  Predictive or treatment selection biomarkers are usually evaluated in a
subgroup or regression analysis with focus on the treatment-by-marker
interaction. Under a potential outcome framework (Huang, Gilbert and Janes
[Biometrics 68 (2012) 687-696]), a predictive biomarker is considered a
predictor for a desirable treatment benefit (defined by comparing potential
outcomes for different treatments) and evaluated using familiar concepts in
prediction and classification. However, the desired treatment benefit is
unobservable because each patient can receive only one treatment in a typical
study. Huang et al. overcome this problem by assuming monotonicity of potential
outcomes, with one treatment dominating the other in all patients. Motivated by
an HIV example that appears to violate the monotonicity assumption, we propose
a different approach based on covariates and random effects for evaluating
predictive biomarkers under the potential outcome framework. Under the proposed
approach, the parameters of interest can be identified by assuming conditional
independence of potential outcomes given observed covariates, and a sensitivity
analysis can be performed by incorporating an unobserved random effect that
accounts for any residual dependence. Application of this approach to the
motivating example shows that baseline viral load and CD4 cell count are both
useful as predictive biomarkers for choosing antiretroviral drugs for
treatment-naive patients.
