Applying StatXact® 9 New Methods

1. Tests for Two Ordered Correlated Multinomials

StatXact 9 example - Wilcoxon Rank Sum, Normal Scores, Savage Scores and Permutation tests with general scores for correlated data.

The data is gathered on two multinomial populations. For each population the response categories are ordered. Each population can have multiple clusters but no cluster is shared by both of the populations. We adopt the exponential family model in Heagerty and Zeger (1996) and conditional analysis suggested by Corcoran et.al.(2001) and make the following assumptions:

1. Exchangeability between observations within cluster

2. Three way and higher association parameters are assumed to be zero

3. Assume cluster independence

Wilcoxon Rank Sum test

We illustrate the use of the Wilcoxon Rank Sum test for two ordered correlated multinomial distributions by considering partial data from Miller and Landis (1991). The data comes from a randomized study which compares an investigative drug to a placebo in relieving the symptoms pain and spasms.

The investigators treated and evaluated patients on three levels of response: worse or no change, slight improvement, and more improvement or cured which are coded as 0,1 and 2 respectively. Investigators are treated as clusters, placebo will be represented as 0 and drug as 1.

The test is run on the data with the following output generated:

StatXact® gives the summary of the test statistic as well as the observed test statistic. One-sided left tailed exact p-value is 0.1793 indicating that at 5% level of significance the null hypothesis of no association will be accepted.

StatXact also provides exact 2*1-sided p-value which is 0.3586 for right tailed alternative in this example. Exact P-value for two- sided alternative is also provided which is 0.3595. StatXact builds the exact distribution of the test statistic. The probability that the test statistic value is equal to the observed value is called the point probability which in this example is 0.01194.

2. Exact Designs added to Power and Sample Size menu

Non-inferiority, Superiority and Equivalence tests for ratio of two binomial proportions have been added in this version.

To illustrate the exact design for non-inferiority for ratio of two binomial populations, consider data by Chan (1998) involving childhood nephroblastoma. The standard treatment is nephrectomy followed by post-operative radiotherapy. The experimental treatment is pre-operative chemotherapy to reduce the tumor mass, then nephrectomy.

Suppose we’re interested in computing power for the exact non-inferiority design for ratio of proportions. Upon entering the values in the power and sample size dialog box, clicking ‘Compute Power’ gives the output:

he exact power is computed as 99.73%.
You will also see maximum attained α is 0.0247.

References

Chan ISF (1998). Exact tests of equivalence and efficacy with a non-zero lower bound for comparative studies. Statistics in Medicine 17:1403-1413.

Corcoran C, Ryan L, Senchaudhuri P, Mehta C, Patel N, Molenberghs G. (2001). An exact trend test for correlated data. Biometrics 57:941-948.

Heagerty PJ, Zeger SL (1996). Marginal regression models for clustered ordinal measurements. Journal of the American Statistical Association 91(435):1024-1036.

Krall JM, Uthoff VA, Harley JB. (1975). A step-up procedure for selecting variables associated with survival data. Biometrics 31: 49-57.