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has been cited by the following article:

• TITLE: Causal Measures for Prognostic and Predictive Biomarkers

  AUTHORS: Yasutaka Chiba

  KEYWORDS: Causal Inference, Interaction, Potential Outcome, Response Type

  JOURNAL NAME: Open Journal of Statistics, Vol.8 No.2, April 2, 2018

  ABSTRACT: Researchers conducting randomized clinical trials with two treatment groups sometimes wish to determine whether biomarkers are predictive and/or prognostic. They can use regression models with interaction terms to assess the role of the biomarker of interest. However, although the interaction term is undoubtedly a suitable measure for prediction, the optimal way to measure prognosis is less clear. In this article, we define causal measures that can be used for prognosis and prediction based on biomarkers. The causal measure for prognosis is defined as the average of two differences in status between biomarker-positive and -negative subjects under treatment and control conditions. The causal measure for prediction is defined as the difference between the causal effect of the treatment for biomarker-positive and biomarker-negative subjects. We also explain the relationship between the proposed measures and the regression parameters. The causal measure for prognosis corresponds to the terms for the biomarker in a regression model, where the values of the dummy variables representing the explanatory variables are -1/2 or 1/2. The causal measure for prediction is simply the causal effect of the interaction term in a regression model. In addition, for a binary outcome, we express the causal measures in terms of four response types: always-responder, complier, non-complier, and never-responder. The causal measure for prognosis can be expressed as a function of always- and never-responders, and the causal measure for prediction as a function of compliers and non-compliers. This enables us to demonstrate that the proposed measures are plausible in the case of a binary outcome. Our causal measures should be used to assess whether a biomarker is prognostic and/or predictive.