On Regression Models When the Predictor Is Subject to Censoring

• Activity Number: 622
• Type: Invited
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): David Oakes*+
• Companies: University of Rochester
• Keywords: Biomarkers ; Expectation of Life ; Kaplan-Meier ; Mean Residual Life ; Missing Data ; Survival Analysis

Abstract

There is now a voluminous literature on regression models when the response variable is subject to right censoring. There is relatively little work on regression analysis when the response variable is available for all individuals but the predictor is subject to right censoring. This problem is becoming of increasing importance due to the use of such variables as biomarkers in clinical studies (Cai et al., Biostatistics, 7, 187-197, 2006). Unlike the case of censored responses, omission of observations where the predictor is censored does not typically lead to bias. However there may be substantial efficiency loss, as the sample size is reduced and the omitted observations will tend to be those of high leverage and so the most informative as to the dependence of the response on the predictor. Tsimikas et al. (Computational Statistics and Data Analysis, 56, 1858-1864, 2012) study ways of recovering partial information from the censored observations, using a parametric model for the distribution of the predictor. Here we propose a fully nonparametric approach using properties of the mean residual life function (Yang, Stochastic Processes and their Applications 6, 33-39, 1977).