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Multivariate logistic regression with incomplete covariate and auxiliary information. (English) Zbl 1198.62070

Summary: We propose and explore a multivariate logistic regression model for analyzing multiple binary outcomes with incomplete covariate data where auxiliary information is available. The auxiliary data are extraneous to the regression model of interest but predictive of the covariate with missing data. N. J. Horton and N. M. Laird [Maximum likelihood analysis of logistic regression models with incomplete covariate data and auxiliary information. Biometrics 57, 34–42 (2001)] described how the auxiliary information can be incorporated into a regression model for a single binary outcome with missing covariates, and hence the efficiency of the regression estimators can be improved. We consider extending this method to the case of a multivariate logistic regression model for multiple correlated outcomes, and with missing covariates and completely observed auxiliary information. We demonstrate that in the case of moderate to strong associations among the multiple outcomes, one can achieve considerable gains in efficiency from estimators in a multivariate model as compared to the marginal estimators of the same parameters.

MSC:

62J12 Generalized linear models (logistic models)
62H12 Estimation in multivariate analysis
62P10 Applications of statistics to biology and medical sciences; meta analysis
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