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Tests for qualitative treatment‐by‐centre interaction using a ‘pushback’ procedure
Author(s) -
Ciminera Joseph L.,
Heyse Joseph F.,
Nguyen Ha H.,
Tukey John W.
Publication year - 1993
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780121104
Subject(s) - pooling , statistic , statistics , standard deviation , allowance (engineering) , mathematics , term (time) , gaussian , normal distribution , sample (material) , normality , standard error , econometrics , medicine , computer science , operations management , physics , quantum mechanics , artificial intelligence , economics , chemistry , chromatography
In multicentre clinical trials using a common protocol, the centres are usually regarded as being a fixed factor, thus allowing any treatment‐by‐centre interaction to be omitted from the error term for the effect 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 quantitative. To make allowance for the estimated uncertainties of the centre means, we propose choosing a reference value (for example, the median of the ordered array of centre means) and converting the individual centre results into standardized deviations from the reference value. The deviations are then reordered, and the results ‘pushed back’ by amounts appropriate for the corresponding order statistics in a sample from the relevant distribution. The pushed‐back standardized deviations are then restored to the original scale. The appearance of opposite signs among the destandardized values for the various centres is then taken as ‘substantial evidence’ of qualitative interaction. Procedures are presented using, in any combination: (i) Gaussian, or Student's t ‐distribution; (ii) order‐statistic medians or outward 90 per cent points of the corresponding order statistic distributions; (iii) pooling or grouping and pooling the internally estimated standard deviations of the centre means. The use of the least conservative combination — Student's t , outward 90 per cent points, grouping and pooling — is recommended.