Cohpasisons of improved bonferroni and sidak/slepian bounds with applications to normal markov processes

The recent literature contains theorems improving on both the standard Bonferroni inequality (Hoover (1990)) and the Sidak/Slepian inequalities (Glaz and Johnson (1984)), The application of these improved theorems to upper bounds for non coverage of simultaneous confidence intervals on multivariate normal variables is explored. The improved Bonferroni upper bounds always hold, while improved Sidak/Slepian bounds only apply to special cases. It is shown that improved Sidak/Slepian bounds will always hold for Normal Markov Processes, a commonly occuring and easily identifiable class of multivariate normal variables. The improved Sidak/Slepian upper bound, if it applies, is proven to be superior to the computationally equivalent improved Bonferroni bound. This improvement, however, is not great when both methods are used to determine upper bounds for Type I error in the range of .01 to .10.     

Improving the Regulation of Carcinogens by Expediting Cancer Potency Estimation1

The statutory language of the Safe Drinking Water and Toxic Enforcement Act of 1986 (Proposition 65; California Health and Safety Code 25249.5 et seq.) encourages rapid adoption of “no significant risk levels” (NSRLs), intakes associated with estimated cancer risks of no more than 1 in 100,000. Derivation of an NSRL for a carcinogen listed under Proposition 65 requires the development of a cancer potency value. This paper discusses the methodology for the derivation of cancer potencies using an expedited procedure, and provides potency estimates for a number of agents listed as carcinogens under Proposition 65. To derive expedited potency values, default risk assessment methods are applied to data sets selected from an extensive tabulation of animal cancer bioassays according to criteria used by regulatory agencies. A subset of these expedited values is compared to values previously developed by regulatory agencies using conventional quantitative risk assessment and found to be in good agreement. Specific regulatory activities which could be facilitated by adopting similar expedited procedures are identified.