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Use of transformed data in clinical trials
Author(s) -
Powell R. N.,
Highfield J. E.,
Murkell J. F.
Publication year - 1978
Publication title -
journal of clinical periodontology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.456
H-Index - 151
eISSN - 1600-051X
pISSN - 0303-6979
DOI - 10.1111/j.1600-051x.1978.tb01912.x
Subject(s) - statistics , analysis of variance , mathematics , null hypothesis , variance (accounting) , econometrics , ordinal data , variable (mathematics) , repeated measures design , one way analysis of variance , medicine , mathematical analysis , accounting , business
The conduct of clinical trials requires that satisfactory indices are available for the objective measurement of clinical signs and symptoms. While no ideal index exists, it is nevertheless possible to use existing indices, despite their ordinal nature, in such a manner that more sophisticated and complex null hypotheses may be tested. In particular the Analysis of Variance (ANOVA) permits significance tests of interactions between two or more variables. In the case of dental trials, tested differences between groups using one‐way statistical analyses imply that such differences arise from the effects of one variable only. If two variables are manipulated together, their effects are confounded. The capacity of ANOVA to attribute data variability to main effects and interactions is its great power. To enable plaque and gingival inflammation scores to be analysed in this manner it is suggested that a derived frequency score, the G‐ratio, should be employed. Where there are four possible scores (0,1,2,3), there are three possible G‐ratios – G(0), G(O,1) or G(0,2). The G‐ratio which gives an overall mean closest to 0.50 is chosen for any particular investigation in order to avoid skew data distribution. In order to meet ANOVA assumptions, the G‐ratio should be formed on groups of not less than 10 surfaces. Since the distribution of any measure based on a proportion is unlikely to be normal, the data should also be transformed so that X'= are sin x which is to say that the transformed score is equal to the angle whose sine is the square root of the raw score. A clinical study of the effects of lectures and individual instruction in oral hygiene was subjected to analysis by a five‐way ANOVA. Location and jaw effects were markedly qualified by interactions. Such considerations point to the need for care in the design of trials where subject variability, repeated measurements, trial manipulations and interactions occur.