Interval estimation of the median effective dose for a logistic dose-response curve

In 1986, Williams showed how, assuming a logistic dose-response curve, one can construct a confidence interval for the median effective dose from the asymptotic likelihood ratio test. He gave reasons for preferring this likelihood ratio interval to the established interval calculated by applying Fieller's theorem to the maximum-likelihood estimates. Here, we assess the impact a applying a Bartlett adjustment to the likelihood ratio statistic and introduce the score test as an alternative approach for constructing a confidence interval for the median effective dose.