Measuring differential treatment benefit across marker specific subgroups: The choice of outcome scale.

Clinical and epidemiological studies of anticancer therapies increasingly seek to identify predictive biomarkers to obtain insights into variation in treatment benefit. For time to event endpoints, a predictive biomarker is typically assessed using the interaction between the biomarker and treatment in a proportional hazards model. Interactions are contrasts of summaries of outcomes and depend upon the choice of the outcome scale. In this paper, we investigate interaction contrasts under three scales - the natural logarithm of hazard ratio, the natural logarithm of survival probability, and survival probability at a pre-specified time. We illustrate that we can have a non-zero interaction on survival or logarithm of survival probability scales even when there is no interaction on the logarithm of hazard ratio scale. Since survival probabilities have clinically useful interpretation and are easier to convey to patients than hazard ratios, we recommend evaluating a predictive biomarker using survival probabilities. We provide empirical illustration of the three scales of interaction for evaluating a predictive biomarker using reconstructed data from a published melanoma study.