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Eur J Cardiothorac Surg 2006;29:856
© 2006 Elsevier Science NL
Letter to the Editor |
a National Centre of Epidemiology, Surveillance and Health Promotion, Istituto Superiore di Sanità, Via Giano della Bella, 34, I-00161 Rome, Italy
b Department of Epidemiology – ASL RME, Rome, Italy
Received 6 February 2006; accepted 7 February 2006.
* Corresponding author. Tel.: +39 06 49904234; fax: +39 06 49904230. (Email: fulvias{at}iss.it).
Key Words: Coronary artery bypass graft • Outcome • Risk-adjustment • Mortality
We have already addressed the issues of recruitment, accuracy of information, and volume-outcome association in another letter that will be published in a forthcoming issue of this Journal. Now, we will discuss the remaining topics treated by Biondi-Zoccai et al. concerning the Italian CABG Outcome Study [1].
The rate of missing data in the studied population was 3.5%. Only for three centres we found significant differences in mortality between records with and without missing data. For these centres, in the website http://bpac.iss.it, we reported the estimates obtained assuming, for each patient, the two extreme hypotheses: alternatively presence or absence of all the missing comorbidities. The same analysis on all the other Centres proved the absence of this potential bias.
All criticisms risen by Biondi-Zoccai regarding model validation suit prognostic models, developed to predict the outcome of future patients. Actually, we pursued an explanatory objective: identification and control of confounders of the association between mortality and exposure (hospitals). For example, age is an important predictor of mortality. If age is homogenously distributed among hospitals, it can be excluded from risk adjustment because it is not a confounder. This will reduce calibration and discrimination capacity of the model but the estimated effects measure for hospitals will not change. Moreover, we deal with multiple comparisons. Theoretically a specific risk adjustment model should be developed for each comparison, because real confounders actually vary between hospitals. For example, among selected 14 hospitals with more than 700 CABG, age acts as a real confounder only in four comparisons. For parsimony and comparability of analysis we included in the risk adjustment model only factors acting as confounders in at least one comparison. As a consequence our model tends to be redundant (i.e. including variables which are not actual confounders in some comparisons). However, the use of factors that are not confounders will not introduce bias on the estimated effects measure, but will only reduce their precision.
Overfitting represents a problem for predictive/prognostic purposes. Overfitting a model (including variables in the model with truly zero regression coefficients in the population) does not introduce bias when population regression coefficients are estimated. We must be careful, however, to avoid harmful collinearity. This occurs when there is a strong correlation between one or more ‘confounders’ and the ‘main exposure’. In this case, the inclusion of the ‘confounder’ into the model will cause the main exposure estimate to be unstable and its SE to become much larger. Anyway, collinearity between confounders causes loss of precision, not loss of validity of the effects measure in comparisons. This is not our case: no strong correlation between selected factors or their combinations was found.
Finally, the analysis of possible interactions is relevant. As previously described, although based on clinical grounds, we are not interested in defining the best prognostic model using all interactions between factors if these interactions do not involve the exposure.
In observational studies, propensity adjustment and risk adjustment are the two ways to identify and control confounding. In our case, they yield the same results.
References
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