Artikel
Modelling continuous variables with a spike at zero – on issues of a fractional polynomial based procedure
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Autoren
Veröffentlicht: | 10. September 2008 |
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Gliederung
Text
Introduction
In clinical epidemiology, a frequently occurring problem is to model a dose/response function for a variable X which has value 0 for a proportion of individuals (“spike at zero”), and a quantitative value for the others, e.g. cigarette consumption or an occupational exposure. When the individuals with X = 0 are seen as a distinct sub-population, it may be necessary to model the outcome in the subpopulation explicitly with a dummy variable, and the rest of the distribution as a positive continuous variable using a dose-response relationship [Ref. 1].
Methods
The concept of fractional polynomials [Ref. 2] has been shown to be useful for estimating dose-response relationships for continuous variables. A multivariable procedure (MFP) is available to select variables and to determine the functional relationship in many types of regression models. A modification of the function selection component for variables with a spike at zero was proposed in chap 4 of Royston & Sauerbrei [Ref. 3]. A binary variable indicating zero values of X is added to the model. The procedure considers in two stages whether X has any effect, whether individuals with X = 0 should be considered as a separate subgroup and whether an FP functional relationship for the positive values improves the model fit.
Results
In three examples with substantial differences in the distributions of X, strength of the effects and correlations with other variables, we will discuss in a multivariable context issues concerning the modelling of a continuous variable with a spike at zero. The examples will illustrate that sometimes a binary component will be sufficient for a good model fit, whereas in other cases an FP function, with or without the binary component, is a better model.
Discussion
We propose a new procedure which will often improve modeling of continuous variables with a spike at zero. Adjustment for other important predictors can be done in the usual way.
References
- 1.
- Robertson C, Boyle P, Hsieh CC, Macfarlane GJ, Maisonneuve P. Some statistical considerations in the analysis of case-control studies when the exposure variables are continuous measurements. Epidemiology 1994; 5: 164-70.
- 2.
- Royston P, Altman DG. Regression using fractional polynomials of continuous covariates: parsimonious parametric modeling (with discussion). Applied Statistics 1994; 43 (3): 429-467.
- 3.
- Royston P, Sauerbrei W. Multivariable regression modelling. A pragmatic approach based on fractional polynomials for modelling continuous variables. Wiley; 2008.