Preface to First Edition - lib

74 CONDITIONAL INFERENCE4.3.3 Gastrointestinal DamageHere we are interested in the comparison of two groups of patients, where onegroup received a placebo and the other one Misoprostol. In the trials shownhere, the response variable is measured on an ordered scale – see Table 4.2.Data from four clinical studies are available and thus the observations arenaturally grouped together. From the data.frame Lanza we can construct athree-way table as follows:R> data("Lanza", package = "HSAUR2")R> xtabs(~ treatment + classification + study, data = Lanza), , study = Iclassificationtreatment 1 2 3 4 5Misoprostol 21 2 4 2 0Placebo 2 2 4 9 13, , study = IIclassificationtreatment 1 2 3 4 5Misoprostol 20 4 6 0 0Placebo 8 4 9 4 5, , study = IIIclassificationtreatment 1 2 3 4 5Misoprostol 20 4 3 1 2Placebo 0 2 5 5 17, , study = IVclassificationtreatment 1 2 3 4 5Misoprostol 1 4 5 0 0Placebo 0 0 0 4 6We will first analyse each study separately and then show how one caninvestigate the effect of Misoprostol for all four studies simultaneously. Becausethe response is ordered, we take this information into account by assigning ascore to each level of the response. Since the classifications are defined by thenumber of haemorrhages or erosions, the midpoint of the interval for each levelis a reasonable choice, i.e., 0, 1, 6, 17 and 30 – compare those scores to thedefinitions given in Table 4.2. The corresponding linear-by-linear associationtests extending the general Cochran-Mantel-Haenszel statistics (see Agresti,2002, for further details) are implemented in package coin.© 2010 by Taylor and Francis Group, LLC