Nonparametric Predictive Inference With Combined Data Under Different Right-Censoring Schemes

Abstract

This article 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 formulas for the NPI lower and upper survival functions to be presented that are generally applicable. The approach is illustrated through an example using a small data set from the literature, for which several scenarios are presented.

AMS Subject Classification:

• 62G99
• 62N99
• 62N05

keywords:

• Combined data
• Lower and upper probability
• Meta-analysis
• Nonparametric predictive inference
• Right-censoring
• Progressive censoring
• Lifetime data

Notes

1. It is important to emphasize that NPI does not use the corresponding Dempster–Shafer framework for statistical inference.

2. R functions for this are available from www.npi-statistics.com

Additional information

Funding

The initial ideas for this work resulted from discussions with Professor Balakrishnan (McMaster University, Canada) during his visit to Durham University in April 2010, which was funded by the London Mathematical Society (LMS). We thank LMS for their financial support.