Nonparametric inference for median costs with censored data

Increasingly, estimations of health care costs are used to evaluate competing treatments or to assess the expected expenditures associated with certain diseases. In health policy and economics, the primary focus of these estimations has been on the mean cost, because the total cost can be derived directly from the mean cost, and because information about total resources utilized is highly relevant for policymakers. Yet, the median cost also could be important, both as an intuitive measure of central tendency in cost distribution and as a subject of interest to payers and consumers. In many prospective studies, cost data collection is sometimes incomplete for some subjects due to right censoring, which typically is caused by loss to follow-up or by limited study duration. Censoring poses a unique challenge for cost data analysis because of so-called induced informative censoring, in that traditional methods suited for survival data generally are invalid in censored cost estimation. In this article, we propose methods for estimating the median cost and its confidence interval (CI) when data are subject to right censoring. We also consider the estimation of the ratio and difference of two median costs and their CIs. These methods can be extended to the estimation of other quantiles and other informatively censored data. We conduct simulation and real data analysis in order to examine the performance of the proposed methods.