Data Briefing

Patient reported outcome measures: how are we feeling today?

BMJ 2012; 344 doi: (Published 11 January 2012)
Cite this as: BMJ 2012;344:d8191

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An example of regression to the mean?

John Appleby's figure, a plot of preoperative score against "Health gain" (postoperative score-preoperative score) shows a tendency for better preoperative health to be associated with smaller health gains. Isn't this an example of regression to the mean [1] and so wouldn't a more preferable way of depicting any association be via a plot of postoperative score against the mean of both the preoperative and postoperative scores?
Perhaps Bland or Altman could comment!
[1] Bland JM, Altman DG. (1994) Some examples of regression towards the mean. 309, 780.
[2] Bland JM, Altman DG. (1986).Comparing methods of measurement: why plotting difference against standard method is misleading. Lancet, 346, 1085-7.

Competing interests: None declared

Karla Hemming, Statistician

University of Birmingham, Edgbaston, Birmingham, B15 2TT

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The author states that "better preoperative health tends to be associated with smaller, not larger, health gains" and refers to Fig 3, which shows a correlation of around r=-0.57 between preoperative health state and health gain. But this correlation is likely to be spurious.

Because 'health gain' was calculated as the difference between post- and preoperative health state (postoperative-preoperative score), Fig 3 effectively shows the correlation between a variable, x, and y-x.

r[x.y-x] is weighted by r[x.y], which is likely to be moderately to strongly positive, being the correlation between pre- and postoperative scores, and r[x.-x], which is by necessity -1.

Hence, any correlation between preoperative score and ‘health gain’ is nearly always negative, and significantly so if measurement error is sizable, as tends to be the case with PROMs data. This should not be interpreted as a differential effect of treatment, but as an artifact resulting from an index of health gain that is itself dependent on preoperative status.

The author is right to warn of statistical pitfalls when analysing PROMs data: indexing ‘health gain’ as the difference between pre- and postoperative scores should perhaps be added to the list.

Competing interests: None declared

Matthew C Hankins, Senior Lecturer in Public Health

University of Southampton, Faculty of Health Sciences

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I agree that part of the pre-op post-op EQ-5D index correlation is likely to be due to some regression to mean. But this is not inevitable. For eg, it is not necessarily the case that patients with poorer health scores pre op will record higher gains post op than ‘healthier’ pre op patients. Poorer health pre op could mean less capacity to benefit due to co-morbidities or other reasons associated with or causing the low pre op score. However, it would have been better to have placed a warning on the figure!

Competing interests: None declared

John L Appleby, Health economist

The King's Fund

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