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The Cox model is one of the most used statistical models in medical research. It models the hazard rate of an event and its association with covariates through hazard ratios. In the simple setting without competing risks nor time-dependent covariates, there exists a one-to-one mathematical connection between the hazard rate and the risk of experiencing the event within any given time period (e.g., 5 years). This makes it possible to conclude that a covariate associated with a hazard ratio above one is associated with a higher risk of event. Although it is becoming widely known that this connection is lost in the presence of competing risks, it seems that fewer users of the Cox model are aware that this connection is also lost when using time-dependent covariates. In other words, it seems still widely unknown that, when using a time-dependent Cox model, a hazard ratio estimated above one does not necessarily mean that there is a higher risk. Hence, this note aims to clarify why this is not the case with a detailed pedagogical example.

ObjectiveGastrointestinal bleeding (GIB) risk in relation to concomitant treatment with non-vitamin K oral anticoagulants (NOAC) and oral glucocorticoids is insufficiently explored. We aimed to investigate the short-term risk following coexposure.MethodsThis is a register-based, nationwide Danish study including patients with atrial fibrillation on NOACs during 2012–2018. Patients were defined as exposed to oral glucocorticoids if they claimed a prescription within 60 days prior to GIB. We investigated the associations between GIB and oral glucocorticoid exposure, reporting HRs via a nested case–control design and absolute risk via a cohort design. Matching terms were age, sex, calendar year, follow-up time and NOAC agent.Results98 376 patients on NOACs (median age: 75 years (IQR: 68–82), 44% female) were included, and 16% redeemed at least one oral glucocorticoid prescription within 3 years. HRs of GIB were increased comparing exposed with non-exposed patients (<20 mg daily dose, HR 1.54 (95% CI 1.29 to 1.84); ≥20 mg daily dose, HR 2.19 (95% CI 1.81 to 2.65)). 60-day standardised absolute risk of GIB following first claimed oral glucocorticoid prescription increased compared with non-exposed: 60-day absolute risk: 0.71% (95% CI 0.58% to 0.85%) vs 0.38% (95% CI 0.32% to 0.43%). The relative risk was elevated as well: risk ratio of 1.89 (95% CI 1.43 to 2.36).ConclusionsConcomitant treatment with NOACs and oral glucocorticoids was associated with a short-term rate and risk increase of GIB compared with patients only on NOACs. This could have implications for clinical management, necessitating closer monitoring or other risk mitigation strategies during episodes of cotreatment with oral glucocorticoids.

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