Stepwise procedures for the identification of minimum effective dose with unknown variances

Hsu and Berger (J. Amer. Statist. Assoc. 50 (1999) 468) proposed a stepwise confidence interval procedure for identifying the minimum effective dose in dose-response studies under homoscedasticity. In practice, homogeneity of variance is often in doubt. In this paper, we extend Hsu and Berger's stepwise confidence interval procedure to the case of heteroscedasticity (i.e., inequality of variances across dosages). In addition, we show that the new procedure can properly control the family-wise error rate. We illustrate our procedure with a real example. Finally, we investigate the performance of our procedure and a step-down test procedure based on Welch's approximate t-test via a simulation study. Our procedure is shown, empirically, to perform similar to Welch's procedure.