Discrete Trend Testing Versus Quantile Regression

Abstract

Current clinical trials often involve more than two treatments or treatment modalities, e.g., dose-response and dose-finding trials, studies comparing multiple drugs from one class with different potencies, or different formulas from one drug with various bio-availabilities and other pharmacokinetic properties. In such situations small differences in efficacies are to be expected, and we need, particularly, sensitive tests. A standard approach to the analysis of such data is multiple groups analysis of variance (Anova) and multiple groups chi-square tests, but a more sensitive, although, so far, little used, approach may be a trend-analysis. A trend means an association between the order of treatment and the magnitude of response. With discrete data linear regression is impossible, but a chi-square test for trends can be performed. As an example, in a 106 patient parallel-groups study the effects of three incremental dosages of an antihypertensive drug were assessed. It has approximately the same chi-square value, as the Pearson chi-square, but it has only 1 degree of freedom, and, therefore, it reaches statistical significance with a p-value of 0.050. There is, thus, a significant incremental trend of responding with incremental dosages at p = 0.050. Better statistics can be obtained with the help of quantile regression, and, in addition, quantile regressions tend to give a better view of the relationships between predictor and outcome variables. In the example of this chapter quantile analysis not only better precision, but also better insight into the relationship between the predictor and outcome variable was obtained with p-values of 0.0001 rather than 0.050.

1 Supplementary Electronic Material (S)

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