We develop time-varying association analyses for onset ages of two lung infections to address the statistical challenges in utilizing registry data where onset ages are left-truncated by ages of entry and competing-risk censored by deaths. Two types of association estimators are proposed based on conditional cause-specific hazard function and cumulative incidence function that are adapted from unconditional quantities to handle left truncation. Asymptotic properties of the estimators are established by using the empirical process techniques. Our simulation study shows that the estimators perform well with moderate sample sizes. We apply our methods to the Cystic Fibrosis Foundation Registry data to study the relationship between onset ages of Pseudomonas aeruginosa and Staphylococcus aureus infections.
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