Monte Carlo theoretical trials of methods for assessing statistical significance for differences between adjusted odds ratios

Odds are generally defined as the number of successes divided by the number of failures in a given number of trials. An odds ratio is the ratio of one odds divided by another. Odds ratios can be adjusted to reflect associations with the outcome independently of the influence of associations with other variables. These are adjusted odds ratios. There are several well known methods for comparing odds ratios and testing for statistically significant differences between them. Analogous methods for adjusted odds ratios are not well known or well documented. One method for comparing adjusted odds ratios is explained by Hosmer and Lemeshow (Applied logistic regression, 2000). This method is used for the odds ratios for two variables from the same data set. The purpose of this analysis was to apply this method to a different situation: comparing odds ratios for the same variable from two different data sets. Monte Carlo trials were used to assess the performance of the method and these indicated the method performed well.