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Eur J Cardiothorac Surg 2007;31:1151-1152. doi:10.1016/j.ejcts.2007.03.002
Copyright © 2007, European Association for Cardio-Thoracic Surgery. Published by Elsevier B.V. All rights reserved
Letters to the Editor |
Department of Thoracic Surgery, Royal Brompton Hospital, Sydney Street, London SW3 6NP, United Kingdom
Received 27 January 2007; accepted 1 March 2007.
* Corresponding author. Tel.: +44 207 352 8121. (Email: e.lim{at}rbht.nhs.uk).
Key Words: Risk assessment • Statistics
I have read with interest the paper by Gallivan and colleagues [1] on a graphical method for risk assessment. The authors are to be congratulated for deriving such an interpretable method of evaluation of risk assessment models.
I wonder if the authors might comment on a number of possible limitations and elaborate on differences in opinion with regards to the interpretation of MADCAP. According to the authors, systematic divergence of the two plots highlights discrepancies, but it can be very subjective in deciding how much overlap or deviation implies a good or bad fit.
MADCAP is well derived and intuitive, but because it is a cumulative comparison, it carries ‘memory’. In Fig. 1 of the paper, the predicted and observed plots almost overlap in the first 2500 cases and then deviate from 3000 to 7000, but later on, the plots become parallel between the cases 7000 and 9000. The deviation between the plots in the mid-risk profile section is carried forward to the latter section. Similarly, in the plot of the differences, you can have good predictions at the higher-risk end, but because of the cumulated differences in the mid-risk profile, the discrepancy is carried forward to the latter part of the plot (6% or more risk).
It is possible that a model with good predictions in low- and high-risk profile group can be penalized on the visual plots as the mid-plot divergence separates the two lines due to the cumulative derivation. If in the higher-risk group, the assessed model greatly underestimates risk, then the two plots will converge again, giving the visual impression of a good fit but carrying the opposite meaning!
Therefore, I would consider parallelism (or the lack of) as in Fig. 1 more important than divergence (actual distance apart) in the interpretation of MADCAP. Similarly, in the plot of the mean differences (Fig. 2), I would consider it more important to be horizontal than the actual distance apart. The authors commented that the ‘mortality was greater than predicted amongst low-risk cases (0 and 1%) and perhaps also amongst high-risk patients (>7%)’, but deviations in the low-risk group were minor, and my own interpretation is that both plots indicate that the mortality is predicted well in those two groups but not the mid-risk profile.
References
This article has been cited by other articles:
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  S. Gallivan, M. Utley, D. Pagano, and T. Treasure Reply to Lim: Concerning MADCAP plots Eur. J. Cardiothorac. Surg., June 1, 2007; 31(6): 1152 - 1152. [Full Text] [PDF]
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