For diseases with some level of associated mortality, the case fatality ratio measures the proportion of diseased individuals who die from the disease. In principle, it is straightforward to estimate this quantity from individual follow-up data that provides times from onset to death or recovery. In particular, in a competing risks context, the case fatality ratio is defined by the limiting value of the sub-distribution function, associated with death, at infinity. When censoring is present, however, estimation of this quantity is complicated by the possibility of little information in the right tail of of the sub-distribution function, requiring use of estimators evaluated at large or the largest observed death times. With right censoring, the variability of such estimators is large in the tail, suggesting the possibility of using estimators evaluated at smaller death times where bias may be increased but overall mean squared error be smaller. These issues are investigated here for nonparametric estimators of the sub-distribution functions for both death and recovery. The ideas are illustrated on case fatality data for individuals infected with severe acute respiratory syndrome (SARS) in Hong Kong in 2003.
Jewell, Nicholas P.; Lei, Xiudong; Ghani, A. C.; Donnelly, C. A. ; Leung, G. M.; Ho, L. M.; Cowling, B. ; and Hedley, A. J. , "Nonparametric Estimation of the Case Fatality Ratio with Competing Risks Data: An Application to Severe Acute Respiratory Syndome (SARS) " (April 2005). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 176.