From Logic-Respecting Efficacy Estimands to Logic-Ensuring Analysis Principle for Time-to-Event Endpoint in Randomized Clinical Trials with Subgroups

Abstract

An important goal of precision medicine is to identify biomarkers that are predictive, and tailor the treatment according to the biomarker levels of individual patients. Differentiating prognostic versus predictive biomarkers impacts important decision makings for patients and treating physicians. Using Hazard Ratio (HR) can mistake a purely prognostic biomarker for a predictive one leading to a disheartening possibility of depriving patients of beneficial treatment as demonstrated in the OAK trial. This stems from the illogical issue of HR at population level where marginal HR in the overall population can be larger than those in both subgroups. Instead of trying to circumvent this issue by discouraging comparisons between marginal and conditional HRs, we propose to directly fix it by using alternative logic-respecting efficacy estimands such as ratio of medians, ratio and difference of restricted mean survival times and milestone probabilities. These measures are straightforward, easy to interpret and clinically meaningful. More importantly, they will guarantee agreement between marginal and conditional efficacy and provide cohesive message around efficacy profile of the drug in the presence of subgroups. A step further is the application of Subgroup Mixable Estimation (SME) principle to ensure logical estimates when analyzing real clinical trial data. Detailed guidance is provided for the aforementioned logic-respecting estimands using either parametric, semiparametric or nonparametric approaches. Simultaneous inference can be provided with proper multiplicity adjustment to facilitate joint decision making with user-friendly apps.

KEYWORD:

• Estimand
• Hazard ratio
• Logic-respecting
• Milestone probability
• Ratio of median
• Restricted means survival time
• Subgroup
• Subgroup mixable estimation

Supplementary Materials

The appendices in the Online Supplementary Materials provide additional technical details and case examples for Section 3.

Acknowledgments

This article has been written within the industry working group estimands in oncology, which is both, a European special interest group “Estimands in oncology,” sponsored by PSI and European Federation of Statisticians in the Pharmaceutical Industry (EFSPI) and a scientific working group of the biopharmaceutical section of the American Statistical Association. Details are available on www.oncoestimand.org. We would like to thank two reviewers and the associate editor for their careful review and constructive comments on this article.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.