title: Adjusting for unmeasured confounding due to either of two crossed factors with a logistic regression model.
abstract: Motivated by an investigation of the effect of surface water temperature on the presence of Vibrio cholerae in water samples collected from different fixed surface water monitoring sites in Haiti in different months, we investigated methods to adjust for unmeasured confounding due to either of the two crossed factors site and month. In the process, we extended previous methods that adjust for unmeasured confounding due to one nesting factor (such as site, which nests the water samples from different months) to the case of two crossed factors. First, we developed a conditional pseudolikelihood estimator that eliminates fixed effects for the levels of each of the crossed factors from the estimating equation. Using the theory of U-Statistics for independent but non-identically distributed vectors, we show that our estimator is consistent and asymptotically normal, but that its variance depends on the nuisance parameters and thus cannot be easily estimated. Consequently, we apply our estimator in conjunction with a permutation test, and we investigate use of the pigeonhole bootstrap and the jackknife for constructing confidence intervals. We also incorporate our estimator into a diagnostic test for a logistic mixed model with crossed random effects and no unmeasured confounding. For comparison, we investigate between-within models extended to two crossed factors. These generalized linear mixed models include covariate means for each level of each factor in order to adjust for the unmeasured confounding. We conduct simulation studies, and we apply the methods to the Haitian data. Copyright © 2016 John Wiley & Sons, Ltd.
authors.affiliation: Department of Biostatistics, College of Public Health and Health Professions, College of Medicine, University of Florida, Gainesville, 32611, FL, U.S.A.
authors.forename: Li
authors.initials: L
authors.lastname: Li
authors.affiliation: Department of Biostatistics, College of Public Health and Health Professions, College of Medicine, University of Florida, Gainesville, 32611, FL, U.S.A.
authors.forename: Babette A
authors.initials: BA
authors.lastname: Brumback
authors.affiliation: Emerging Pathogens Institute, University of Florida, Gainesville, 32611, FL, U.S.A.
authors.forename: Thomas A
authors.initials: TA
authors.lastname: Weppelmann
authors.affiliation: Emerging Pathogens Institute, University of Florida, Gainesville, 32611, FL, U.S.A.
authors.forename: J Glenn
authors.initials: JG
authors.lastname: Morris
authors.affiliation: Emerging Pathogens Institute, University of Florida, Gainesville, 32611, FL, U.S.A.|Department of Environmental and Global Health, College of Public Health and Health Professions, University of Florida, Gainesville, 32611, FL, U.S.A.
authors.forename: Afsar
authors.initials: A
authors.lastname: Ali
mesh_terms: D003198:Computer Simulation; D015986:Confounding Factors, Epidemiologic; D003627:Data Interpretation, Statistical; D006205:Haiti; D016014:Linear Models; D016015:Logistic Models; D014734:Vibrio cholerae / Q000302:isolation & purification; D014881:Water Supply
keywords: between-within model; composite likelihood; conditional likelihood; confounding; logistic regression; pseudolikelihood