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Fay MP, Feuer EJ. Confidence intervals for directly standardized rates: a method based on the gamma distribution. Stat Med; 16: 791-801

National Cancer Institute, Division of Cancer Prevention and Control, Bethesda, Maryland 20892-7354, USA.
Statistics in Medicine (Impact Factor: 2.04). 05/1997; 16(7):791-801. DOI: 10.1002/(SICI)1097-0258(19970415)16:73.0.CO;2-#
Source: PubMed

ABSTRACT We offer an approximation to central confidence intervals for directly standardized rates, where we assume that the rates are distributed as a weighted sum of independent Poisson random variables. Like a recent method proposed by Dobson, Kuulasmaa, Eberle and Scherer, our method gives exact intervals whenever the standard population is proportional to the study population. In cases where the two populations differ non-proportionally, we show through simulation that our method is conservative while other methods (the Dobson et al. method and the approximate bootstrap confidence method) can be liberal.

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    • "I (estimate coverage probability for the j-th generated scenarios ≤ 0.94) where I (A) is the indicator function of event A. Most statisticians and practitioners want guaranteed coverage with the shortest width confidence interval and some want central confidence intervals (Fay and Feuer, 1997) while others will allow non-central intervals in order to get a shorter width (Casella and Robert, 1989); thus we will compare the performance of the confidence interval Table 8 Simulated coverage properties (in %) of various 95% confidence intervals with 6 i=1 θ i = "
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