Odds ratios for a continuous outcome variable without dichotomizing.

The loss of information from dichotomizing a continuous outcome is well documented in the literature. One advantage of dichotomizing is that it allows estimation of odds ratio parameters through a logistic regression analysis. The objective of this paper is to develop a new estimator of the same odds ratio parameters through regression analysis on the original continuous outcome without the inherent loss of information caused by dichotomizing. Through a mathematical, asymptotic development the relative sample sizes required to attain a specified power when testing the odds ratio parameter are compared for the dichotomizing procedure and the proposed approach. The comparison highlights the substantial sample size savings attained by the proposed approach, particularly for large values of the odds ratio parameter and for small proportions of dichotomized successes or failures. In a Monte Carlo simulation the variances and absolute biases of the two odds ratio estimators and the length of their respective confidence intervals again demonstrate the improvement attained by the proposed approach. In addition, coverage probabilities of the confidence intervals of the proposed approach converge quickly to the nominal levels. The cost savings due to the reduction in required sample size when using this method make it a very attractive study design and analysis tool for medical researchers.