Modeling Variables With a Spike at Zero: Examples and Practical Recommendations.

Abstract

In most epidemiologic studies and in clinical research generally, there are variables with a spike at zero, namely variables for which a proportion of individuals have zero exposure (e.g., never smokers) and among those exposed the variable has a continuous distribution. Different options exist for modeling such variables, such as categorization where the nonexposed form the reference group, or ignoring the spike by including the variable in the regression model with or without some transformation or modeling procedures. It has been shown that such situations can be analyzed by adding a binary indicator (exposed/nonexposed) to the regression model, and a method based on fractional polynomials with which to estimate a suitable functional form for the positive portion of the spike-at-zero variable distribution has been developed. In this paper, we compare different approaches using data from 3 case-control studies carried out in Germany: the Mammary Carcinoma Risk Factor Investigation (MARIE), a breast cancer study conducted in 2002-2005 (Flesch-Janys et al., Int J Cancer. 2008;123(4):933-941); the Rhein-Neckar Larynx Study, a study of laryngeal cancer conducted in 1998-2000 (Dietz et al., Int J Cancer. 2004;108(6):907-911); and a lung cancer study conducted in 1988-1993 (Jöckel et al., Int J Epidemiol. 1998;27(4):549-560). Strengths and limitations of different procedures are demonstrated, and some recommendations for practical use are given.