Incorporating frailty in a multi-state model: application to disease natural history modelling of adenoma-carcinoma in the large bowel

Homogeneous multi-state models of disease progression have been widely used for designing and evaluating cancer screening programs. However, in screening for premalignant conditions of the cervix or large bowel, it is unlikely that all premalignant lesions have the same underlying propensity for progression. Incorporating frailty into multi-state models raises practical difficulties as it precludes the derivation of finite transition probabilities by matrix solution of the Kolmogorov equations. We address this problem by formulating a heterogeneous process as a series of homogeneous processes linked by transitions which are subject to heterogeneity (frailty). Continuous frailty and discrete mover-stayer models were developed. We applied these to the example of progression of adenoma to colorectal cancer in a three-state model and to a five-state model including consideration of adenoma size. Results were compared with those of purely homogeneous models in a previous study in terms of cumulative risk of malignant transformation from adenoma to invasive colorectal cancer.