Using the Bernoulli trial approaches for detecting ordered alternatives

Abstract

BackgroundDiagnostic problems in clinical trials are sometimes ordinal. For example, colon tumor staging was performed according to the TNM classification. However, clinical data are limited by markedly small sample sizes in some stage.MethodsWe propose a distribution-free test for detecting ordered alternatives in a completely randomized design. The new statistic is based on summing all correctly (ascending) ordered samples.ResultsThe exact mean and variance of the null distribution are derived and it is shown that this distribution is asymptotically normal. Furthermore, we show using Monte Carlo simulation that the proposed test is a significant improvement over the Terpstra-Magel test. That is, power is decreased where the investigator falsely assumes an a priori ordering relationship.ConclusionsWe conclude that these tests frequently detect an ordered trend when, in fact, one does not exist. However, the new test can reduce the error rate, at least not to the extent in which the Jonckheere-Terpstra test does.

A New Nonparametric Test for Testing Equality of Locations Against Umbrella Alternatives

“…The JT test was first proposed by Terpstra [1] and Jonckheere [2] to test the null hypothesis of equality of location parameters against an ordered alternative hypothesis. Later, Chacko [3], Puri [4], May and Konkin [5], Odeh [6], Cuzick [7], Hettmansperger and Norton [8], Beier and Buning [9], Neuhäuser, et al [10], Buning and Kossler [11], Terpstra and Magel [12], Chang and Yen [13], Terpstra, et al [14], Chang, et al [15], Shan, et al [16] and Gaur [17] developed alternative tests for ordered alternative hypothesis.…”

A Semi-Parametric Test for Umbrella Ordering of Binary Response Probabilities at Unknown Peak

“…Later, the tests by Ferdhiana, Terpstra, and Magel 10 and Terpstra, Chang, and Magel 11 replace indicator kernel of the TM test statistic by Spearman's rank correlation coefficient and Kendall's tau correlation coefficient, respectively. Chang et al 12 , based on the idea of k-tuplet method of the TM test, provide a test, in which the kernel under each k-tuplet comparison is computed on the basis of Bernoulli trial approach. In our setting, for example, the TM test statistic for H 1 ( H 2 ) becomes equal to the count of (0, 0, 1) and (0,…”