How to calculate confidence interval for median to test differences between more than two groups

[EmilieRo]

Hi,

Context : the objective is to compare the effect of 8 treatments on a quantitative variable. Data were available for 223 patients (+ or - 27 patients per group).

The data don't follow a normal distribution so i would like to calculate median differences between groups with corrected 95%CIs.

This paper describe how to calculate median differences and 95%CIs between two groups https://www.lexjansen.com/pharmasug/2000/Coders/cc01.pdf

But i don't find statistical formula to directly calculate the 95% CI for medians between more than two groups...

Do you know what procedure will do this? Or do you have documentations about this?

Thanks 

[Ksharp]

I remembered @Rick_SAS wrote a blog about it before.

[Rick_SAS]

I haven't done this for more than two groups, but here are two ideas:

1. PROC MULTTEST was designed to allow for nonnormal distributions. You can use the BOOTSTRAP or PERMUTATION options on the PROC MULTTEST statement to perform pairwise comparisons of means (not medians, as you requested).

2. If you really want medians, you can use PROC QUANTREG to examine the difference of medians. My blog post shows how to use the ESTIMATE statement to perform s test for the significance of the difference. You can use the ADJUST= option to adjust for multiple comparisons.

[ballardw]

I would ask what is type of analysis or what do you want to say about the "more than two groups"?

And what type of data is your sample: categorical, ordinal or interval?

Maybe Kruskal-Wallis test or Proc Npar1way Median ?

[EmilieRo · Accepted solution]

To begin, thank you for your answers.

@ballardw : I used kruskal-Wallis one-way analysis with Dunn's post-tests and i presented the data with median and IQR in the paper. The reviewers asked me to describe data with median differences and 95%CI between groups. He said :"generally  it is not helpful to refer to a "statistical difference". As a reader i would like to see the magnitude of the difference and the confidence intervals that should be applied to it"

I would like to calculate this median differences and adjusted for multiple comparisons. There are 8 treatments groups so i had to realise 28 multiples comparisons.

The treatment variable is categorical

I tested the @Rick_SAS's method, i did proc quantreg and i used the estimate statment but i don't know what test i have to use for multiple comparisons, Sidak?

I read in papers that authors used bootstrap approach, is it a better approach?

Thanks