Simulation study: comparison of methods for competing risks in pragmatic trials

What is being explored by the simulation study?

In survival analysis, the censoring of patients is a very important issue that has been dealt with in many different ways through different methodologies. For example, the Cox proportional hazard method, possibly the most commonly used method in survival analysis, assumes that the censoring is independent across all patients. This is not always the case as often this censoring can tell us something about the experience of the patient in question. In particular, when a patient suffers from an event which is not our primary outcome (for example, death from a different condition which is not under analysis).

General methods of survival analysis assess the time to a certain event and disregard events of any other type. By accounting for the information gathered from these competing events, a more robust analysis can be performed. This area is often neglected but will increasingly be needed with the emergence of more pragmatic trials which often have a more patients likely to have competeing events, such as those that are elderly, have multiple morbidities or who are likely to have higher rates of comorbidities.

What was examined in the simulation study?

The aim of this study was to analyse two different methodologies of competing risk analysis using simulation studies. The study used populations which can have both the ‘event-of-interest’ and a second competing event. Under each methodology, a treatment effect (this can be the effect of any kind of treatment on the time to event) was estimated on the event-of-interest and the standardised bias (distance from actual treatment effect divided by standard error) was analysed under different parameters. This provided an estimate of how close the estimate generated by each methodology is to the true treatment effect. The two methodologies are described here:

  • Cause Specific Hazard (CSH) – patients who do not have the event-of-interest are considered to be censored. Analysis continues using the Cox proportional hazards model and all covariates as normal. The treatment effect is taken to be the coefficient of the treatment in the output.
  • Proportional Subdistribution Hazard (PSH) – a cumulative incidence function (CIF) is first generated for each of the competing risks (event-of-interest and competing event). The CIF is similar to a Kaplan-Meier plot, however it takes the competing risks into account by keeping patients with a competing event in the risk set rather than deleting them as in K-M. The CIF, G, then provides a time-dependent weight, W, for each patient:
    where Ti is the end date (minimum of event time or censored time), δ is the event type (0 for censored, 1 for event-of-interest and 2 for competing event). Analysis then continues using a method similar to Cox proportional hazards model, except that the weight is time dependent, whereas under the usual Cox model it is fixed.

What were the findings and conclusions?

  • The simulations are yet to be completed. Preliminary results were presented to GetReal members in September 2016 to positive feedback.

Key contributor

Michael Barrowman, University of Manchester