Shrinkage Empirical Likelihood Approach For Longitudinal Data With Missing Values And Time-Dependent Covariates

Missing data and time-dependent covariates often arise in longitudinal studies,thus directly applying classical approaches can result in a loss of efficiency and biased esti-mates.Under the missing at random mechanism,we first propose weighted corrected estimating equations,followed by developing a shrinkage empirical likelihood estima-tion approach for the parameters of interest when time-dependent covariates are present.Such an approach guarantees improved efficiency over generalized estimation equations approach with working independent assumption,via combining the independent estimat-ing equations and the extracted additional information from the estimating equations that are excluded by the independence assumption.The contribution from the remaining estimating equations is weighted according to the likelihood of each equation being a con-sistent estimating equation and the information it carries.We show that the estimators are asymptotically normally distributed and the empirical likelihood ratio statistic and its profile counterpart asymptotically follow central chi-square distributions when evalu-ated at the true parameter.The theoretical properties and practical performance of our approach are demonstrated through numerical simulations and data analysis.