Statistics in Medicine

Constrained empirical‐likelihood confidence regions in nonignorable covariate‐missing data problems

Journal Article

Missing covariates in regression analysis are a pervasive problem in medical, social, and economic researches. We study empirical‐likelihood confidence regions for unconstrained and constrained regression parameters in a nonignorable covariate‐missing data problem. For an assumed conditional mean regression model, we assume that some covariates are fully observed but other covariates are missing for some subjects. By exploitation of a probability model of missingness and a working conditional score model from a semiparametric perspective, we build a system of unbiased estimating equations, where the number of equations exceeds the number of unknown parameters. Based on the proposed estimating equations, we introduce unconstrained and constrained empirical‐likelihood ratio statistics to construct empirical‐likelihood confidence regions for the underlying regression parameters without and with constraints. We establish the asymptotic distributions of the proposed empirical‐likelihood ratio statistics. Simulation results show that the proposed empirical‐likelihood methods have a better finite‐sample performance than other competitors in terms of coverage probability and interval length. Finally, we apply the proposed empirical‐likelihood methods to the analysis of a data set from the US National Health and Nutrition Examination Survey.

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