At the end of the lecture students should be able to:
- Identify the advantages and problems of using repeated measures in research
- Describe simple approaches to analysing repeated measures
Altman, D.G., 1991. Practical statistics for medical research, pp. 326-336. Chapman & Hall, London.
How to deal with repeated measures by two way analysis of variance.
Altman, D.G., 1991. Practical statistics for medical research, pp. 426-433. Chapman & Hall, London.
An outline of the problem of serial measurements.
Bland J.M. & D.G. Altman, 1994. Correlation, regression, and repeated data, BMJ 308: 896.
A brief description of the problem. See also discussion on letters page, BMJ 308: 1510.
Matthews J.N.S., D.G. Altman, M.J. Campbell & D. Royston, 1990. Analysis of serial measurements in medical research, BMJ 300: 230-235.
Description of a method to deal with the problem of analysing serial measurements.
In many clinical situations we measure the same quantity on a single subject many times for example:
- Measuring pH in the mouth at several points
- Measuring the amount of plaque on each tooth of each patient
This introduces an extra source of variation into the study: there is now within as well as between subject variability.
Repeated measures can be a good idea because:
- They can improve precision
- They can provide a measure of consistency within and between observers
Repeated measures are bad idea because:
- They are more difficult to analyse
One way of avoiding the problems associated with repeated measures is to choose a summary measure. The particular summary measure depends on the question we want to answer. Some possible measures are (from Matthews et al.):
|Question to be answered||Summary measure|
|Is the overall value of the outcome variable the same in different groups?||Overall mean (for equal time intervals). Area under curve (for unequal time intervals)|
|Is the maximum (minimum) response different?||Maximum (minimum) value|
|Is the time to maximum (minimum) response different?||Time to maximum (minimum) value|
Other techniques to deal with repeated measurements
Most simple statistical techniques can be adapted to allow for repeated measurements. When reading results we might encounter the phrase 'the variances have been adjusted to allow for clustering' or something similar; this is an indication that repeated measures have been included in the analysis correctly.
Another option for dealing with repeated measurements is the explicit use of modelling techniques. We can use statistical methods such as ANOVA (ANalysis Of VAriance) or regression to look at several factors at once
Reading the literature
A key thing to look out for when looking through the published literature to check if repeated measures have been dealt with properly is the quoted sample size. This is not necessarily the same as the number of measurements. For example if 290 teeth from 29 patients are measured then the sample size will, in most cases, be 29 not 290. If a figure higher than 29 is quoted it must be justified.
Serial measurements are a special case of repeated measurements which involve a series of measurements on subjects carried out at a sequence of time points.
We get better results if we use a summary measure of some sort. The summary measure we use depends on the questions we wish to answer; we should decide on the summary measure at the design stage NOT at the analysis stage.
A study compared the plaque scores (on a scale of 0 to 10) in patients who had recently been taught how to floss correctly and those who had not. Plaque scores were taken at the start of the study and then at intervals over the next three weeks. In the diagram below the mean scores are shown along with bars indicating +/-1·96 standard errors.
We should not think that we have shown that flossing has an effect from week 2 onwards.
Alternative possibilities for analysing the results in this situation include:
- The time taken to reach a sub-clinical level plaque score
- The final plaque score
- The area under the curve (can be seen as representative of the cumulative effect of intervention)
- The lowest plaque score recorded
More than one summary measure could be looked at to give a more rounded picture