Panel Discussion: Do we still need hazard ratios?

Jan Beyersmann (Ulm University), Oliver Kuß (Düsseldorf), Andreas Wienke (Halle)

Do we still need hazard ratios? (I)
Oliver Kuß
German Diabetes Center, Leibniz Institute for Diabetes Research at Heinrich Heine University Düsseldorf, Institute for Biometrics and Epidemiology

It is one of the phenomenons in biostatistics that regression models for continuous, binary, nominal, or ordinal outcomes almost completely rely on parametric modelling, whereas survival or time-to-event outcomes are mainly analyzed by the Proportional Hazards (PH) model of Cox, which is an essentially non-parametric method. The Cox model has become one of the most used statistical models in applied research and the original article from 1972 ranks below the top 100 papers (in terms of citation frequency) across all areas of science.

However, the Cox model and the hazard ratio have also been criticized recently. For example, researchers have been warned to use the magnitude of the HR to describe the magnitude of the relative risk, because the hazard ratio is a ratio of rates, and not one of risks. Hazard ratios, even in randomized trials, have a built-in “selection bias”, because they are conditional measures, conditioning at each time point on the set of observations which is still under risk. Finally, the hazard ratio has been criticized for being non-collapsible. That is, adjusting for a covariate that is associated with the event will in general change the HR, even if this covariate is not associated with the exposure, that is, is no confounder.

In view of these disadvantages it is surprising that parametric survival models are not preferred over the Cox model. These existed long before the Cox model, are easier to comprehend, estimate, and communicate, and, above all, do not have any of the disadvantages mentioned.

Do we still need hazard ratios? (II)
Jan Beyersmann
Ulm University, Germany

The answer to the question whether we need hazard ratios depends to a good deal on the answer to the question what we need hazards for. Censoring plays a key role. Censoring makes survival and event history analysis special. One important consequence is that less customized statistical techniques will be biased when applied to censored data. Another important consequence is that hazards remain identifiable under rather general censoring mechanisms. In this talk, I will demonstrate that there is a Babylonian confusion on „independent censoring“ in the textbook literature, which is a worry in its own right. Event-driven trials in pharmaceutical research or competing risks are two examples where the textbook literature often goes haywire, censoring-wise. It is a small step from this mess to misinterpretations of hazards, a challenge not diminished when the aim is a causal interpretation. Causal reasoning, however, appears to be spearheading the current attack on hazards and their ratios.

In philosophy, causality has pretty much been destroyed by David Hume. This does not imply that statisticians should avoid causal reasoning, but it might suggest some modesty. In fact, statistical causality is mostly about interventions, and a causal survival analysis often aims at statements about the intervention „do(no censoring)“, which, however, is not what identifiability of hazards is about. The current debate about estimands (in time-to-event trials) is an example where these issues are hopelessly mixed up.

The aim of this talk is to mix it up a bit further or, perhaps, even shed some light. Time permitting, I will illustrate matters using g-computation in the form of a causal variant of the Aalen-Johansen-estimator.