Prognostic and Predictive Values and Statistical Interactions in the Era of Targeted Treatment

The current era of targeted treatment has accelerated the interest in studying gene-treatment, gene-gene, and gene-environment interactions using statistical models in the health sciences. Interactions are incorporated into models as product terms of risk factors. The statistical significance of interactions is traditionally examined using a likelihood ratio test (LRT). Epidemiological and clinical studies also evaluate interactions in order to understand the prognostic and predictive values of genetic factors. However, it is not clear how different types and magnitudes of interaction effects are related to prognostic and predictive values. The contribution of interaction to prognostic values can be examined via improvements in the area under the receiver operating characteristic curve due to the inclusion of interaction terms in the model (AUC). We develop a resampling based approach to test the significance of this improvement and show that it is equivalent to LRT. Predictive values provide insights into whether carriers of genetic factors benefit from specific treatment or preventive interventions relative to noncarriers, under some definition of treatment benefit. However, there is no unique definition of the term treatment benefit. We show that AUC and relative excess risk due to interaction (RERI) measure predictive values under two specific definitions of treatment benefit. We investigate the properties of LRT, AUC, and RERI using simulations. We illustrate these approaches using published melanoma data to understand the benefits of possible intervention on sun exposure in relation to the MC1R gene. The goal is to evaluate possible interventions on sun exposure in relation to MC1R.