Approaches to retrospective sampling for longitudinal transition regression models

Abstract

For binary diseases that relapse and remit, it is often of interest to estimate the effect of covariates on the transition process between disease states over time. The transition process can be characterized by modeling the probability of the binary event given the individual's history. Designing studies that examine the impact of time varying covariates over time can lead to collection of extensive amounts of data. Sometimes it may be possible to collect and store tissue, blood or images and retrospectively analyze this covariate information. In this paper we consider efficient sampling designs that do not require biomarker measurements on all subjects. We describe appropriate estimation methods for transition probabilities and functions of these probabilities, and evaluate efficiency of the estimates from the proposed sampling designs. These new methods are illustrated with data from a longitudinal study of bacterial vaginosis, a common relapsing-remitting vaginal infection of women of child bearing age.

Keywords: Markov model; Survey sampling; Weighted maximum likelihood.

Figure 1

Contour plots of the ratio of the asymptotic variance estimates for the different sampling/estimation methods. The first column shows the ratio of the variance estimates for β₀ for the three unbiased methods. The last two columns show the ratio of the variance estimates for β₁ for the all methods.