Estimation of censored medical cost with dependent censoring using copula method

Abstract

Medical cost modeling presents many challenges because available data are often right-censored due to early termination or follow-up loss of data observations. The prevailing methods for estimating the average of cumulative costs fall into three categories, (a) the inverse probability weighted (IPW) estimators; (b) the generalized survival-adjusted estimators; (c) the joint-modeling methods. However, under violation of independent censoring assumption, traditional survival analysis methods have been shown to be biased when employed on medical data. However, the prevailing methods were established under independent censoring. Generally, the medical costs for failure event and censoring time tend to be positively correlated (Etzioni et al. 1999; Lin 2003). Therefore, it is necessary to consider the joint distribution of survival and censoring time under dependent censoring. Copula function is attractive in statistical modeling because it gives a flexible and promising tool to modeling with dependence between survival and censoring time. For analysis of survival under dependent censoring, we use the copula-graphic estimator and copula-based univariate Cox regression employed an assumed copula. In this study, we evaluate the prevailing methods for estimating the medical cost under independent censoring assumption. Also, we proposed new estimators that are expanding scheme on IPW and generalized survival-adjusted estimators under dependent censoring assumption. The purpose of this study is to adapt the copula method to estimation medical cost with survival data including dependent censoring. We evaluate our proposed estimators with a series of simulations. We conduct a simulation study assuming various scenarios to appraise the performance of bias and S.E in estimation of medical costs for dependent censoring. In addition, we illustrated the prevailing and proposed method using National Health Insurance Service National Sample Cohort (NHIS-NSC) data.