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The Subgroup Mixable Estimation principle makes stratified conditional HR match the marginal HR, and cures an oversight in stratified analysis in computer packages

Presented During: A Principled Approach Using the Subgroup Mixable Estimation for Logic-respecting Causal Estimand, Including Making Stratified Conditional Efficacy Exactly Equal to Marginal Efficacy for Time-to-event Outcome

Jason Hsu Speaker
The Ohio State University

Monday, Aug 4: 10:55 AM - 11:15 AM
Topic-Contributed Paper Session

Music City Center

I will start by deriving simply the connect between Hazard Ratio (HR) and Living Longer Probability (LLP) using Cox's originally Mann-Whitney testing definition of HR, a connection that not only medical officer can understand but also makes all subsequent explanations easier.

Liu et al (2022, Biometrical Journal 64:198–224) showed that mixing HR in subgroups dilutes them if the biomarker has a Prognostic effect, giving the illusion that patients with high and low biomarker values benefit more from the new treatment. Key message of that paper is patients with middling biomarker values may be unfairly deprived of lifesaving new treatments.

Reversing the thought process for HR, separating patients into subgroups by prognostic factors boosts the apparent efficacy of the new treatment in each stratum. In turn, if stratified analysis for ratio efficacy ignores the prognostic effect (as in all the computer packages currently), then a sponsor can game the system by stratifying on as many prognostic factors as possible, to artificially lower HR for the overall population, a danger to public health.

The Subgroup Mixable Estimation (SME) principle takes the prognostic effect into account to properly mixes ratio efficacy in subgroups, removing such danger. In the case of HR, Liu et al (2022, Biometrical Journal 64:246–255) describes how SME mixes by first converting each conditional HR to an LLP, mixes LLPs, then converting the mixed/unconditional LLP to get the marginal HR. Using a real data set, I will show in fact SME mixing makes the conditional HR and marginal HR equal in the population/parameter space, dispelling the notion that they are apples and oranges.

Keywords

Hazard Ratio (HR)

Dilution in mixing due to Prognostic effect

Mann-Whitney testing

Living Longer Probability (LLP)

Subgroup Mixable Estimation (SME) principle

Conditional HR equal Marginal HR