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Measurement errors usually arise during the longitudinal data collectionprocess. Ignoring the effects of measurement errors will lead to invalidestimates. The Lifestyle Education for Activity and Nutrition (LEAN) study wasdesigned to assess the effectiveness of intervention for enhancing weight lossover nine months. The covariates systolic blood pressure (SBP) and diastolicblood pressure (DBP) were measured at baseline, month 4, and month 9. At eachassessment time, there were two replicate measurements for SBP and DBP. Thereplicate measurement errors of SBP follow different distributions, as doesDBP. To account for the distributional difference of replicate measurementerrors, a new method for analyzing longitudinal data with replicate covariatemeasurement errors is developed based on the empirical likelihood method. Theasymptotic properties of the proposed estimator are established under someregularity conditions. The confidence region for the parameters of interest canbe constructed based on the chi-squared approximation without estimating thecovariance matrix. Additionally, the proposed empirical likelihood estimator isasymptotically more efficient than the estimator of Lin et al. (2018).Extensive simulations demonstrate that the proposed method can eliminate theeffects of measurement errors in the covariate and has a high estimationefficiency. The proposed method indicates the significant effect of theintervention on BMI in the LEAN study.

Empirical likelihood inference for longitudinal data with covariate measurement errors: An application to the LEAN study