An efficient design strategy for logistic regression using outcome- and covariate-dependent pooling of biospecimens prior to assay

Potential reductions in laboratory assay costs afforded by pooling equal aliquots of biospecimens have long been recognized in disease surveillance and epidemiological research and, more recently, have motivated design and analytic developments in regression settings. For example, Weinberg and Umbach (1999, Biometrics 55, 718–726) provided methods for fitting set-based logistic regression models to case-control data when a continuous exposure variable (e.g., a biomarker) is assayed on pooled specimens. We focus on improving estimation efficiency by utilizing available subject-specific information at the pool allocation stage. We find that a strategy that we call “(y,c)-pooling,” which forms pooling sets of individuals within strata defined jointly by the outcome and other covariates, provides more precise estimation of the risk parameters associated with those covariates than does pooling within strata defined only by the outcome. We review the approach to set-based analysis through offsets developed by Weinberg and Umbach in a recent correction to their original paper. We propose a method for variance estimation under this design and use simulations and a real-data example to illustrate the precision benefits of (y,c)-pooling relative to y-pooling. We also note and illustrate that set-based models permit estimation of covariate interactions with exposure.