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.