Non-parametric estimation of the case fatality ratio with competing risks data: an application to Severe Acute Respiratory Syndrome (SARS).
Jewell NP., Lei X., Ghani AC., Donnelly CA., Leung GM., Ho L-M., Cowling BJ., Hedley AJ.
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, F(1)(t) = Pr(T infinity, where T denotes the time from onset to death (J = 1) or recovery (J = 2). When censoring is present, however, estimation of F(1)(infinity) is complicated by the possibility of little information regarding the right tail of F(1), requiring use of estimators of F(1)(t(*)) or F(1)(t(*))/(F(1)(t(*))+F(2)(t(*))) where t(*) is large, with F(2)(t) = Pr(T