Optimal observation times for multistate Markov models-applications to pneumococcal colonization studies

Abstract

Applications of finite state Markov transition models are numerous and the problem of estimating transition rates of such processes has been considered in many fields of science. Because these processes cannot always be followed in continuous time, the investigators often confront the question of when to measure the state of the process. The estimation of transition rates then needs to be based on a sequence of discrete time data, and the variance and estimability of the estimators greatly depend on the time spacings between consecutive observations. We study optimal time spacings for a sequence of discrete time observations to estimate the transition rates of a time homogeneous multistate Markov process. For comparative studies, optimal time spacings to estimate rate ratios are considered. Optimality criteria are formulated through the minimization of the variances of the parameter estimators of interest and are investigated assuming a stationary initial distribution. For practical purposes, we propose a simple approximation for the optimal time spacing and study the limits for its applicability. The work is motivated by studies of colonization with Streptococcus pneumoniae.