On Recensoring for Censored Paired Data

Abstract

In comparing two treatment regimens, a matched-pair design is often used for nonhomogeneous experimental units. A standard method of analyzing the resulting data is to consider the difference within pairs, so that the nuisance parameters due to the heterogeneity between pairs can be eliminated and the parameter of interest—the treatment effect—can be estimated. This procedure becomes invalid when the data are subject to censoring, however. In addition, the available likelihood based methods for handling censored data may suffer from the inconsistency problem incurred by the increasing number of nuisance parameters. In this article, we propose a new approach for eliminating the nuisance parameters based on a crucial notion of “recensoring.” Assuming that the censoring time for each observation is known, recensoring is a natural way to force a common lag between the two censoring times within each pair by resetting one of them to a smaller value. After recensoring, we may treat the new observed times as the survival times without censoring. Standard paired data analysis can be applied. M estimation is studied in detail. Root n consistency is established, and the asymptotic variance is obtained. Residual plots can be constructed in the usual way to check model assumptions. Application to a real data set is reported. Comparisons with the work of Holt and Prentice and Wei and Pee are made both in theory and in a simulation study.

KEY WORDS:

• Consistency
• Location models
• M estimation
• Nuisance parameters
• Residual plots