Comorbidity scores (such as Charlson and Elixhauser) are widely used to adjust for the patients’ comorbidities in observational studies. They’re usually based on regressing the outcome on several, often dozens of comorbidities on a large historical cohort and then publishing the coefficients in some form.
I think many aspects can be questioned about using such scores, but now lets focus on one single issue: if the components of the score are available individually in our study (i.e. we have the dummy variables indicating the presence of each comorbidity), should we still use the score as a covariate or add all the components instead?
My intuition was that it is almost surely better to add the components individually (this means finer control, much-much more importantly, the weights will pertain to our concrete dataset, and not borrowed from a cohort form another country, at another time, with other patients…). The only drawback is of course that it is less efficient as we’ll have more parameters that are to be estimated, which is clearly important for small sample sizes. (Which, according to my understanding, is specifically the reason why these scores were developed at all!)
But I now have a database with tens of thousands of patients, so I thought that in this case there is absolutely no reason why I should use the score instead of the components.
However, I recently came across this paper: Steven R. Austin, Yu-Ning Wong, Robert G. Uzzo, J. Robert Beck, and Brian L. Egleston. Why summary comorbidity measures such as the Charlson Comorbidity Index and Elixhauser score work. Med Care. 2015 Sep; 53(9): e65–e72. doi: 10.1097/MLR.0b013e318297429c.
They claim that they’ve demonstrated “…the utility of the summary comorbidity measures as substitutes for use of the individual comorbidity variables”, and they even present a mathematical proof for this.
But I simply don’t understand them. What they prove ( E[ Y ∣ X , b( X ) ]= E[ Y ∣ b( X ) ], where b( X ) is the comorbidity score ) is of course true, but is totally irrelevant: it says that adding the variables individually in addition to the score is not better, but no one wants to add them in addition, we are talking about adding them instead of the score!!
(Their derivation also seems to assume that the coefficients obtained from the historical cohort are miraculously the same as what we would get for the particular sample we have.)
Nevertheless, it is published in a peer-reviewed journal, I have found no obvious reply or errata, so I was thinking that I might overlook something after all…