Sample Sizes to Compare Two Poisson Rates

In this note, procedures for determining the sample sizes needed to compare the rates of two Poisson populations to achieve a pre-specifi ed power at a given ratio of the rates are proposed. The fi rst method relies on a conditional uniformly most powerful test (CUMPT) which leads to sample sizes that will guarantee the desired power, but at the cost of using more units than necessary. The second method relies on a normal approximation and may not always guarantee that the desired power will be achieved, but generally yields a power close to the pre-specifi ed value and prescribes smaller sample sizes than the CUMPT-based method. Properties of the procedures are examined using simulation studies. The particular applicability and motivating situations leading to these procedures are in colon cancer research. Illustrations of the applicability of the procedures in studies dealing with tumor counts in mice are presented.