| Summary: | The prevalence of screen-detected premalignancies is too large for it to be feasible that all can progress to carcinoma at the same average rate, unless that rate is very low indeed. There are likely to be frailties in the rates of progression. Failure to take heterogeneity into account will lead to biased estimates and could result in inappropriate screening policy. Approaches to investigation of heterogeneity in the propensity for screen-detected disease to progress comprise the main objectives of this project. We used Markov models with constant hazard rates in sequence throughout the process of disease natural history within subjects, with heterogeneity terms by means of (1) frailty models for continuous heterogeneity, (2) mover-stayer models for dichotomous heterogeneity (in both cases for progression between sequential homogeneous models), and (3) latent variables and states to estimate the parameters of progressive disease natural history in the presence of unobserved factors. Approaches had to be developed to address problems of tractability and estimation. For example, in the presence of frailty, solution of the Kolmogorov equations by routine matrix algebra is no longer possible. Heterogeneous models, both discrete and continuous, were found to be tractable, and estimation was possible for a variety of designs and data structures. Such models illuminated various issues in real screening applications. Quantifying heterogeneity of potential progress of disease is of potential importance to the screening process. There are trade-offs between model complexity, identifiability and data availability, but there are clear examples, such as that of cervical screening, where a heterogeneous model improves model fit and gives more realistic estimates than a homogenous.
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