Exact tests of non-inferiority from independent binomial data based on second order test statistics

Chris Lloyd, Melbourne Business School

Abstract

Recent advances in likelihood asymptotics (Reid, 2003) lead to pivotal quantities that are closer to standard normal than standard pivotals and also respect some kind of conditionality. It is less clear the extent to which these methods work for discrete models. On the other hand, in the context of binomial trials conditional pivotals can lead to more efficient unconditional inferences, see Boschloo (1970) and Lloyd and Moldovan (2007). This suggests that second order pivotals that respect local conditionality might provide more powerful exact tests. For testing the rate ratio from independent binomial samples, we investigate 5 first order pivotals and the second order pivotal. Each of these is used to generate an exact test my maximising with respect to the nuisance parameter. We also consider the effect of pre-estimating the nuisance parameter.