win ratio, win odds and net benefit

[Eperke Merkel]

I am trying to calculate win ratios, win odds and net benefit with 95% CIs
With the winratio command I successfully did for win ratio (proportion of wins/losses)
Is there any command or option to get win odds [(PW+0.5PT)/(PL+0.5PT)], and net benefit (PW−PL)?

Here is my command and results for win ratio:

winratio Number trt, outcomes(Died2 tf days_death) outcomes(HFH tf days_HF) outcomes(responder c >) outcomes(BNP_change_5 c >)
------------------------------------------------------------
Total number of patients: 360
Number in control group: 145
Number in active group: 215
Number of comparisons: 31175
------------------------------------------------------------
Wins Losses Ties
------------------------------------------------------------
Outcome 1 3354 1633
Outcome 2 5990 1087
Outcome 3 6656 974
Outcome 4 369 403
------------------------------------------------------------
Total 16369 4097 10709
------------------------------------------------------------
Win Ratio: 4.00, 95% CI(2.80, 5.70) P=0.0000
------------------------------------------------------------

Thank you

[Tiago Pereira]

Hi, Eperke.

Welcome to the Statalist!

I am not aware of any program in Stata that calculates the win odds or net benefit. It is also unclear the design of your study, which is also crucial to discuss the most appropriate approximations for the variances.

However, there are relatively simple approximations for the variance of log(win odds) and log(NB) under the null, which could be implemented manually. An alternative would be bootstrapping.

[Rich Goldstein]

these are stats that I do not use; however, using the -hsearch- command in Stata, I found a number of programs; here is what I typed

hsearch win

for more on the command, see

h hsearch

it is deprecated but still available and I use it at least once/month (and wish that StataCorp would tweak the algorithm and un-deprecate it

[Eperke Merkel]

thank you for your quick responses, it was a randomized controlled trial with two arms - one treatment, one control
thank you, I will check those out.

[Leonardo Guizzetti]

I have written a program called winprob (available on SSC) which will calculate win probability and is suited to your two arm RCT design. There is existing literature to show how to convert this into win odds with confidence intervals. I will look for the reference when I am at my desk.

[Leonardo Guizzetti]

As promised, here is the reference I mentioned to translate the win probability directly to the win odds. The paper has applications focused of clusters but the formula provided uses the summary measure of win probability and its variance directly. Some other transformations are also discussed.

Davies Smith E, Jairath V, Zou G. Rank-based estimators of global treatment effects for cluster randomized trials with multiple endpoints on different scales. Statistical Methods in Medical Research. 2025;34(6):1267-1289. doi:10.1177/09622802251338387

[Eperke Merkel]

I am so grateful for your help and input!

[Rich Goldstein]

whoops - clarification of my comment in #3 above - hsearch searches help files but they must already be on your system - so it will not find user-written commands that have not yet been installed - see -search- for that