Generalized Linear Models for Longitudinal Data with Biased Sampling Designs: A Sequential Offsetted Regressions Approach

• Activity Number: 407
• Type: Topic Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Lee McDaniel* and Jonathan Schildcrout and Enrique F. Schisterman and Paul J. Rathouz
• Companies: Louisiana State University Health Sciences Center and Vanderbilt University and NIH and University of Wisconsin - Madison
• Keywords: Biased Sampling Designs ; Longitudinal Data ; Generalized Linear Models ; Outcome-Dependent Sampling

Abstract

Biased sampling designs can be highly efficient when studying rare or low variability endpoints. We consider longitudinal data settings in which the probability of being sampled depends on a repeatedly measured response through an outcome-related, auxiliary variable. Such auxiliary variable- or outcome-dependent sampling aims to improve response and exposure variability over random sampling, even though the auxiliary variable is not of interest. We propose a generalized linear model based approach to estimation using a sequence of offsetted regressions. The first estimates the relationship of the auxiliary variable to the response and covariate data using an offsetted logistic regression model, with an offset based on the known ratio of sampling probabilities. Results from the auxiliary model are used to estimate observation-specific probabilities of being sampled conditional on the response and covariates, which are used to account for bias in the target population model. We provide asymptotic standard errors and perform simulation studies that demonstrate bias reduction in estimation, correct coverage probability, and improved efficiency over simple random sampling.