Semiparametric Regression Analysis Of Doubly Censored Longitudinal Data With Informative Observation Times

Longitudinal data is common in statistical analysis.However,in many statistical applications,longitudinal data may be doubly censored by both an upper and lower limit due to data collection methods.In addition,the observation times tend to be informative.Therefore,it is important to take into account of this double censoring data wiht informative observation times in statistical analysis.In this paper,semiparametric regression models are intorduced for the analysis of doubly censored longitudinal data with informative observation times.Under some assumptions,a statistical procedure based on an estimation equation is proposed for the estimation of the parameters in the model.At the same time,we point out that there are nuisance parameters in the asymptotic distribution of estimators,such as the density function of error.However,the density function at the censoring point is hard to estimate.In order to study the statistical inference of the estimators,we use the random weighting method to calculate the asymptotic distribution of the estimators,and claim that the conditional asymptotic distribution of random weighting estimators is the same as that of estimators,which avoid estimating nuisance parameters.An algorithm based on the alternating direction method of multipliers is proposed to compute these estimates in practical applications.Simulation studies are performed to evaluate the performance of our method.The proposed model and procedures are also applied to analyze a dataset from a clinical trial in patients with advanced colorectal cancer and draw some conslusions that the observation times and cetuximab influence patients’ quality of life.