They already do acknowledge socioeconomic (and other confounding factors) in the analysis.
The primary analysis they perform is a ‘Propensity Score Match’ which is a technique used specifically to address for confounders in observational studies, and they do report balanced cohorts.
Still they write in their discussion “Although we adjus-
ted for several available proxies of socioeconomic and lifestyle status,
direct measures of income, insurance coverage, or out-of-pocket
payment were not available in the TriNetX database. Residual confounding related to unmeasured socioeconomic factors, therefore,
cannot be excluded“
Given the size of the dataset, the effect size, significance and sensitivity testing they did I think it’s very strong evidence for GLP1s causing this and it would be very very surprising to me to see the effect disappear even if they had perfect socioeconomic data.
With so many signs of improvement, even if some of them happens to be just flukes, from so many different areas, it feels like a penicillin moment. And i suppose penicillin also was initially mostly available to the ones with better socio-economy.
Your exact intuition about the implausibility of many large effect sizes is called the “Piranha problem” by my favourite statistician Andrew Gelman first here in a blog post:
https://statmodeling.stat.columbia.edu/2017/12/15/eats/
Given the size of the dataset, the effect size, significance and sensitivity testing they did I think it’s very strong evidence for GLP1s causing this and it would be very very surprising to me to see the effect disappear even if they had perfect socioeconomic data.