Competing stochastic models of the incubation period: An investigation of age‐at‐diagnosis of familial and sporadic retinoblastoma

Abstract

This study is based on the assumption that the distribution of age-at-diagnosis (a synonym for the incubation period) of a disease can convey information with respect to its pathogenetic mechanisms. To this end, an analysis of 3 retinoblastoma (RB) international data sets was undertaken. The molecular and cellular basis of RB is well understood and may serve our purpose well. RB is broken down into familial bilateral, unilateral, and sporadic unilateral forms. Survival and hazard functions were computed. Several competing stochastic models (up to 9 per RB form) were fit. Each conveyed a meaningful pathogenetic mechanism. Between-model discrimination was achieved by examining chi-square goodness-of-fit values to select the best fitting model. Well-known survival models, such as the simple exponential and the lognormal (Sartwell model) were ruled out. Age-at-diagnosis of familial RB proved to be best explained by 2 interfering exponentials (a diffonential function); the logistic was retained as the best adjusted model of the incubation period of sporadic cases of RB. As to familial unilaterals, both the diffonential and the logistic models fit equally well. The 3 data sets are consistent in these results, ruling out the less well-fit competing models. The results suggest the existence of 2 opposing but independent balancing internal mechanisms at the origin of familial RB. Sporadic RB appears to be due to a single host-dependent self-limiting cellular mechanism. Familial unilaterals which share both of these component mechanisms would involve a lower retinoblast turnover rate. The cellular implications of these findings are discussed with regard to the relative importance of endogenous and exogenous induction factors in RB. It is concluded that, according to the RB form, RB occurrence results from 2 cellular interfering forces of different strength and organization.