Foundational Issues Concerning the Analysis of Censored Data

Abstract

The common approach to analyzing censored data utilizes "competing risk" models; a class of distribution is first chosen and then the sufficient statistics are identified! An "operational Bayesian" approach (Barlow 1993) for analyzing censored data would require a somewhat different methodology. In this approach, we first determine potentially observable parameters of interest. We then determine the data summaries (sufficient statistics) for these parameters. Tsai (1994) suggests that the observed sample frequency is sufficient for predicting the population frequency. Invariant probability measures (likelihoods), conditional on the parameters of interest, are then derived based on the principle of sufficiency and the principle of insufficient reason.