TY - JOUR
T1 - Empirical Likelihood Approach for Longitudinal Data with Missing Values and Time-Dependent Covariates
AU - Zhang , Yan
AU - Zhang , Weiping
AU - Guo , Xiao
JO - Annals of Applied Mathematics
VL - 2
SP - 200
EP - 220
PY - 2022
DA - 2022/06
SN - 32
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/20638.html
KW - empirical likelihood, estimating equations, longitudinal data,
missing at random.
AB - <p style="text-align: justify;">Missing data and time-dependent covariates often arise simultaneously in
longitudinal studies, and directly applying classical approaches may result in
a loss of efficiency and biased estimates. To deal with this problem, we propose weighted corrected estimating equations under the missing at random
mechanism, followed by developing a shrinkage empirical likelihood estimation
approach for the parameters of interest when time-dependent covariates are
present. Such procedure improves efficiency over generalized estimation equations approach with working independent assumption, via combining the independent estimating 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 consistent 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 follow central chi-square distributions asymptotically when
evaluated at the true parameter. The practical performance of our approach
is demonstrated through numerical simulations and data analysis.</p>