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Department of Anaesthesia Critical Care and Pain Medicine, Royal Infirmary of Edinburgh, Edinburgh, Scotland
To the Editor:
Swaminathan et al. (1) highlighted in their study one of the limitations of dichotomizing tests of cognitive function that is regression to the mean. This is but one of several serious pitfalls of dichotomization that can lead to spurious statistical results, and there can no longer be any justification for its use (2). Cognition is a continuum, and therefore their use of a cognitive index is most appropriate.
However, their use of change scores for cognition also has limitations. First, change scores take no account of baseline value, and patients with high preoperative cognitive scores may tend to decline more than those who have low scores. Thus, change scores are also prone to regression to the mean. Second, a fundamental tenet of statistics is that predictor and outcome variables should be independent of each other. As cognitive change scores are an arithmetical construct that includes preoperative values, they are not independent variables. This limitation is also applicable to the percentage change in creatinine values. A more robust approach to their analysis would have been to examine change variance, as this avoids regression to the mean and is independent of the preoperative scores (3,4).
References
Department of Anesthesiology, Duke University Medical Center, Durham, NC
In Response:
We thank Dr. Alston for pointing out that regression to the mean is an issue of great concern among all researchers who grapple with change over time. It is a subtle, ubiquitous phenomenon and easy to miss. We also agree that a continuous measure of function is a more powerful tool with which to capture change than is a dichotomous measure. We are aware, however, that not all researchers share this perspective, and therefore we chose to present our data in both a dichotomous and continuous fashion. Because patients who have higher initial values are more subject to decline, we control for baseline function in both our dichotomous and our continuous models.
We are always open to better methods for dealing with these issues. In the two references cited in which Dr. Alston is an author, we were struck by the fact that the analytical method was a linear regression model, with the follow-up cognitive (or neurologic) function as the outcome, while adjusting for baseline function. As is easily demonstrated, with respect to the predictors of interest this method is mathematically identical to modeling change scores, adjusting for baseline function. In regard to independence of predictor and outcome variables, we expect Dr. Alston agrees that it makes sense to control for those factors that we know influence outcome, such as baseline function. In either case, the outcomes and predictors in Dr. Alston’s approach and our approach are equally nonindependent. We think that there is great benefit in raising these issues and in continuing the search for the best analysis method, and we appreciate the opportunity to revisit these important discussions.
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