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Do five different chemotherapy methods differ significantly in treatment response?
A small pilot study was performed with five chemotherapy regimens: Cytoxan (CTX) alone, Cyclohexyl-chloreoethyl nitrosourea (CCNU) alone, Methotrexate (MTX) alone, CTX and MTX together, and CTX, CCNU, and MTX together. Tumor regression was measured on a three-point scale: no response, partial response, and complete response. The results are displayed below:
|
No. of Patients |
|
Chemo
|
No Response |
Partial Response |
Complete Response |
| CTX |
2 |
0 |
0 |
| CCNU |
1 |
1 |
0 |
| MTX |
3 |
0 |
0 |
| CTX+CCNU |
2 |
2 |
0 |
| CTX+CCNU+MTX |
1 |
1 |
4 |
Assume for the moment that there is no ranking to the types of chemotherapy or to the types of response -- each type is different from the other but no ordering is involved. Under this assumption, we would run the Pearson's Chi Squared test for unordered RxC contingency tables. The asymptotic p-value is .0815, while the exact p-value is .0691. Neither shows significance at the .05 level, so according to this test, there is no difference between the chemotherapies in terms of the type of responses elicited.
However, that analysis was performed on the assumption that both rows and columns were unordered. Clearly, the responses are ordered, with no response being the worst outcome, and complete response being the best outcome. We re-run the analysis, using the Kruskal-Wallis test for singly-ordered RxC contingency tables. The resulting asymptotic p-value, .0695, is still not significant, but the exact p-value, .0390, is significant. This indicates that exact test has used the additional information of ordering in the response and has become more sensitive in detecting the overall difference among the different types of therapies.
We later learn that the ordering of the five therapies in the rows coincide with their ranking on their efficacy potential- CTX being at the lowest level and CTX+CCNU+MTX being at the highest level. With this information, the above RxC table becomes a doubly-ordered one, and the Jonckheere-Terpstra test is an appropriate test to apply here. The results of this test show a further decrease in p-values, to .0031 (asymptotic) and .0018 (exact).
It is important to note that how the exact test becomes quickly more sensitive in detecting differences by utilizing the ordering information in the data. With StatXact®, you can easily perform the right exact tests for the type of ordering that best describes your table, increasing your ability to discern the actual relationships in your data.
|
Unordered |
Singly-ordered |
Doubly-ordered |
| Asymptotic |
0.0815 |
0.0695 |
0.0031 |
| Exact |
0.0691 |
0.0390 |
0.0018 |
