Correcting random effect distributions to account for survivorship bias in individual heterogeneity Cormack-Jolly-Seber models.

Abstract

Survivorship (or selection) bias arises within statistical analyses where the observed data are subject to some underlying selection process prior to entry into the sampled data. For example, within capture-recapture studies, a primary selection mechanism is the survival until initial capture time. The common Cormack-Jolly-Seber model conditions on the first time an individual is observed, leading to potential survivorship bias. However, while the issue of survivorship bias has been well studied in many fields, there has been little exploration within the capture-recapture framework. In particular, we focus on individual (continuous) random effect Cormack-Jolly-Seber models, where it is assumed that individuals have different survival probabilities, specified to be from some common underlying distribution. We discuss the implications of the survivorship bias within the data collection process, and describe a novel modeling approach that accounts for the survivorship bias within an ecologically sensible manner. Using simulated data, we demonstrate the significant impact of ignoring the survivorship bias present in the data. We fit the corrected model to a guillemot data set and demonstrate that even with relatively mild selection bias, the individual heterogeneity variability is substantially underestimated when ignoring this survivorship bias.