Survival models for developmental genetic data: Age of onset of puberty and antisocial behavior in twins

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Abstract
The use of survival analysis for developmental genetic data is discussed. The main requirements for models based on the decomposition of frailty distributions into shared and unshared components are outlined for the simple case of twins. Extending the earlier work of Clayton, Oakes, and Hougaard, among others, three forms of hazard model are presented, all of which can be applied to pedigree data with flexible baseline hazards without the use of numerical integration. The first two models use an additive decomposition of frailty, with either gamma or positive stable law distributed (PSL) components. The third model previously described by Hougaard involves a multiplicative PSL decomposition. The models are applied to data on the onset of puberty in male twins and illustrate the importance of correct specification of the baseline hazard for correct inference about genetic effects. The difficulty of assessing model specification using information only on the margins is also noted. Overall, the new model with additive PSL components appeared to fit these data best. A second application illustrates the use of a time‐varying covariate in examining the impact of puberty on the onset of conduct disorder symptomotology.