A stepwise confidence interval procedure based on an asymmetric loss function with applications to toxicological evaluation

The purpose of toxicological studies is a safety assessment of compounds (e.g. pesticides, pharmaceuticals, industrial chemicals and food additives) at various dose levels. Because a mistaken declaration that a really non-equivalent dose is equivalent could have dangerous consequences, it is important to adopt reliable statistical methods that can properly control the family-wise error rate. We propose a new stepwise confidence interval procedure for toxicological evaluation based on an asymmetric loss function. The new procedure is shown to be reliable in the sense that the corresponding family-wise error rate is well controlled at or below the pre-specified nominal level. Our simulation results show that the new procedure is to be preferred over the classical confidence interval procedure and the stepwise procedure based on Welch's approximation in terms of practical equivalence/safety. The implementation and significance of the new procedure are illustrated with two real data sets: one from a reproductive toxicological study on Nitrofurazone in Swiss CD-1 mice, and the other from a toxicological study on Aconiazide.