A Robust Two-Stage Multiple Comparison Procedure with Application to a Random Drug Screen

SUMMARY A high-volume random drug screen is used to detect drugs that are effective in reducing atherogenic low density lipoproteins. A two-stage analysis, consisting of an overall F-test along with a multiple comparison procedure to detect differences between treatments and a placebo, seemed appropriate. Due to observations with heavy right tails and more than occasional outliers in the left tail, this analysis based on least squares estimates had insufficient power. As a solution to this problem we present a similar analysis based on the class of robust R-estimates. In general, it was more powerful than the least squares analysis. Furthermore, by a prudent choice of rank score functions, this robust analysis can take advantage of the underlying skewed error structure. Its validity and power are verified in a Monte Carlo study. Atherosclerosis is a leading cause of death in the United States. The search continues for an effective agent to treat this condition. Rather than searching for drugs that reduce serum total cholesterol, the random drug screen discussed in this paper attempts to find agents effective in reducing atherogenic low density lipoproteins. The screen uses the normocholesterolemic male SEA (Susceptible to Experimental Atherosclerosis) Japanese quail as the animal model; see Chapman, Stafford, and Day (1976) for further details on the use of this animal for such studies. Prior to drug testing the birds were randomly allocated to 10-15 groups of 10 quails each. They were housed individually in ten-cage units and fed a commercial diet for 5 days. The drugs to be tested were dissolved or dispersed in ethanol and mixed with the diet. Control groups received a diet mixed with ethanol alone. After 1 week on the diets each bird was bled from the right jugular vein and serum samples were obtained. The response of interest was the amount of beta cholesterol obtained from these birds. From a statistical point of view each application of the screen results in a one-way design. A two-stage procedure seems to be the appropriate analysis. This would include an overall