Misspecification of Covariate Functional Form in the Nested Case-Control Design

• Activity Number: 609 - New Approaches to Improving Accuracy, Precision, and Robustness of Survival Analysis
• Type: Contributed
• Date/Time: Thursday, August 1, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Michelle M. Nuño* and Daniel L. Gillen
• Companies: University of California, Irvine and University of California, Irvine
• Keywords: survival analysis; nested case-control design; model misspecification; efficient sampling

Abstract

Cox’s proportional hazards model is typically used to analyze survival data collected via a simple random sample. If the event of interest is rare and covariates are difficult or expensive to collect, the nested case-control (NCC) design provides reduced costs with relatively minimal impact on inferential precision. When the scientific goal is to conduct inference, a priori specification of the model is essential to avoid multiple testing bias. The functional form of a continuous covariate is generally complex, however, and a priori specification of correct covariate transformations are difficult to impossible. We show that under an NCC design and misspecification of covariate functional form, the Cox estimator is consistent for a quantity that depends on the number of controls sampled at each event time and the censoring distribution. Using this theoretical result, we propose a class of estimators that recover the estimand for the Cox estimator under simple random sampling and provide censoring robust estimation. We assess the proposed estimators using simulation and illustrate the significance of the methods in the context of biomarker discovery in Alzheimer’s Disease.