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Left-truncated and interval-censored data, termed dynamic cohort data, arise in longitudinal studies with rolling admissions and only occasional follow-up. The authors compared four approaches for analyzing such data: a constant hazard model; maximum likelihood estimation with flexible parametric models; the midpoint method, in which the midpoint of the last negative and first positive test result is used in a Cox proportional hazards model that accounts for left truncation; and a semiparametric method that uses imputed failure times in the Cox model. By using a simulation study, they assessed the performance of these approaches under conditions that can arise in observational studies: changes in disease incidence and changes in the underlying population. The simulation results indicated that the constant hazard model and midpoint method were inadequate and that the flexible parametric model was useful when enough parameters were used in modeling the baseline hazard. The semiparametric method ensured correct parameter (odds ratio) estimation when the baseline hazard was misspecified, but the trade-off increased computational complexity. In this paper, a study of the incidence of human immunodeficiency virus in patients repeatedly tested for the virus at a sexually transmitted disease clinic in New Orleans, Louisiana, illustrates the methods used.