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

Our plain-English summary of Modeling Variables With a Spike at Zero: Examples and Practical Recommendations, by E. Lorenz, C. Jenkner, W. Sauerbrei, et al (American Journal of Epidemiology, 2017).

The study

• Authors: E. Lorenz, C. Jenkner, W. Sauerbrei, H. Becher
• Journal: American Journal of Epidemiology
• Published: 2017;185(8):650-660
• Cited by: 24 articles, as counted by NIH iCite
• Read it: PubMed · Publisher

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.

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In plain English

This was a statistics methods paper, not a new study of asbestos. The authors compared five ways of analyzing an exposure that many study participants never had (a "spike at zero"). They reanalyzed three earlier German case-control studies, including one of lung cancer and lifetime hours of asbestos exposure (1,004 cases and 1,004 controls, 1988 to 1993). In the asbestos data, 65.44% of cases and 71.81% of controls reported no asbestos exposure. In the original grouped analysis, the lowest asbestos exposure group showed no increased risk, while the middle and high groups showed similar, significantly increased risks. Both curve-fitting methods tested selected a model in which the log of the odds ratio rose in a straight line with lifetime asbestos hours. More complex curves were not significantly better. The authors said the data varied a lot at random and that the study may have been too small to detect more complex curves. The authors concluded that alternatives to grouping exposure would have been a better choice in these studies. The article does not name asbestos fiber types.

We wrote this plain-English summary from the full article with the help of AI, and a second AI model checked each sentence against the article. It is not the authors' wording; the abstract and the article are their own account.

What the study did and found

• Design: Methodological (statistical) paper comparing 5 regression methods by reanalyzing data from 3 previously published case-control studies
• Who was studied: Asbestos example: a hospital-based case-control study of 1,004 lung cancer cases and 1,004 population controls in 2 areas of Germany, 1988 to 1993. Other examples: the MARIE breast cancer study (3,464 cases, 6,657 controls, 2002 to 2005) and the Rhein-Neckar Larynx Study (257 cases, 769 controls, 1998 to 2000)
• Exposure: Lifetime number of hours of asbestos exposure (fiber type not specified). The other examples used duration of hormone therapy use and lifetime hours of occupational cement dust exposure
• Main results:
  • In the lung cancer study, 65.44% of cases and 71.81% of controls reported zero asbestos exposure
  • In the original categorized analysis of asbestos and lung cancer, the low-exposure group showed no increased risk. The middle and high exposure categories showed similar, significantly increased risks
  • For asbestos and lung cancer, both the standard fractional polynomial method and the FP-spike method selected the linear default model. Here 'linear' means linear in the log odds ratio, not in the odds ratio itself
  • The linear method assumes the log odds ratio is linear in exposure, an assumption the authors note may be invalid
  • For asbestos, more complex curve shapes were not significantly better than the linear model
  • In the FP-spike procedure for asbestos, the first-step test did not reach statistical significance (P = 0.06)
  • In the breast cancer example, both fractional polynomial methods selected a log transformation of hormone therapy duration, with similar fit
  • In the laryngeal cancer example, the FP-spike procedure selected a model with only an exposed/unexposed indicator. The standard method selected a first-degree fractional polynomial
• The authors' conclusion: The authors concluded that, in these 3 studies, alternative approaches to categorizing the exposure would have been a better choice
• Limitations the authors state:
  • The three data sets do not cover all possible practical data situations
  • In the asbestos lung cancer data, estimates from finer exposure categories were irregular, indicating large random variation
  • Nonlinear curves for asbestos might have been selected with a larger sample size
  • In the laryngeal cancer study, the small number of exposed people limited the power to detect complex dose-response shapes
  • Methods with an exposed/unexposed indicator give a risk curve that may not start at 1 near zero dose, which is unwanted for low-dose extrapolation
  • General recommendations are difficult because they depend on the goal of the analysis

Topics

Medical terms in this study, explained in our Lexicon: Carcinoma, Laryngeal Cancer, Lung Cancer.

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