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Abstract:
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Logistic regression is widely used to evaluate the association between risk factors and a binary outcome. Alternative families, such as the additive Gompertz or Guerrero-Johnson models, have been proposed in various scenarios due to their asymmetry: disease risk may initially increase rapidly and be followed by a longer period where the rate of growth slowly decreases. Suppose the outcome and an additive function of the risk factors are indeed related through an asymmetric function, but we model the relationship using a logistic function. We illustrate that higher-order terms, such as pairwise interactions and quadratic terms, may be required in a logistic regression model to obtain a good fit to the data. Importantly, as significant higher-order terms may be a manifestation of model misspecification, these terms should be cautiously interpreted; a more pragmatic approach is to develop contrasts of disease risk coming from a good fitting model. We illustrate these concepts in 2 cohort studies of early death for late-stage colorectal and pancreatic cancer cases, and 2 case-control studies of NAT2 acetylation and smoking in advanced colorectal adenoma and bladder cancer.
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