Sample Size Determination for Comparing Two Poisson Rates

Procedures for determining the sample sizes to use in comparing the rates of two Poisson populations in order to achieve a pre-specified power at a given ratio of the rates are proposed. The first method relies on a conditional uniformly most powerful test (CUMPT) which leads to sample sizes that will guarantee that the desired power will always be achieved, but at the cost of using more units than what is necessary. The second method relies on a normal approximation and leads to a procedure that may not always guarantee that the specified power will be achieved, but which generally yields a power that is close to the pre-specified value and at the same time dictates a smaller number of units 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. An illustration of how the procedures could be used is demonstrated in the context of studies on mice dealing with tumor counts. Computer codes in the R language for implementing the procedures are also provided