Notes on Use of the Odds Ratio under the Sequential Parallel Comparison Design with Binary Outcomes

ABSTRACT

When the patient response is dichotomous, the effects due to a treatment and other covariates are often not additive. Thus, the risk difference (RD) may vary between phases in the sequential parallel comparison design (SPCD). The weighted average of RD's over two phases in these cases is not a meaningful summary measure of the treatment effect. Since it is more common to encounter the binary data in which the treatment and other covariates effects are additive on the logit scale, we advocate use of the odds ratio (OR) to measure the treatment effect. Under the homogeneity assumption of OR, we show that the weighted-least-squares method can be easily employed to derive both point and interval estimators for the OR under the SPCD. When the OR varies between phases, we note that Woolf logit interval estimator can be applied to estimate the OR for each phase separately. We apply Monte Carlo simulation to evaluate the performance of these estimators in a variety of situations under the SPCD. We use the placebo-controlled trial employing the SPCD to assess the efficacy of a low dose of aripiprazole in treatment of patients with major depressive disorder to illustrate the use of estimators developed here.

KEYWORDS:

• Binary outcome
• Interval estimator
• Odds ratio
• Point estimation
• Risk difference

Acknowledgements

The author wishes to thank the associate editor and two referees for many valuable comments and suggestions to improve the clarity and contents of this article.