Population-based family studies offer an opportunity both to make inference on the relative risks or hazards associated with measured covariates and to assess whether diseases, as evidenced by age at onset, aggregate by family. This latter assessment is of particular interest because it suggests that shared genes and environment play a role in disease etiology. A common regression approach to analyzing family data is random effects or frailty models for survival data. Traditionally, such models have concentrated on very simple frailty structures. Recently, emphasis has shifted to more complex frailty structures to mirror the more complex family structures typical in real data. Unfortunately, computation of the corresponding partial likelihood increases exponentially. This study proposes a computationally feasible pseudo-partial likelihood that allows inference regarding covariates and disease aggregation. The question of disease aggregation by family or more generally heterogeneity of a characteristic across clusters is of primary interest. Are family members more alike than if they were unrelated? Full-service regression methodologies, as described above to answer this question, make distributional assumptions on the outcome variable and random effects. Mixture-model score tests of heterogeneity make distributional assumptions on the outcome variable only but provide no measure of heterogeneity. Both approaches are very sensitive to deviations from the assumptions. This proposal features a new measure of heterogeneity along with estimators and nonparametric tests that rely on no assumptions. These procedures will be suitable to discrete and continuous outcomes and to left, right, and interval-censored data.
