TESTS FOR QUALITATIVE TREATMENT-BY-CENTER INTERACTION USING A PUSHBACK PROCEDURE

In multicentre clinical trials using a common protocol, the centres ar e usually regarded as being a fixed factor, thus allowing any treatmen t-by-centre interaction to be omitted from the error term for the effe ct of treatment. However, we feel it necessary to use the treatment-by -centre interaction as the error term if there is substantial evidence that the interaction with centres is qualitative instead of quantitat ive. To make allowance for the estimated uncertainties of the centre m eans, we propose choosing a reference value (for example, the median o f the ordered array of centre means) and converting the individual cen tre results into standardized deviations from the reference value. The deviations are then reordered, and the results 'pushed back' by amoun ts appropriate for the corresponding order statistics in a sample from the relevant distribution. The pushed-back standardized deviations ar e then restored to the original scale. The appearance of opposite sign s among the destandardized values for the various centres is then take n as 'substantial evidence' of qualitative interaction. Procedures are presented using, in any combination: (i) Gaussian, or Student's t-dis tribution; (ii) order-statistic medians or outward 90 per cent points of the corresponding order statistic distributions; (iii) pooling or g rouping and pooling the internally estimated standard deviations of th e centre means. The use of the least conservative combination - Studen t's t, outward 90 per cent points, grouping and pooling - is recommend ed.