Controlling error rates using prior information and marginal totals to select tumor sites

Carlin and Louis (1985) propose a selection procedure designed to control the problems of multiplicity associated with P-values reported from carcinogen bioassays. Instead of searching the data for statistically significant tumor site/type combinations, the procedure uses site/type specific prior information and conditioning statistics to select sites and types with potentially significant P-values. Any single P-value selected by this method retains its usual meaning, and the size of the test procedure is controlled. We apply the Carlin and Louis procedure to a random sample of bioassays using male and female mice and rats from the National Cancer Institute's data base. From these data we estimate priors for lifetime incidence and dose effect. Then, we compare the performance of the selection procedure to use of Bonferroni adjusted and unad- justed minimum observed P-values. Estimated priors for the occurrence of any malignancy show that overall prevalence in controls is about 25%, and that generally there is a positive association between dose and malignancy. Mice are far more sensitive than rats, with male rats the least sensitive. The association between dose and survival to terminal sacrifice shows a negative association with dose, so control rodents tend to live longer than others, suggesting that proper analysis should adjust for time until tumor. For all tumor sites, the prior standard deviation on the dose effect is high, allowing the bioassay to contribute important information on determining carcinogenicity. The liver, mammary gland, spleen, and skin show at least a moderate positive dose effect, while lymphosarcomas show a con- sistently negative association between dose and lifetime tumor incidence. Our investigation indicates that the conditional selection approach has a rejection rate for the 5% level test competitive with unadjusted minimum P-values, and generally greater than that for adjusted P-values. Certain sites are picked quite frequently. Generally these sites have high a priori power, but the conditional power frequently does change the a priori indications. Plots of the empirical cumulative distribution functions for the P-values selected by the various rules show that the conditional selection approach produces a distribution that is between that for unad- justed and the Bonferroni adjusted minimum observed P-values. Theoretical development sup- ports these observations.