### Article

## Modelling continuous variables with a spike at zero – on issues of a fractional polynomial based procedure

### Search Medline for

### Authors

Published: | September 10, 2008 |
---|

### Outline

### 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.