Logistic regression with incompletely observed categorical covariates: A comparison of three approaches

Abstract

SUMMARY A logistic regression analysis based on the complete cases neglects the information due to subjects with missing values in at least one but not in all covariates. Three different approaches allowing the use of this information are compared: maximum likelihood estimation, pseudo maximum likelihood estimation, and probability imputation. The first two yield consistent estimates of the regression coefficients and asymptotic normality allows the construction of asymptotically valid confidence intervals. The only necessary assumption is that the probability for the occurrence of missing values does not depend on the true value of the hidden covariates, whereas there may be a dependence on completely observed covariates and on the outcome variable. Their relative efficiency and the gain relative to a complete case analysis is investigated. Comparison with imputation methods shows that imputation of conditional probabilities can be regarded as a close approximation to the pseudo maximum likelihood estimation, whereas imputation of unconditional probabilities is associated with serious bias.