Quantifying epidemiologic risk factors using non-parametric regression: model selection remains the greatest challenge.
Logistic regression is widely used to estimate relative risks (odds ratios) from case-control studies, but when the study exposure is continuous, standard parametric models may not accurately characterize the exposure-response curve. Semi-parametric generalized linear models provide a useful extension. In these models, the exposure of interest is modelled flexibly using a regression spline or a smoothing spline, while other variables are modelled using conventional methods. When coupled with a model-selection procedure based on minimizing a cross-validation score, this approach provides a non-parametric, objective, and reproducible method to characterize the exposure-response curve by one or several models with a favourable bias-variance trade-off. We applied this approach to case-control data to estimate the dose-response relationship between alcohol consumption and risk of oral cancer among African Americans. We did not find a uniquely 'best' model, but results using linear, cubic, and smoothing splines were consistent: there does not appear to be a risk-free threshold for alcohol consumption vis-à-vis the development of oral cancer. This finding was not apparent using a standard step-function model. In our analysis, the cross-validation curve had a global minimum and also a local minimum. In general, the phenomenon of multiple local minima makes it more difficult to interpret the results, and may present a computational roadblock to non-parametric generalized additive models of multiple continuous exposures. Nonetheless, the semi-parametric approach appears to be a practical advance.
Rosenberg
Philip S
PS
National Cancer Institute, Division of Cancer Epidemiology and Genetics, Biostatistics Branch, 6120 Executive Boulevard, EPS 7006, Rockville, MD 20852, USA. philip_rosenberg@nih.gov
Katki
Hormuzd
H
Swanson
Christine A
CA
Brown
Linda M
LM
Wacholder
Sholom
S
Hoover
Robert N
RN
D001741:Black or African American / Q000706:statistics & numerical data*; D000428:Alcohol Drinking / Q000009:adverse effects / Q000453:epidemiology* / Q000208:ethnology; D016022:Case-Control Studies; D004305:Dose-Response Relationship, Drug; D006801:Humans; D015233:Models, Statistical; D009062:Mouth Neoplasms / Q000453:epidemiology* / Q000208:ethnology; D012044:Regression Analysis; D018570:Risk Assessment / Q000379:methods* / Q000706:statistics & numerical data; D012307:Risk Factors; D018709:Statistics, Nonparametric; D014481:United States / Q000453:epidemiology