Double seminar in biostatistics: Causal conclusions based on Cox regression analysis
Speakers: Morten Valberg, OCBE and Torben Martinussen, University of Copenhagen
Causal conclusions based on Cox regression analysis
14:30-14:55: Potential causal consequences of observed proportional hazards.
Speaker: Morten Valberg, OCBE, Oslo University Hospital
The hazard ratio (HR) is by far the most frequently used effect measure in applied time-to-event analyses. However, the causal interpretation of the HR is not necessarily simple, even in the context of randomized controlled trials (RCTs). Even if randomization ensures treatment groups that are balanced for all observed and unobserved factors at baseline, these groups would become increasingly unbalanced as time passes. The reason is that if one treatment is effective, then it will keep individuals from having the event of interest for a longer time period than if these same individuals were not given the effective treatment. Hence, more vulnerable, or frail, individuals will be in the at-risk population in the group receiving the effective treatment than in the group receiving a less effective treatment, at any time point after the first event have occurred in the study population. The hazard rate by definition conditions on being event-free up to each time point. Thus, the groups will no longer be balanced after the first event has occurred. Recently, such selection effects have received some attention, and have been used to explain decreasing HRs in RCTs. However, the same type of selection occurs also when the observed HR is constant, i.e. when all assumptions of Cox’ proportional hazards model are satisfied. Taking a frailty modelling point of view, we will discuss some potential causal implications of observed proportional hazards, also in the presence of competing risks.
14:55-15:30: Subtleties in the interpretation of hazard ratios.
Speaker: Torben Martinussen, Section of Biostatistics, University of Copenhagen, Denmark.
The hazard ratio is one of the most commonly reported measures of
treatment effect in randomised trials, yet the source of much misinterpretation. This point
was made clear by Hernán (2010) in a commentary, which emphasised that the hazard ratio
contrasts populations of treated and untreated individuals who survived a given
period of time, populations that will typically fail to be comparable - even in a
randomised trial - as a result of different pressures or intensities acting on both populations.
The commentary has been very influential, but also a source of surprise and confusion. In
this talk, I aim to provide more insight into the subtle interpretation of hazard ratios
and differences, by investigating in particular what can be learned about a treatment effect
from the hazard ratio becoming 1 after a certain period of time. I will further define a
hazard ratio that has a causal interpretation and study its relationship to the Cox hazard