Related to pairs in Win ratio analysis

[Tom Hsiung]

Hi, everyone

A recent couple of years, I occasionally read several randomized clinical trials that analyzed data by the win ratio method. In these studies, observations need to be paired in order to derive the win-or-lose status. I am not familiar with this win ratio method and I wonder, how to determine each pair from the sample data. I mean, for instance, observation m# in the intervention group can be paired with observation n# in the control group, but it also could be with observation X#, Y#, or Z# in the control group. How do we figure out the pairing issue?

Thank you for reading my posts and your help would be much appreciated.

Tom

[Tiago Pereira]

Hi, Tom

The win ratio (WR) can be applied when we have two groups. You can try the new command -winratiotest-.

ssc install winratiotest

In case you have 3 groups, you can do multiple comparisons, say, A vs C, B vs C and A vs B. Multiple testing could be an issue.

https://pubmed.ncbi.nlm.nih.gov/21900289/

[Tom Hsiung]

Hello, Tiago

Thank you for your post and it is really impressive! I read the attached paper and it is really inspiring!

In the paper the authors described matched and unmatched methods for win ratio analysis, using composite endpoint of CV death and HF hospitalization as an example. The author concluded that matched method is preferred over the unmatched method due to the statistical complicated math of the latter. So, I think I should start with the matched way.

I wonder if we can use a 1:1 propensity score match (PSM) procedure to derive a list of comparable pairs between intervention and control and then count the win or loss of this PSM cohort. I guess it is practical with a logistic regression model. Thank you again for reply my thread.

[Tiago Pereira]

Recently, our perspective has changed a bit: we now prefer the unmatched approach because it maximizes the use of participants. This approach has shown higher statistical power and is easier to implement than the matched approach. I am not aware of people using propensity score matching, but some have suggested using inverse probability of treatment weighting.

[Leonardo Guizzetti]

In case you have 3 groups, you can do multiple comparisons, say, A vs C, B vs C and A vs B. Multiple testing could be an issue.

https://pubmed.ncbi.nlm.nih.gov/21900289/

An unresolved conflict in this area of win ratio, with odds, win probability is that they are defined in comparison to 2 groups. When trying to apply this to 3 or more groups, there is the possibility of the so-called transitivity paradox. This is a problem more well known in network meta-analysis, but it goes like this. Suppose you have 3 groups, A, B and C. Pairwise tests can show that A > B, B > C and A<C which is the contradiction. I haven't read that literature in a while so I don't know if there are convincing or robust ways to handle those scenarios in general.

Tiago Barreira how do you handle ties in your -winratiotest- package?

[Leonardo Guizzetti]

Hi, everyone

A recent couple of years, I occasionally read several randomized clinical trials that analyzed data by the win ratio method. In these studies, observations need to be paired in order to derive the win-or-lose status. I am not familiar with this win ratio method and I wonder, how to determine each pair from the sample data. I mean, for instance, observation m# in the intervention group can be paired with observation n# in the control group, but it also could be with observation X#, Y#, or Z# in the control group. How do we figure out the pairing issue?

Thank you for reading my posts and your help would be much appreciated.

Tom

If I understand the question, you aren't talking about matching, just mathematically how are the pairs derived? The notion is to compare every one individual with every other individual from the other group. The brute-force way to do this is to compare all m-by-n pairs for 2 groups of size m and n, then sum them up by individual. However, that approach is quite cumbersome and there are more elegant techniques available in the win ratio and win probability literature. I highly recommend you read this paper by Zou and colleagues (open-access) for an approachable application of win probability in the area of stroke, and then you can read further work from G Zou for more detailed statistical methods.


Zou G, Zou L, Choi YH. Distribution-Free Approach to the Design and Analysis of Randomized Stroke Trials With the Modified Rankin Scale. Stroke. 2022 Oct;53(10):3025-3031. doi: 10.1161/STROKEAHA.121.037744. Epub 2022 Aug 17. PMID: 35975666.

[Tiago Pereira]

An unresolved conflict in this area of win ratio, with odds, win probability is that they are defined in comparison to 2 groups. When trying to apply this to 3 or more groups, there is the possibility of the so-called transitivity paradox. This is a problem more well known in network meta-analysis, but it goes like this. Suppose you have 3 groups, A, B and C. Pairwise tests can show that A > B, B > C and A<C which is the contradiction. I haven't read that literature in a while so I don't know if there are convincing or robust ways to handle those scenarios in general.

Tiago Barreira how do you handle ties in your -winratiotest- package?

I agree. That's why I referred to comparing to a common control group: A vs C and B vs C only.

-winratiotest- is not authored by me. It was developed by some folks at the London School of Hygiene and Tropical Medicine. Ties are managed in the conventional manner by being excluded, consistent with the win ratio definition. If ties occur at all levels of the hierarchical outcomes, they are ignored and do not influence the win ratio estimation.

[Leonardo Guizzetti]

Thanks for info on the win ratio test. I don’t agree that ties being dropped is benign nor that it affects estimation, because at the very least it should affect precision of the estimate. However this is strongly dependent on the nature and scale of the outcome and my remarks apply to ordinal scales with say 7 levels or less.

[Tom Hsiung]

Thanks, everybody. I have tried the winratiotest procedure and it is really easy and straightforward to handle. I appreciate your contributions to this topic, guys.