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Keywords:

  • Classification accuracy;
  • Constrained maximum likelihood;
  • Monotone treatment effect;
  • Potential outcomes;
  • Sensitivity analysis;
  • Treatment-selection marker

Summary Treatment-selection markers are biological molecules or patient characteristics associated with one’s response to treatment. They can be used to predict treatment effects for individual subjects and subsequently help deliver treatment to those most likely to benefit from it. Statistical tools are needed to evaluate a marker’s capacity to help with treatment selection. The commonly adopted criterion for a good treatment-selection marker has been the interaction between marker and treatment. While a strong interaction is important, it is, however, not sufficient for good marker performance. In this article, we develop novel measures for assessing a continuous treatment-selection marker, based on a potential outcomes framework. Under a set of assumptions, we derive the optimal decision rule based on the marker to classify individuals according to treatment benefit, and characterize the marker’s performance using the corresponding classification accuracy as well as the overall distribution of the classifier. We develop a constrained maximum-likelihood method for estimation and testing in a randomized trial setting. Simulation studies are conducted to demonstrate the performance of our methods. Finally, we illustrate the methods using an HIV vaccine trial where we explore the value of the level of preexisting immunity to adenovirus serotype 5 for predicting a vaccine-induced increase in the risk of HIV acquisition.