Competing Risks Analysis: When More Than One Outcome Matters

What if one of the most common methods in medical research is quietly giving you the wrong answer?

In studies where patients can experience more than one outcome, standard survival analysis methods like Kaplan-Meier can overestimate risk—sometimes by a lot.

In this episode, we break down competing risks analysis, why traditional approaches fail, and how methods like cause-specific hazards and the Fine-Gray model give you the correct answer.

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Transcript

SPEAKER_01 0:00

Imagine a study like in an elderly cohort. Six months in, a patient tragically dies of a heart attack. You'd assume the math just adjusts.

SPEAKER_00 0:09

You would think so. Well, it actually doesn't.

SPEAKER_01 0:11

And that is why today we are taking you on a deep dive into the paper, The Mechanics of Competing Risks in Survival Analysis.

SPEAKER_00 0:20

It's a really fascinating look at how we measure data.

SPEAKER_01 0:23

And our mission here is to uncover why standard medical data is, well, fundamentally flawed sometimes and how to fix it. Okay, let's unpack this.

SPEAKER_00 0:32

So the issue really starts with standard Kaplan minor analysis. It relies heavily on something called non-informative censoring.

SPEAKER_01 0:39

Which is like if a patient just moves away.

SPEAKER_00 0:40

Right.

SPEAKER_01 0:41

Like administrative dropout.

SPEAKER_00 0:42

Exactly. And that is mathematically fine. But a competing risk, like a fatal heart attack, is inherently informative. I mean, it permanently prevents the cancer from ever being the cause of death.

SPEAKER_01 0:53

You obviously can't get cancer if you're already dead.

SPEAKER_00 0:55

The standard analysis sort of pretends that's not the case.

SPEAKER_01 0:58

Yeah, when I was reading through this, I realized standard Kaplan Meyer is basically creating mathematical zombies.

SPEAKER_00 1:04

Oh wow, zombies. That is a great way to put it.

SPEAKER_01 1:08

Because it keeps deceased patients in the risk pool denominator. Like they're just still walking around waiting to get cancer. If you are counting zombie patients, you're wildly overestimating the probability of the actual event.

SPEAKER_00 1:19

Yes, you're estimating incidents in this hypothetical world where people literally cannot die of anything else.

SPEAKER_01 1:26

Which is crazy for elderly populations.

SPEAKER_00 1:29

Completely. The competing mortality is naturally high there. So this overestimation, it just skews every clinical and policy decision built on those numbers.

SPEAKER_01 1:38

Okay, so if traditional Kaplan Meyer creates zombies, how do we find the actual biological rates? Like how do we mathematically strip away that noise?

SPEAKER_00 1:46

Well, that brings us to cause-specific hazards. This is really perfect for etiological research.

SPEAKER_01 1:51

Etiological means like understanding the underlying biological why.

SPEAKER_00 2:06

Got it. By doing that, you get the pure instantaneous rate of that specific event, just among people who haven't experienced any event yet.

SPEAKER_01 2:16

But wait, let me push back on that. If we're just censoring the competing events again to isolate a pure biological rate, aren't we still failing to predict the real world probability of what happens? We're still mathematically pretending the heart attack didn't happen, right?

SPEAKER_00 2:30

Yes, you've hit on the exact limitation of cause-specific hazards. I mean, they're great for finding the biological why, but terrible for predicting a patient's actual future.

SPEAKER_01 2:39

Because the real world has other risks.

SPEAKER_00 2:40

Exactly. So to find out what will actually happen to a patient in the real world, you have to use the cumulative incidence function, or CIF. And alongside that, the fine-gray model.

SPEAKER_01 2:51

Okay, but how does the fine gray model actually solve the zombie problem without just deleting the data?

SPEAKER_00 2:58

So we use something called a sub-distribution hazard.

SPEAKER_01 3:00

Subdistribution hazard? Sounds pretty intense.

SPEAKER_00 3:03

It's really just a way to structure the math. Instead of dropping patients who experience a competing event, the fine gray model actually keeps them in the risk set. It keeps them in the denominator, but it mathematically dilutes their presence over time.

SPEAKER_01 3:16

I see.

SPEAKER_00 3:16

By doing that, it effectively lowers the overall incidence rate, forces the math to reflect reality, which is that fewer people are getting the cancer because they're dying of other causes first.

SPEAKER_01 3:26

Oh wow. That is so interesting. You are holding on to the data, but you're weighting it to reflect reality. What does this all mean? It sounds like we have a golden rule here for you listening. If you want to understand the mechanism, like the why, you use cause-specific hazards.

SPEAKER_00 3:42

Right. And if you want to predict reality for a patient, the what will happen, you use the fine-gray model.

SPEAKER_01 3:47

Perfect. They aren't competing against each other.

SPEAKER_00 3:49

No, not at all. They answer fundamentally different questions. And you know, that's why modern biostatistics recommends reporting both to get the full picture.

SPEAKER_01 3:58

Aaron Powell So for you listening, the big takeaway is to never treat a competing event as if it just didn't happen.

SPEAKER_00 4:03

Aaron Powell Absolutely. And when you are visualizing the data, you should look for stacked CIF plots.

SPEAKER_01 4:09

Aaron Powell Those are the ones that show the probability of each event type physically stacked on top of each other.

SPEAKER_00 4:15

Aaron Powell Exactly. It gives you the actual proportional landscape of what a patient faces. Aaron Powell Which is crucial.

SPEAKER_01 4:21

But you know, it leaves me with one final thought for you to chew on. Well, these models assume a competing risk permanently prevents the primary event. But what happens if a competing risk doesn't kill you, but permanently alters or accelerates your trajectory toward that primary event? How do we mathematically model a cascading risk? Something to think about until next time.