Inference on covariate effect types for treatment effectiveness in a randomized trial with a binary outcome

Abstract

Background/aims Some randomized clinical trials seek to establish covariate effect types that indicate whether a covariate is predictive and/or prognostic, in addition to endpoint evaluation. Here, for a case with a binary outcome, we propose that the covariate effect type should be assessed in terms of four types of potential responses: activated- (always-), inert- (never-), causative-, and preventive-responder. Methods We introduce a new concept of covariate effect types differing from the commonly used “prediction” and “prognosis.” We summarize the covariate effect types by inspecting the proportions of subjects in each response type in two subgroups of a covariate, and indicate whether the fractions are augmented, depleted, or neutral as one changes the level of the covariate. Although these proportions cannot generally be identified, we can derive the posterior distributions of the proportions by applying a recently developed Bayesian method. On the basis of the distributions, we would say that the covariate is “augmented-causative” if the difference between the proportions of causative-responders (who would respond if they received the treatment but would not if they did not) in two subgroups is positive, rather than that it is predictive. Similarly, we would say that the covariate is “neutral-activated” if the difference in the proportion of activated-responders (who would respond regardless of their randomized treatment assignment) is close to zero, rather than saying that the covariate is not prognostic. We further describe the relationship between our approach and standard subgroup analysis. Results We applied our approach to data from a randomized clinical trial comparing nivolumab and docetaxel for subjects with advanced nonsquamous non-small-cell lung cancer; we assessed the covariate effect type of PD-L1 status, where PD-L1 is a ligand of the programmed death 1 (PD-1) receptor expressed by activated T cells. When the endpoint was the overall response rate, the posterior distributions for the differences between the proportions of subjects in response types in the PD-L1-positive and negative subgroups yielded an expected-a-posteriori estimate of 0.243 (95% credible interval (CI): 0.094, 0.374) for causative-responders and 0.014 (95% CI: −0.087, 0.125) for activated-responders. Thus, PD-L1 status was augmented-causative for nivolumab effectiveness, to an extent of 24.3%, and was neutral-activated. Conclusion Our approach characterizes the covariate effect types in terms of the response types, and to what extent. In a randomized clinical trial with a binary outcome, our approach is a potentially valuable addition to standard subgroup or regression analysis.