Estimation and assessment of markov multistate models with intermittent observations on individuals

Abstract

SummaryMultistate models provide important methods of analysis for many life history processes, and this is an area where John Klein made numerous contributions. When individuals in a study group are observed continuously so that all transitions between states, and their times, are known, estimation and model checking is fairly straightforward. However, individuals in many studies are observed intermittently, and only the states occupied at the observation times are known. We review methods of estimation and assessment for Markov models in this situation. Numerical studies that show the effects of inter-observation times are provided, and new methods for assessing fit are given. An illustration involving viral load dynamics for HIV-positive persons is presented.

Armitage Lecture 2011: the design and analysis of life history studies

“…However, as for progressive models, we can estimate the marginal probabilities of being in specific states reasonably well; this is valuable for predicting population‐level outcomes and associated costs. Qualitatively similar results apply to more complex models .…”

Estimation of state occupancy probabilities in multistate models with dependent intermittent observation, with application to HIV viral rebounds

“…Model‐checking procedures are provided in msm (see also ), but they do not handle internal covariates and can be biased when observation times are state‐dependent. This was pointed out by Lawless and Nazeri Rad , who suggested a remedy that included nonparametric prevalence estimation. They did not consider alternatives or properties of a suggested prevalence estimate.…”

“…An imputation approach has been implemented in the msm package and is discussed further in section 2.2 of . As discussed in , these estimators require that observation times for individuals be independent of their multistate processes; if not, they can be biased. In this section, we propose nonparametric estimators that use weighting to adjust for dependent observation processes.…”

“…In this paper, we provide nonparametric estimation procedures that deal with process‐dependent visit times and compare their properties with estimates that require independent observation times. The approach we use was mentioned by Lawless and Nazeri Rad , but not studied by them, and is based on inversely weighting the contributions of individuals in a study according to their probability of being observed at specific times . Previous work on this topic has not considered multistate models, and our approach requires some novel developments, including special models for the visit process when the multistate models have absorbing states, monotonic estimators in cases where prevalence functions must be monotonic and the use of smoothing to deal with very irregular observation times.…”

Approximate Bayesian Inference for Discretely Observed Continuous-Time Multi-State Models

“…In the latter case, Kalbeisch and Lawless () introduced numerical approximations. Recently, Lawless and Rad () reviewed the estimation methods and model assessment for this class of models. For semi‐Markov models, where the state transitions depend on the time that has passed since entry into the current state, the likelihood function for panel data is not generally available in closed form and numerical approximations can be difficult to achieve.…”