Saddlepoint approach to inference for response probabilities under the logistic response model

This paper studies lower confidence limits of response probabilities based on sensitivity testing data set. The saddlepoint approximation to a conditional distribution is developed. Based on it we give a modified algorithm to find approximate confidence limits for the parameter of interest. A simulation study shows that the saddlepoint approximation with proper corrections gives better coverage probability than the direct saddlepoint approximation and the asymptotic normality approximation. Finally, we apply the proposed approximation to a real data set.