Dear Allstat members,

During RCTs here, we routinely collect patient data at baseline, prior
to treatment, then again at some specified endpoint. Often this data is
ordinal (e.g. Quality of Life data, in which responses to questionnaire
data are often scored 0=no, 1=yes, and then a total score is obtained).
In order to compare the change in scores of patients receiving either
drug therapy or placebo, with parametric data we would subtract the
baseline value from the endpoint value for each patient, giving a
'change score', then compare these change scores between treatment
groups with an independent t-test (or ANCOVA) as appropriate. However,
when analysing ordinal data, it is my understanding that it is not valid
to calculate change scores. Ordinal scales may measure a continuous
underlying construct, but obviously the intervals between values on the
scale are not necessarily consistent, so the 'true' distance between
them might look like this:

[1.........2.3.4.....5..6..7......8.9.10]

On this basis, a patient whose score increases from 1 to 2 may have
shown an absolute increase in the underlying variable of interest (e.g.
quality of life) that is greater than the absolute increase made by a
patient whose score goes up from 2 to 4. However, if one calculates a
change score for each, then the opposite trend will be recorded: the
first patient's change score will be lower than that of the second
patient.

Despite this, I regularly see change scores for ordinal variables in
published papers. What confuses me is that the calculations underlying
the Wilcoxon signed rank test essentially rely on change scores, and I
had assumed this was a suitable test for ordinal data. If I want to see
whether QoL has significantly improved within my placebo group during
'treatment', for example, the Wilcoxon test will subtract the first
measurement from the second, then rank the differences, then add
together the negative and positive ranks to obtain a test statistic. Is
this process not going to be vulnerable to these same problems caused by
the potential difference between the change in score and the absolute
change in the underlying variable? My question really boils down to
this: what is the best way to compare the change in an ordinal scale
between patient groups? Is it valid to calculate change scores and
perform Mann-Whitney U tests on those? If not, is it also not valid
therefore to perform Wilcoxon tests to look for within group
differences?

I would greatly appreciate your advice,

Thanks,

Liz Hensor

 

 

Dr Elizabeth M A Hensor PhD

Data Analyst

Academic Unit of Musculoskeletal and Rehabilitation Medicine

36 Clarendon Road

Leeds 

West Yorkshire

LS2 9NZ

Tel: +44 (0) 113 3434944

Fax: +44 (0) 113 2430366

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