Estimation of cumulative odds ratios

PURPOSE: Standard estimation of ordered odds ratios requires the constraint that the etiologic effects of exposure are homogenous across thresholds of the ordered response. We present a method to relax this often-unrealistic constraint. METHODS: The kernel of the proposed method is the expansion of observed data into "person-thresholds." Using standard statistical software, for each subject we create a separate record for each response threshold and then apply binary logistic regression to estimate generalized cumulative odds ratios for one or more exposures. RESULTS: Two examples demonstrate that the proposed method provides increased flexibility in assessing the etiologic effects of exposures. A Monte Carlo simulation study supports the proposed approach by suggesting the estimated cumulative odds ratios are unbiased with proper confidence interval coverage attained by use of generalized estimating equations. CONCLUSION: The proposed method provides simple estimates of ordered odds ratios that allow the etiologic effects of exposure to vary across levels of the ordered response.