Nonparametric predictive inference with combined data under different right-censoring schemes.

Abstract

This paper presents nonparametric predictive inference (NPI) for meta-analysis in which multiple independent samples of lifetime data are combined, where different censoring schemes may apply to the different samples. NPI is a frequentist statistical approach based on few assumptions and with uncertainty quantified via lower and upper probabilities. NPI has the flexibility to deal with a mixture of different types of censoring, mainly because the inferences do not depend on counterfactuals, which affect several inferences for more established frequentist approaches. We show that the combined sample, consisting of differently censored independent samples, can be represented as one sample of progressively censored data. This allows explicit formulae for the NPI lower and upper survival functions to be presented which are generally applicable. The approach is illustrated through an example using a small data set from the literature, for which several scenarios are presented.