Markov models

Incorporating time-dependent covariates in survival analysis using the LVAR method

In survival analysis, use of the Cox proportional hazards model requires knowledge of all covariates under consideration at every failure time. Since failure times rarely coincide with observation times, time-dependent covariates (covariates that vary over time) need to be inferred from the observed values. In this paper, we introduce the last value auto-regressed (LVAR) estimation method and compare it to several other established estimation approaches via a simulation study. The comparison shows that under several time-dependent covariate processes this method results in a smaller mean square error when considering the time-dependent covariate effect.

A mixed model for two-state Markov processes under panel observation

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.