Simple linear approximations to the likelihood equation for combining evidence in multiple 2×2 tables: A critique of conventional procedures

Summary The conventional procedures for a common odds ratio in multiple 2×2 tables are explored and critiqued. Three types of linear approximation to the likelihood equations under some models of common measures of association are used to derive the popular conventional estimators and test statistics. Some of them are derived using the model of the common standardized difference which is an unacceptable measure. The derivation provides us with some characteristics of the procedures. The advantages of procedures based on the conditional and unconditional likelihoods are discussed. The Institute of Statistical Mathematics