Adjusted risk ratios and risk differences after logistic regression

[Martin Mueller]

Dear Statalist users

I am currently working on a study protocol for a stratified randomised controlled trial (RCT) with a binary outcome (0/1) and a binary exposure (0/1).
As suggested by Kahan and Morris (DOI: 10.1002/sim.4431) the primary analysis in such a RCT should be adjusted on the (categorical) stratification variable (=stratification_var, 0-4 in my case).
Thus, my primary approach is simple; use a logistic regression adjusted for the stratification variable, i.e.

logistic outcome exposure i.stratification_var

However, there are multiple authors (e.g. Austin 10.1016/j.jclinepi.2008.11.004) that recommend to use adjusted risk ratios (ARR) and risk differences (ARD) as effect sizes in such a RCT and not the odds ratio (OR) as the "OR is difficult to interpret and only approximates the ARR".
Fortunately, there is a nice user written command - adjrr - by Norton, Miller and Kleinman (https://www.stata-journal.com/articl...article=st0306) which can be used after a logistic regression model to calculate the ARR and ARD.
Alternatively, I found this beautiful link from UCLA (https://stats.oarc.ucla.edu/stata/fa...ohort-studies/) to estimate the ARR using GLM

[In my opinion, the ARD can easily be calulated using

margins r.exposure

after the logistic regression command.]

However, the results between the approaches to calculate the ARR with 95% CI differ a bit. Thus, I wonder if you have any advice

1. if the ARR/ARD is preferred over OR in this scenario and
2. if the ARR is preferred, what is the best way to calculate it: using i) the - adjrr - command, ii) a relative risk estimation by log-binomial regression, or iii) a relative risk estimation by Poisson regression with robust error variance?

Thank you very much for your valuable thoughts on this problem.
Martin

[Leonardo Guizzetti]

There are a couple of definitive texts on the statistical analysis of cluster RCTs. The first and original, but slightly hard to find now, is by Donner and Klar. The second is by Richard Hayes, now in second edition I believe. This might also be more friendly for you as you can follow along with the datasets and presented Stata code. Also you should know that there is an extension of the CONSORT guidelines specifically for cluster RCTs.

i think an important aspect of this post that has been glossed over and is a key distinction to individually randomized trials is what is the level of inference that is of interest? Sure, clusters are randomized, but is the interventional effect relevant also at the cluster level or at the individual level? This will guide your analysis, but I will presume that it is the latter.

Some useful advice for all RCTs is to show relative and absolute effects. This gives the reader as much information as possible to judge the clinical importance and impact of the intervention. However, your analysis plan will focus on one outcome measure.

Since you want a RR effect measure, why not estimate it directly? You may consider GEE or GLM models with log link and Poisson family, with cluster robust standard errors, adjusting for stratification. Adjusted risk differences could be obtained using margins after this model, or estimating a similar model with linear link (and possibly Gaussian family). Log binomial is another way to get risk difference, but you’ll often find convergence issues, so with avoid it or plan for a fallback estimation fails. You will get different results using different estimation methods, but they should be pretty similar. If they’re not, that’s a clue about some underlying issue with the model or data.

[Martin Mueller]

Thank you very much for your reply!

Just to be clear (maybe my writing was misleading): The randomisation scheme of this RCT is stratified on one factor (e.g. on smoking status), this is not a cluster RCT.

I agree with you, all the methods lead to more or less similar results.

[Leonardo Guizzetti]

Oops, that's a silly mistake on my part. I shouldn't post late in the evening. You are safe to ignore the clustering bits, but the last paragraph is still applicable for your situation.