Modelling age-specific survival in nesting studies, using a general approach for doubly-censored and truncated data

In typical nest survival studies, the observed sample of nests is usually biased by left-truncation (i.e., only active nests enter the study); additionally the failure data may be doubly censored, because the exact dates of nest initiation and failure are uncertain. We present a general bivariate contingency table approach for analyzing such data. We use weakly structured step spline hazard models, which avoid estimability problems encountered in a strictly nonparametric approach, yet still permit flexibility. Our method eliminates a potential source of bias noted by Heisey and Nordheim (1990, Biometrics 46, 855-862) in the nest survival method of Pollock and Cornelius (1988, Biometrics 44, 397-404). We compare our approach to related techniques developed for estimating the incubation distribution of AIDS.