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Life rarely boils down to one single possible event looming on the horizon. In fact, the same principle applies to real-world data. Competing risk analysis is a subfield of statistics (specifically within survival analysis) that focuses on situations where a subject can experience one of multiple, mutually exclusive events, each with its own level of risk.

Let’s uncover what competing risk analysis is and the main methods used to perform it.

Survival Analysis and Competing Risk Analysis

Standard survival analysis focuses on one event, such as a town getting flooded after heavy rain, paying particular attention to the time until that event takes place.

Meanwhile, competing risk analysis comes into play when a subject — such as a town, a patient, etc. — can experience one of several distinct events, but the occurrence of one prevents the others from happening. Take an old building, for example. The event of the building collapsing after an earthquake would automatically prevent another event, such as that same building being burned down by wildfires. These “mutually exclusive” events surrounding a subject are known as competing events.

In probabilistic terms, once one of the competing events occurs, the probability of the others becomes zero.

Competing risk analysis is frequently needed in fields like:

• Medicine: a patient’s death from cancer and death from a heart attack are competing risks.
• Finance: mortgage default and early loan pay-off constitute another example of competing risks.
• Education: a student graduating vs. a student dropping out.

Among the multiple events, one often represents the specific analysis question we attempt to answer. This event is often known as the primary event. For example, in the education scenario, this could be the student’s graduation.

Common Methods and Illustrative Example

Standard risk estimation methods like Kaplan–Meier are not adequate for competing risk analysis, due to their tendency to overestimate risks. More suitable approaches include the cumulative incidence function (CIF), which computes the probability of each type of event while treating the remaining events as competitors linked to the same subject(s). There are also specialized regression approaches, such as Fine–Gray modeling and cause-specific hazards models, with the latter often used to understand the drivers behind a particular event.

Now, let’s illustrate a simple application scenario for competing risk analysis. Suppose a Japanese city has an old quarter with 100 historic wooden buildings, and we track them for 10 years to analyze how many of them collapse due to earthquakes — this will be our primary event of study.

After this period, we find that:

• 70 buildings survived and remained intact.
• 10 buildings collapsed due to an earthquake (primary event).
• 20 buildings were destroyed by wildfires (a competing risk).

Standard survival methods like Kaplan–Meier would overestimate the risk of collapse due to earthquakes by treating the 20 buildings destroyed by wildfire as censored observations. Here’s the dangerous point: these approaches assume that burned-down buildings could still experience earthquake-related collapse at a later time, which is no longer plausible because those buildings are already destroyed.

Note also that a rigorous application of Kaplan–Meier would require time-to-event information, which is beyond the scope of this simplified example. The bottom line is that standard methods yield inflated estimates of the cumulative incidence of the primary event when competing events arise, because they do not account for the truly precluding nature of those events.

In contrast, the CIF method acknowledges that buildings destroyed by wildfire can no longer collapse after an earthquake. Therefore, the observed cumulative incidence of earthquake-related collapse over 10 years is 10%.