Departamento de Epidemiología y Bioestadística Escuela Nacional de Sanidad Instituto de Salud Carlos III Madrid 28029, Spain
Department of Epidemiology and Welch Center for Prevention Epidemiology and Clinical Research Johns Hopkins Medical Institutions Baltimore, MD 212052223
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INTRODUCTION |
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As stated in our paper (2), all inferences presented, such as confidence intervals or tests of hypothesis, were based on the assumption of existence of the change-point. Although we did not explicitly address the problem of testing for this assumption, we recognized, as stated in the Discussion section of our paper, that further research is needed in this area. Ulm (3
) suggested a test procedure based on a quasi one-sided
21 distribution. The justification of this method was supported by a simulation study, but it would be desirable to have a more rigorous theoretical justification. In our opinion, alternative methods to test formally for the existence of change-points are still needed.
With respect to the example of alcohol intake and risk of myocardial infarction, several points need to be clarified. This example illustrates the applicability of two-segmented logistic models to estimate and provide inferences about the location of the change-point and the magnitude of other parameters of effect, when the change-point actually exists. If there is no change-point (i.e., ß2 = 0), the model reduces to a standard logistic regression, and hence, the change-point is not well defined. In such circumstances, the standard asymptotic properties of Wald and likelihood ratio statistics do not hold (8). Finally, we would like to stress that, although several models are used to display the dose-response relation of alcohol with the risk of myocardial infarction, only the quadratic-linear model provides a statistical estimation of the change-point.
We concur with Ulm and Küchenhoff (1) on the importance of careful modeling and interpretation in assessing change-points and, as already discussed in our article (2
), we suggest using nonparametric regression to check the appropriate parameterization of segmented models. Alternative parametric change-point models, which can accommodate many epidemiologic dose-response relations, are also described in the Discussion section of our paper. In conclusion, we believe that the two-segmented logistic regression model provides valuable inference procedures when threshold effects are anticipated and that it deserves wider use in epidemiologic dose-response analyses.
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REFERENCES |
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