Stochastic model for non-standard case-cohort design

Application of case-cohort design to multi-state disease progression in epidemiological studies has been barely addressed. To estimate multi-state disease natural history, we proposed non-homogeneous exponential regression stochastic model to accommodate the data requiring a non-standard case-cohort design. We allowed transition rates to vary with time by modelling the time of transitions between two states with Weibull distribution. The exponential regression model was used to assess the effect of patient-specific covariates on multi-state disease progressions. This method was successfully applied to two epidemiological applications. The first application was to elucidate the effect of betel quids, smoking and alcohol on three-state disease progression, from normal, through leukoplakia and finally to oral cancer. The second application was to extend the three-state to a five-state model to estimate transition rates from normal to diminutive adenoma to small adenoma to large adenoma and finally to invasive carcinoma of the colon and rectum. Finally, an index for assessing the treatment efficacy for pre-cancerous lesion was developed by comparing transition probabilities derived from the proposed model with the probabilities of malignant transformation after a medical regime.