Each week, we will be publishing layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.
Xing, L., Zhang, X., Burstyn, I. and Gustafson, P. (2021), On logistic Box–Cox regression for flexibly estimating the shape and strength of exposure‐disease relationships. Can J Statistics. https://doi.org/10.1002/cjs.11587
There are numerous examples of environmental exposures that adversely affect health in a dose-dependent manner. However, mechanistic considerations inform us that the rate of the risk increase is typically not the same at all intensities of exposure and can even be flat beyond certain thresholds. This changing pattern is challenging to estimate using the standard statistical models that assume a constant rate of change for the log odds-ratio with no threshold. Applied researchers often resort to an intuitive remedy, which includes a transformation of exposures to achieve an apparent steady rate of change in risk relative to the transformed exposure metric, followed by fitting the standard model. The enforced step on transformation is very rough, which may cause unacknowledged loss of information. As an alternative, we propose a logistic Box-cox regression for dichotomous outcomes (e.g. disease vs. not diseased). It can better capture the instantaneous risk and provides a precise estimate of the shape of the association between exposure and risk of disease. As an extension of logistic regression, it has a wide application in machine learning, medicine, and social sciences. For instance, it can model the dose-response curve in drug efficacy and toxicity, predict the probability of failure of an engineering process, and forecast the market up or down in finance.