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# Power Computations for Designing Comparative Poisson Trials

Mitchell Gail
Biometrics
Vol. 30, No. 2 (Jun., 1974), pp. 231-237
DOI: 10.2307/2529645
Stable URL: http://www.jstor.org/stable/2529645
Page Count: 7
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## Abstract

Power calculations are given for designing comparative Poisson trials based on independent random samples from two populations with parameters $\lambda_1$ and $\lambda_2$. Power curves for testing $\rho$ = $\lambda_2$/$\lambda_1$ = 1 against one-sided alternatives $\rho$ > 1 are presented for sizes $\alpha$ = 0.01 and $\alpha$ = 0.05. Such curves might be used, for example, to define the duration of an experiment designed to demonstrate differences in the incidence of a rare disease, or, to specify sample sizes for a comparative binomial trial with very small binomial parameters. That total number of events T, from both populations, required to assure given power ($\gamma$ = 0.9 or $\gamma$ = 0.5) for sizes $\alpha$ = 0.01 or $\alpha$ = 0.05 when using an exact test, conditional on T, is tabulated. This table permits one to design a trial which ends when a fixed total number of events, T, has been observed.

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