Applying StatXact® 9 New Methods

FDA Animal Toxicology Data Yields Sky-Scraper Distribution for Stratified Trend Test

The data for this example were provided by the U.S. Food and Drug Administration (FDA). Animals were treated with four dose levels of a carcinogen and then observed (at necropsy) for the presence or absence of a tumor type. The data were stratified by survival time (in weeks) into the four time-intervals 0-50, 51-80, 81-104, and terminal sacrifice. Since there were no tumors found in the first time-interval, this stratum may be excluded from data entry. The data for the remaining three strata are given below:

Stratum 1: 51-80 weeks of survival

	Dose of Carcinogen
Disease Status	None	1 unit	5 units	50 units	Total
Tumor Present	0	0	0	1	1
Tumor Absent	7	10	6	8	31

Stratum 2: 81-104 weeks of survival

	Dose of Carcinogen
Disease Status	None	1 unit	5 units	50 units	Total
Tumor Present	0	1	0	1	2
Tumor Absent	11	9	13	14	47

Stratum 3: Sacrificed at end of 104 weeks

	Dose of Carcinogen
Disease Status	None	1 unit	5 units	50 units	Total
Tumor Present	1	1	1	2	5
Tumor Absent	29	26	28	20	103

Since the scores are unequally spaced, we use the stratified Permutation test with general scores (Breslow and Day, Statistical Methods in Cancer Research, 1980, page 148) to determine if there is a dose-response relationship between the level of carcinogen and the presence of tumors. The test statistic is of the form:

where wj is the jth dose of carcinogen (w1 = 0, w2 = 1, w3 = 5, w4 = 50), and Xij is the number of animals with tumors at the jth dose level in the ith stratum. The p-value results from StatXact are tabulated below:

P-Values	One-Sided	Two-Sided	Double One-Sided
Exact	.0651	.0769	.1302
Asymptotic	.0410	.0820	.0820

StatXact shows that there are large differences between the exact and asymptotic one-sided p-values, and they lead to different conclusions about the significance of the dose-response relationship. They also show that the usual practice of doubling the one-sided p-value is unnecessarily conservative with asymmetric distributions. But the most interesting finding of all is that the distribution of T has multiple towers. A normal approximation would be seriously misleading. This is shown below:

StatXact Example Library

1. New-Born Behavior Level Study: Friedman Rank Aligned Test
2. Histological Data: Test for Correlation in Correlated Categorical Data
3. Teratology Study: Test for trend in Correlated data
4. Neurotoxicity Study: Test of Trend in Multiple Endpoints Correlated Data
5. Meta Analysis with StatXact
6. Does Type of Reward Influence Reaction to Task Disruption?
7. FDA Animal Toxicology Data Yields Sky-Scraper Distribution for Stratified Trend Test
8. Minority Discrimination: An Analysis of Ill-Conditioned Data
9. Leukemia Deaths Among Hiroshima Atomic Bomb Survivors
10. Cochran-Armitage Exact Test of Trend for Imbalanced Data
11. Adverse Reactions in Children Infected with Varicella
12. Comparison of Five Modes of Therapy for the Treatment of Depression
13. Did Entrance Exam for Firefighters Discriminate Against Minorities?
14. StatXact Shows Small Differences in Cardiovascular Outcomes to be Statistically Significant
15. Do Five Different Chemotherapy Methods Differ Significantly in Treatment Response?
16. Do Birds with More Immaculate Plumage Frequent the Best Feeding Sites?
17. How Accurately do Pregnant Women Report Whether They Smoke?
18. Do Older Employees Get Poorer Job Ratings?
19. StatXact & LogXact: Is the New Analgesic More Effective than Aspirin?