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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 <or=t and J = 1), associated with death, as 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 <or=t and J = 2) being the analogous sub-distribution function associated with recovery. With right censored data, the variability of such estimators increases as t(*) increases, suggesting the possibility of using estimators at lower values of t(*) where bias may be increased but overall mean squared error be smaller. These issues are investigated here for non-parametric estimators of F(1) and F(2). The ideas are illustrated on case fatality data for individuals infected with Severe Acute Respiratory Syndrome (SARS) in Hong Kong in 2003.

Original publication

DOI

10.1002/sim.2691

Type

Journal article

Journal

Statistics in medicine

Publication Date

04/2007

Volume

26

Pages

1982 - 1998

Addresses

Division of Biostatistics and Department of Statistics, University of California, Berkeley, USA. jewell@stat.berkeley.edu

Keywords

Humans, Severe Acute Respiratory Syndrome, Mortality, Data Interpretation, Statistical, Statistics, Nonparametric, Disease Outbreaks, Computer Simulation