Most analysis of health care costs examine costs for fixed periods of time (e.g., annual) but are not well suited for the analysis of either lifetime costs or per episode of illness cost, such as those that occur in cost-effectiveness and some cost of illness analyses. These questions involve use of data with varying periods of observation and right censoring of cases before death or the end of the episode of illness. Although some work has been done on this issue, there are concerns about the robustness of the existing methods, especially given the extreme skewness typical of health care costs generally and these data specifically, as well as the prominence of observations with no expenditure for some short periods of observation. In this paper, we identify a major bias associated with estimators that use inverse probability weighting with the survival from censoring probabilities in estimating mean cumulative costs (Bang-Tsiatis-Lin). We propose an alternative that extends the class of two-part models to deal with random right censoring (e.g., administrative censoring), and more fully incorporates the information from the censored periods. Our model also addresses issues about the time to death in these analyses. Several simulations are conducted to highlight our proposed estimator compared to alternatives. The results support the theoretical result indicating that estimators based on inverse probability weighting yield biased estimates of accumulated costs in situations with substantial censoring. Our alternative is consistent and more efficient for these designs. We apply this approach and compare it to the alternatives from the literature using data from the Medicare-SEER files on prostate cancer using within and split sample methods. Our results indicate that the Bang-Tsiatis-Lin approach yields negative estimates of the ten year incremental costs of worse stages of prostate cancer relative to better initial grade. Our alternative indicates the opposite. The discrepancy is large in magnitude and statistically significant.
