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.