A paper recently came out in NEJM on COVID-19 patients using remdesivir:

https://abs.twimg.com/emoji/v2/... draggable="false" alt="📰" title="Newspaper" aria-label="Emoji: Newspaper"> https://www.nejm.org/doi/full/10.1056/NEJMoa2007016

Bonovas">https://www.nejm.org/doi/full/... & @piov1984 wrote a great critique pointing out that the analysis had a flaw!

https://www.nejm.org/doi/full/10.1056/NEJMc2015312?source=nejmtwitter&medium=organic-social

This">https://www.nejm.org/doi/full/... thread is on *competing risks* & why it is so important! 1/13

First let& #39;s talk about the *question* https://abs.twimg.com/emoji/v2/... draggable="false" alt="⁉️" title="Exclamation question mark" aria-label="Emoji: Exclamation question mark">

I believe the authors are interested in telling us about https://abs.twimg.com/emoji/v2/... draggable="false" alt="✅" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> clinical improvement in this cohort of patients taking remdesivir, in particular they want to estimate the cumulative incidence of clinical improvement by 28 days.

2/13

They define "clinical improvement" as:

https://abs.twimg.com/emoji/v2/... draggable="false" alt="☝️" title="Up pointing index" aria-label="Emoji: Up pointing index"> being discharged alive or
https://abs.twimg.com/emoji/v2/... draggable="false" alt="✌️" title="Victory hand" aria-label="Emoji: Victory hand"> having a decrease of 2 points or more in a 6-level ordinal scale of oxygen support:

https://abs.twimg.com/emoji/v2/... draggable="false" alt="☹️" title="Frowning face" aria-label="Emoji: Frowning face"> ECMO
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🙁" title="Slightly frowning face" aria-label="Emoji: Slightly frowning face">Mechanical ventilation
https://abs.twimg.com/emoji/v2/... draggable="false" alt="😕" title="Confused face" aria-label="Emoji: Confused face"> NIPPV
https://abs.twimg.com/emoji/v2/... draggable="false" alt="😐" title="Neutral face" aria-label="Emoji: Neutral face"> High-flow oxygen
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🙂" title="Slightly smiling face" aria-label="Emoji: Slightly smiling face"> Low-flow oxygen
https://abs.twimg.com/emoji/v2/... draggable="false" alt="😊" title="Smiling face with smiling eyes" aria-label="Emoji: Smiling face with smiling eyes"> Ambient air

3/13

SO we want to quantify the time to this event. To do this, we need to classify each patient as https://abs.twimg.com/emoji/v2/... draggable="false" alt="✅" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> having the event (improving) and record https://abs.twimg.com/emoji/v2/... draggable="false" alt="⏲️" title="Timer clock" aria-label="Emoji: Timer clock"> WHEN it happened, or https://abs.twimg.com/emoji/v2/... draggable="false" alt="🤷‍♀️" title="Woman shrugging" aria-label="Emoji: Woman shrugging"> we will censor them, meaning we didn& #39;t observe the event and record the last time https://abs.twimg.com/emoji/v2/... draggable="false" alt="⏲️" title="Timer clock" aria-label="Emoji: Timer clock"> we saw the patient
4/13

I spent some time trying to recreate the analysis by pulling from their Figure 2, and I wasn’t quite about to do it. So I’ve painstakingly pulled every number from Figure 3A https://abs.twimg.com/emoji/v2/... draggable="false" alt="😅" title="Smiling face with open mouth and cold sweat" aria-label="Emoji: Smiling face with open mouth and cold sweat">. Here& #39;s what I got in case you& #39;d like to follow along in #rstats

https://livefreeordichotomize.com/2020/05/22/survival-model-detective-2/

5/13">https://livefreeordichotomize.com/2020/05/2...

And here is the plot, yielding an estimated cumulative incidence of ~84% at 28 days. (replicating Figure 3A from the paper). Ok, cool what& #39;s the problem? Remember how we classified each patient as https://abs.twimg.com/emoji/v2/... draggable="false" alt="✅" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> having the event (improving) or https://abs.twimg.com/emoji/v2/... draggable="false" alt="🤷‍♀️" title="Woman shrugging" aria-label="Emoji: Woman shrugging"> censoring them? The https://abs.twimg.com/emoji/v2/... draggable="false" alt="🤷‍♀️" title="Woman shrugging" aria-label="Emoji: Woman shrugging"> is crucial here!
6/13

A key assumption is that the censoring is *non-informative* the patient is followed for a certain time, never has the event, & then is no longer followed. Our best guess is we know they didn’t have the event up until the last day we saw them, so we censor them on that day.
7/13

In order for the assumptions to be appropriately met, it must be the case that patients who have been censored are just as likely to have the event as those who are still being followed in the study. Let’s pull up a Figure to see the trajectory of all patients.
8/13

The black squares for 7 patients indicate they died! If someone dies we know that they are not going to improve later. This is not non-informative censoring!! Luckily there is a very straightforward way to deal with this in statistics: competing risks!
9/13

(Side note, I think this plot is very cool, if you& #39;d like to learn how to make it using #rstats, check out this post)

https://livefreeordichotomize.com/2020/05/21/survival-model-detective-1/
10/13">https://livefreeordichotomize.com/2020/05/2...

Ok, competing risks! In a competing risk analysis, we can separate out the the death outcome from the remaining censored outcomes. We can then appropriately estimate the cumulative incidence of improving. I& #39;ve fixed the data to account for the 7 deaths as a *competing risk*
11/13

Now we can plot the outcomes separately. Under this corrected framework, the estimated cumulative incidence of clinical improvement by day 28 is 74%
12/13

Competing risk analyses are so important and come up all the time in medical statistics.

Here are some great resources:

https://abs.twimg.com/emoji/v2/... draggable="false" alt="⭐️" title="Medium star" aria-label="Emoji: Medium star"> @zabormetrics has a great tutorial on doing these in #rstats: #cumulative_incidence_for_competing_risks">https://www.emilyzabor.com/tutorials/survival_analysis_in_r_tutorial.html #cumulative_incidence_for_competing_risks
https://www.emilyzabor.com/tutorials... class="Emoji" style="height:16px;" src=" https://abs.twimg.com/emoji/v2/... draggable="false" alt="⭐️" title="Medium star" aria-label="Emoji: Medium star"> I like quick explainer: https://pubmed.ncbi.nlm.nih.gov/15305188/ 
13/13">https://pubmed.ncbi.nlm.nih.gov/15305188/...

A Note on Competing Risks in Survival Data Analysis - PubMed

Survival analysis encompasses investigation of time to event data. In most clinical studies, estimating the cumulative incidence function (or the probability of experiencing an event by a given time)...

https://www.emilyzabor.com/tutorials/survival_analysis_in_r_tutorial.html#cumulative_incidence_for_competing_risks

You can find a summary of this explainer on competing risks here:

https://livefreeordichotomize.com/2020/05/22/survival-model-detective-2/

Take">https://livefreeordichotomize.com/2020/05/2... aways: Learn about proper survival analyses or befriend a statistician to help you!

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