When studying treatments for psychiatric diseases in a placebo-controlled trial, we may consider use of the sequential parallel comparison design (SPCD) to decrease the number of patients needed through the reduction of the high placebo response rate. Using the conditional arguments to remove nuisance parameters, we derive the conditional maximum likelihood estimator (CMLE) for the odds ratio (OR) of responses under the SPCD. We further derive three asymptotic interval estimators and an exact interval estimator for the OR of responses. We employ Monte Carlo simulation to evaluate the performance of these interval estimators in a variety of situations. We find that asymptotic interval estimators and the exact interval estimator can all perform well. We use the double-blind, placebo-controlled study to assess the efficacy of a low dose of aripiprazole adjunctive to antidepressant therapy for treating patients with major depressive disorder (MDD) to illustrate the use of estimators developed here.