Because the evaluation of rodent carcinogenicity studies involves performing a statistical analysis at each tumor site encountered it is important to understand the extent to which this multiplicity affects the false positive rate. It is equally important to apply methods of accounting for this multiplicity in the analysis.
In this paper we discuss one such method which involves calculating the overall significance level associated with P1, the most extreme isolated trend P-value observed among the tumor sites encountered. The method constructs the distribution of trend scores simultaneously for each tumor site using a multiresponse randomization procedure. As such, it recognizes the discrete nature of the data and incorporates inherent dependencis that may exist between the tumor sites.
For small studies it is possible to perform a complete rerandomization and compute an exact adjusted trend P-value. However, for moderate or large studies the need exists for approximations based on efficient resampling plans. We report one such approximation proposed by Dr. John Tukey which involves correcting the exact Bonferroni upper bound. Also, we show that the independence assumption used in methods proposed by Mantel (1980) and Mantel et al. (1982) seems to be a reasonable approximation for the study discussed in the present report. This result needs to be supported further using additional studies.
[1]
N Mantel,et al.
Assessing laboratory evidence for neoplastic activity.
,
1980,
Biometrics.
[2]
Marcello Pagano,et al.
An Algorithm for Finding the Exact Significance Levels of r × c Contingency Tables
,
1981
.
[3]
J. Tukey,et al.
Tumorigenicity Assays, Including Use of the Jackknife
,
1982
.
[4]
J W Tukey,et al.
Testing the statistical certainty of a response to increasing doses of a drug.
,
1985,
Biometrics.