Logistic Regression with a Right-Skewed Exposure Variable Measured in Pools and Subject to Errors

• Activity Number: 367 - SPEED: Statistical Epidemiology
• Type: Contributed
• Date/Time: Tuesday, July 31, 2018 : 11:35 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Dane R Van Domelen* and Emily M Mitchell and Enrique F Schisterman and Neil Perkins and Robert Lyles
• Companies: Rollins School of Public Health, Emory University and Agency for Healthcare Research and Quality and Eunice Kennedy Shriver National Institute of Child Health and Human Development and DIPHR/NICHD/NIH and Emory University
• Keywords: pooling; maximum likelihood; Gamma; replicates; measurement error

Abstract

In the logistic regression setting where measuring a biomarker requires an expensive assay, a design in which one measures it in pooled samples from multiple cases/controls can be highly cost-effective. The odds ratio (OR) can be estimated via a modified logistic regression model, and likelihood-based methods are available to correct for errors caused by processing samples and/or assay imprecision. We modify these methods to accommodate a positive right-skewed biomarker, motivated by cytokine measurements in a substudy of the Collaborative Perinatal Project. We assume (1) a constant-scale Gamma model for exposure X given covariates, which implies covariates are linearly related to log[E(X)] and that V(X) increases linearly with E(X); and (2) lognormal, multiplicative processing and measurement errors acting on the poolwise mean independently of each other and of pool size. The estimated OR relating cytokine level to risk of spontaneous abortion was 1.05 (95% CI 0.83-1.33). AIC favored our approach over assuming a linear model for X given covariates and additive normal errors, although estimates were similar. Both approaches are available in the R package "pooling."