possibly unique to each subject. Data arising from such an observation scheme are called panel data, and methods for related analyses are typically based on Markov assumptions. The purpose of this article is to present a conditionally Markov model that accommodates subject-to-subject variation in the model parameters by the introduction of random effects. We focus on a particular random effects formulation that generates a closed-form expression for the marginal likelihood. The methodology is illustrated by application to a data set from a parasitic field infection survey.

We describe a logistic-bivariate normal mixture model for a two-state Markov chain in which each individual makes transitions between states according to a subject-specific transition probability matrix. The use of the bivariate normal mixing distribution facilitates inferences regarding the correlation of the random effects and hence provides insight as to the nature of the subject-to-subject variability in the transition probabilities. Tests regarding the correlation can be based on likelihood ratio, score, or Wald statistics. Estimates of the transition intensities of a latent continuous time conditionally Markov process may also be computed. We illustrate this methodology by application to a parasitic infection field study and contrast our findings with those previously published on this data set.