  In Survival Analysis, the observed lifetimes often correspond to individuals
for which the event occurs within a specific calendar time interval. With such
interval sampling, the lifetimes are doubly truncated at values determined by
the birth dates and the sampling interval. This double truncation may induce a
systematic bias in estimation, so specific corrections are needed. A relevant
target in Survival Analysis is the hazard rate function, which represents the
instantaneous probability for the event of interest. In this work we introduce
a flexible estimation approach for the hazard rate under double truncation.
Specifically, a kernel smoother is considered, in both a fully nonparametric
setting and a semiparametric setting in which the incidence process fits a
given parametric model. Properties of the kernel smoothers are investigated
both theoretically and through simulations. In particular, an asymptotic
expression of the mean integrated squared error is derived, leading to a
data-driven bandwidth for the estimators. The relevance of the semiparametric
approach is emphasized, in that it is generally more accurate and, importantly,
it avoids the potential issues of nonexistence or nonuniqueness of the fully
nonparametric estimator. Applications to the age of diagnosis of Acute Coronary
Syndrome (ACS) and AIDS incubation times are included.
