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Excerpt
We have read the article by Champion et al. [1] with great interest, and we have some methodologic questions about the Hosmer-Lemeshow goodness-of-fit-statistic used in the paper.
We were not able to find in the text which of the different Hosmer-Lemeshow (H-L) statistics (e.g., statistic H, or C or any other [2,3]) the authors used in their article. In the following editorial comment by Cayten and Hannan, it is stated that the method used by Champion et al. subdivides cases into ten intervals of risk of length 0.1. This description seems consistent with the Hosmer-Lemeshow H statistic [2]: we would like to know if our hypothesis is right, and why they chose this statistic rather than another one. [4]
The second question is about the number of degrees of freedom (df) used in the comparison of H-L statistic with2 distribution.
The authors applied the ASCOT and TRISS models to a new set of data, and, in the abstract, they said that these data were not used in the development of those norms. In Table 7, the authors stated that the H-L statistic has an approximate2 distribution with 8 degrees of freedom. [1] If the fit of the model is being evaluated on the developmental data set, and 10 risk classes are used (as for H and C statistics), the result of the H-L statistic is compared with the2 distribution with a number of df equal to the number of risk classes minus 2 (10 - 2 = 8 df). [2,3] But Hosmer and Lemeshow [3] affirmed that, when an external validation is performed, i.e., when the model calibration is evaluated on a new data set (as in this case, in our opinion), the number of df is equal to the number of risk intervals considered (i.e., df = 10). [3,5] The use of 8 df seems, therefore, to contradict the statements of Hosmer and Lemeshow.
When 10 degrees of freedom are used, the limit for rejection of the hypothesis that the model fits, moves from values of H-L >15.5 to values >18.3. We are aware that this modification does not alter the general significance of the paper by Champion and co-workers (for instance, the p value of H-L for ASCOT in penetrating injuries changes from 0.009 for df = 8 to 0.026 for df = 10, only); yet, we would like to know the methodologic reasons that induced the authors to use 8 df in their paper.
