Put the odds on your side: a new measure for epidemiological associations
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The odds ratio (OR) is a measure of effect size commonly used in observational research. OR reflects statistical association between a binary outcome, such as the presence of a health condition, and a binary predictor, such as an exposure to a pollutant. Statistical inference and interval estimation for OR are often performed on the logarithmic scale, due to asymptotic convergence of log(OR) to a normal distribution. Here, we propose a new normalized measure of effect size, γ', and derive its asymptotic distribution. We show that the new statistic, based on the γ' distribution, is more powerful than the traditional one for testing the hypothesis H_0: log(OR)=0. The new normalized effect size is termed `gamma prime' in the spirit of D', a normalized measure of genetic linkage disequilibrium, which ranges from -1 to 1 for a pair of genetic loci. The normalization constant for γ' is based on the maximum range of the standardized effect size, for which we establish a peculiar connection to the Laplace Limit Constant. Furthermore, while standardized effects are of little value on their own, we propose a powerful application, in which standardized effects are employed as an intermediate step in an approximate, yet accurate posterior inference for raw effect size measures, such as log(OR) and γ'.
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