Sex, Biomarkers, and Paradoxes
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This chapter will begin with an example of Simpson’s Paradox, which may arise in tables of cross-classified categorical data. An explanation of how the paradox may arise will be given, and a method for using the tabulated data to compute correct statistical estimators that resolve the paradox will be illustrated. A second example will be given in the context of comparing the batting averages of two baseball players, where the paradox cannot be resolved. An example of cross-tabulated data on treatment, biomarker status, and response rates will be given in which there appears to be an interactive treatment–biomarker effect on response rate. This example will be elaborated by also including sex in the cross-classification, which leads to different conclusions about biomarker effects. A discussion of latent variables and causality will be given. Latent effects for numerical valued variables in the context of fitting regression models will be illustrated graphically. The importance of plotting scattergrams of raw data and examining possible covariate–subgroup interactions before fitting regression models will be illustrated. An example will be given of data where a fitted regression model shows that a patient covariate interacts with a between-treatment effect, with the consequence that which treatment is optimal depends on the patient’s covariate value.