Weighted p-value adjustments for animal carcinogenicity trend test

A typical animal carcinogenicity experiment routinely analyzes approximately 10-30 tumor sites. Comparisons of tumor responses between dosed and control groups and dose-related trend tests are often evaluated for each individual tumor site/type separately. p-Value adjustment approaches have been proposed for controlling the overall Type I error rate or familywise error rate (FWE). However, these adjustments often result in reducing the power to detect a dose effect. This paper proposes using weighted adjustments by assuming that each tumor can be classified as either class A or class B based on prior considerations. The tumors in class A, which are considered as more critical endpoints, are given less adjustment. Two weighted methods of adjustments are presented, the weighted p adjustment and weighted alpha adjustment. A Monte Carlo simulation shows that both weighted adjustments control the FWE well. Furthermore, the power increases if a treatment-dependent tumor is analyzed as in class A tumors and the power decreases if it is analyzed as in class B tumors. A data set from a National Toxicology Program (NTP) 2-year animal carcinogenicity experiment with 13 tumor types/sites observed in male mice was analyzed using the proposed methods. The modified poly-3 test was used to test for increased carcinogenicity since it has been adopted by the NTP as a standard test for a dose-related trend. The unweighted adjustment analysis concluded that there was no statistically significant dose-related trend. Using the Food and Drug Administration classification scheme for the weighted adjustment analyses, two rare tumors (with background rates of 1% or less) were analyzed as class A tumors and 11 common tumors (with background rates higher than 1%) as class B. Both weighted analyses showed a significant dose-related trend for one rare tumor.     

On weighted Hochberg procedures

We consider different ways of constructing weighted Hochberg-typestep-up multiple test procedures including closed proceduresbased on weighted Simes tests and their conservative step-upshort-cuts, and step-up counterparts of two weighted Holm procedures.It is shown that the step-up counterparts have some seriouspitfalls such as lack of familywise error rate control and lackof monotonicity in rejection decisions in terms of p-values.Therefore an exact closed procedure appears to be the best alternative,its only drawback being lack of simple stepwise structure. Aconservative step-up short-cut to the closed procedure may beused instead, but with accompanying loss of power. Simulationsare used to study the familywise error rate and power propertiesof the competing procedures for independent and correlated p-values.Although many of the results of this paper are negative, theyare useful in highlighting the need for caution when procedureswith similar pitfalls may be used.     

Accounting for variability in the use of permutation testing to detect quantitative trait loci

Locating quantitative trait loci (QTL), or genomic regions associated with known molecular markers, is of increasing interest in a wide variety of applications ranging from human genetics to agricultural genetics. The hope of locating QTL (or genes) affecting a quantitative trait is that it will lead to characterization and possible manipulations of these genes. However, the complexity of both statistical and genetic issues surrounding the location of these regions calls into question the asymptotic statistical results supplying the distribution of the test statistics employed. Coupled with the power of current-day computing, permutation theory was reintroduced for the purpose of estimating the distribution of any test statistic used to test for the location of QTL. Permutation techniques have offered an attractive alternative to significance measures based on asymptotic theory. The ideas of permutation testing are extended in this application to include confidence intervals for the thresholds and p-values estimated in permutation testing procedures. The confidence intervals developed account for the Monte Carlo error associated with practical applications of permutation testing and lead to an effective method of determining an efficient permutation sample size.