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Stat Med. 2016 Aug 15;35(18):3179-88. doi: 10.1002/sim.6916. Epub 2016 Feb 19.

Adjusting for unmeasured confounding due to either of two crossed factors with a logistic regression model.

Author information

1
Department of Biostatistics, College of Public Health and Health Professions, College of Medicine, University of Florida, Gainesville, 32611, FL, U.S.A.
2
Emerging Pathogens Institute, University of Florida, Gainesville, 32611, FL, U.S.A.
3
Department of Environmental and Global Health, College of Public Health and Health Professions, University of Florida, Gainesville, 32611, FL, U.S.A.

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.

KEYWORDS:

between-within model; composite likelihood; conditional likelihood; confounding; logistic regression; pseudolikelihood

PMID:
26892025
DOI:
10.1002/sim.6916
[Indexed for MEDLINE]

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