Likelihood analysis of multi-state models for disease incidence and mortality

Data related to life histories of individuals can be obtained in many different ways, and the usefulness of multi-state models for statistical analysis is generally highly dependent on the type and nature of the data. In this paper, we focus on this, and present an approach to estimation for certain 'difficult' situations associated with retrospective or incomplete prospective observation. The paper begins with the identification of some problem areas in the analysis of data on life history processes. We discuss maximum likelihood estimation in some simple contexts and introduce a pseudo-likelihood which enables the simple analysis of some sampling procedures. This approach is illustrated on standard retrospective and case-cohort designs.