One model, several results: the paradox of the Hosmer-Lemeshow goodness-of-fit test for the logistic regression model.
BACKGROUND
The Hosmer-Lemeshow test, used extensively to assess the fit of the logistic regression model, is performed by several statistical packages. Recent studies have shown some problems in the use of this test when ties are present. These problems were attributed merely to the test implementation.


METHODS
We analysed the order of the observations as an alternative explanation of the problem of ties. Using a data-set of 1393 intensive care unit (ICU) patients we performed the Hosmer-Lemeshow test with all possible subjects dispositions.


RESULTS
We obtained about one million different P values, ranging from 0.01 to 0.95.


CONCLUSIONS
It is already known that when the Hosmer-Lemeshow goodness-of-fit test is performed with a number of covariate patterns lower than the number of subjects, its result may be inaccurate. We showed that the extent of this problem could be relevant under particular conditions. We also suggest a strategy for estimating the extent of the problem and subsequent interpretation.
Bertolini
G
G
Clinical Epidemiology Unit, Institute of Research Pharmacology Mario Negri, Ranica, Bergamo, Italy.
D'Amico
R
R
Nardi
D
D
Tinazzi
A
A
Apolone
G
G
D017052:Hospital Mortality; D006801:Humans; D007362:Intensive Care Units; D007558:Italy; D016015:Logistic Models; D011237:Predictive Value of Tests; D012720:Severity of Illness Index; D013223:Statistics as Topic / Q000379:methods