Improved Horvitz-Thompson Estimation of Model Parameters from Stratified Case-Control Samples

• Activity Number: 559
• Type: Invited
• Date/Time: Wednesday, August 4, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Norman Breslow*+
• Companies: University of Washington
• Keywords: influence function ; calibration of sampling weights ; semiparametric efficiency

Abstract

Stratified case-control studies involve simple random sampling from an infinite superpopulation at phase one and stratified random sampling from a finite cohort at phase two. The asymptotic variance of the Horvitz-Thompson (HT) estimator, of parameters in a variety of (semi)-parametric models, is the sum of two components: the model-based variance of the MLE that would be calculated from complete data for the entire cohort; and the design-based variance from HT estimation of the unknown cohort total of the (efficient) influence function (IF) contributions. The second component may be reduced by adjusting the sampling weights, e.g. by calibration to known cohort totals of auxiliary variables correlated with the IF. We compare improved HT and semiparametric efficient estimates of log odds ratios using simulated case-control samples drawn from an actual cohort study of Wilms tumor.