gms | German Medical Science

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].

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.

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.

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.