A Note on the Censoring Problem in Empirical Case-Outcome Studies

In outcome studies of cases filed within a study window, the sample may be skewed if many cases are still pending when the window closes and not included in the study. We refer to cases that are completed within the window as “observed” and those still pending as “censored.” We propose two methods for reducing possible bias: a “self-consistent” estimator that imputes values to the censored cases and an “inverse probability weighting” estimator that assigns weights to the observed cases. In the body of the article we describe these methods for the nonmathematical reader and in the Appendix give a more mathematical treatment. We then apply the self-consistent estimator first to simulated data and then to the landmark study of reversals in death penalty cases by Professor James S. Liebman and his colleagues. In these examples the two methods are equivalent. Liebman et al. simply excluded censored cases and reported a reversal rate of 68%. Application of our methods to the Liebman data reduces the reversal rate to 62.2% (95% c.i. 60.1%, 64.4%). In general, our method largely removes the bias that affects sample estimates when censored cases are just ignored.