Conditional ecological individual heterogeneity models: Accounting for survivorship bias

Ruth King, University of Edinburgh

Abstract: Selection (or survivorship) bias is a well known problem in studies where the sampled data are not representative of the underlying population due to the selection process for entering the study. Population-level inferences drawn from the observed data, without taking into account the selection process, will subsequently be biased. The impact of selection bias has been well studied in many fields, particularly, for example, in epidemiology and public health. However, the study and impact of potential selection bias within ecological studies due to individually varying survival rates has not drawn much attention to date.

We investigate selection bias in relation to capture-recapture studies, where observers go into the field at a series of capture occasions and record all individuals observed at that occasion. Individuals are assumed to be uniquely identifiable, either via natural markings or via a mark applied at initial capture. The observed data correspond to the capture history of each individual animal observed within the study, detailing at which capture occasion they were (or were not) observed. We assume that the age of an individual is known at initial capture. For these studies the primary selection mechanism for entry in to the observed data is that of survival up to their initial capture, or equivalently until their observed age of initial capture. The common Cormack-Jolly-Seber model subsequently conditions on the first time each observed individual is observed within the study, leading to potential selection bias within the model, as the conditioning explicitly ignores the associated survival selection mechanism.

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 will discuss the implications of the corresponding sampling (or more specifically survivorship) bias within the data collection process, and describe a novel modelling approach that accounts for the survivorship bias within an ecologically sensible manner. A simulation study demonstrates the potential significant impact of ignoring the survivorship bias present in the data, in terms of associated biased estimates of the survival probabilities and individual heterogeneity component. We fit the new model that corrects for the sampling mechanism to a large guillemot data set and demonstrate that even with relatively mild selection bias, the individual heterogeneity variability is substantially underestimated when ignoring the underlying survivorship bias.

This is joint work with Blanca Sarzo (Foundation for the Promotion of Health and Biomedical Research of Valencia Region) and Rachel McCrea (Lancaster University).