Efficient and exact tests of the risk ratio in a correlated 2 × 2 table with structural zero

Abstract

For a correlated 2 × 2 table where the (01) cell is empty by design, the parameter of interest is typically the ratio of the probability of secondary response conditional on primary response to the probability of primary response, also known as a risk ratio. It is common to test whether or not the risk ratio equals one. One method of obtaining an exact P-value is to maximise the tail probability of the test statistic over the nuisance parameter. It is argued that better results are obtained by first replacing the nuisance parameter by its profile estimate in the calculation of its exact significance followed by maximisation-termed an E + MP -value. We consider four standard approximate test ..