Meta-analysis Methods for 2 2 Contingency Tables

Methods for combining 2×2 contingency tables from multiple studies are reviewed and new methods are proposed. Methods for combining 2×2 contingency tables from multiple studies are presented in the context of three different statistical models: the constant coefficient model, the varying coefficient model, and the random coefficient model. The constant coefficient confidence intervals have unacceptable performance characteristics in typical applications where effect sizes and samples sizes are unequal across studies. The random coefficient confidence intervals, which assume that the studies are a random sample from a definable superpopulation of studies and that the superpopulation distribution is normally distributed, exhibit unacceptable performance characteristics. The varying coefficient confidence intervals have excellent performance characteristics under realistic conditions. New methods for comparing parameter values across study populations are presented.