Heterogeneity models of disease susceptibility, with application to diabetic nephropathy.

It is not, in general, possible to include all relevant risk factors in a model of survival or disease incidence. This heterogeneity must be accounted for in the interpretation, as it can imply otherwise unexpected results. This is illustrated by diabetic nephropathy, a serious complication experienced by some diabetic patients. A mathematical model with varying susceptibility can explain that the incidence increases until 20 years duration of diabetes and later decreases. The hospital-based data cover patients diagnosed during 1933-1972. They are interval censored, because early detection of nephropathy requires chemical analysis of urine samples. The data are consistent with a model where less than half of the patients are susceptible, and for each of these the hazard is increasing. The estimated degree of heterogeneity markedly depends on the assumed model. The dependence on age at onset and calendar time of onset is examined. The highest risk is seen at onset age 13-17 years, and the risk decreases with calendar time. The effect of covariates on the hazard is markedly different for the various models, but this is partly a matter of parametrization, as the disagreement is reduced by a reparametrization inspired by accelerated failure time models.