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Ok, I did a bit of visualization to confirm and demonstrate why even if the groups are matched by age, controlling for age can still make the effect of ME/CFS status more significant. We can imagine that we have 20 controls and 20 cases, where each control has a matching case in terms of age...

It should apply to both. They may be weak associations with ME/CFS status, but still very strong associations with each other. For example, if the data for NII-RF was accidentally copied and replaced the data for NII-HR, making them identical, then NII-RF would still have a relatively weak...

If all the different niiXX outcomes are correlated to each other (which we might expect if these are possibly just different effects of a common pathology), then they will tend to have similar results. If the me/cfs_status association with NII-RF has that 0,1 significance pattern, then we can...

Hmm. I'd need to think about it more, but I think if they were well-matched for age, that would mean that without controlling for age, we can expect the predicted coefficient to be accurate (or at least not biased by age). But the variance due to differing age among the cohort (e.g. if some...

Yes, so I think if the strongest correlation is with age, controlling for it can remove so much noise that the increase in significance from better precision outweighs the decrease in significance due to decreased effect size you might expect from controlling for HADS.

I had to multiply by a much smaller number than 0.5 to decrease the correlation meaningfully. But here is the result if multiplying age by 0.05: The correlation is now 0.65, and still about a quarter of the time, it's only significant after adding covariates. But okay, 0.65 is still a high...

I'm not at a PC currently, so can't test it. But I think what's happening is that by increasing the influence of random noise, not only is the correlation of age with niiXX decreasing, but so is the correlation of mecfs_status with niiXX. In which case it's not surprising that mecfs_status is...

I haven't fully parsed this code yet, but I think there's an error here, calling model2 instead of model1:

Do we actually know if it increased differences? I don't see effect sizes or coefficients in the text. The predicted effect of ME/CFS status on the brain metric can decrease (which I agree, I think I would expect that with controlling for HADS), while the p-value still becomes even more...

What was in the paper? They were using real-life data where we're going into it not knowing if the outcome variable is actually dependent on mecfs_status or not. I showed that in the case where it is dependent on mecfs_status, the scenario we're discussing is possible.

We just did force it to happen. In the updated code I posted, in 92% of the trials where niiXX was not significantly associated with ME/CFS status (analogous to them showing no association for the univariate test in the paper), adding a covariate made it a significant association (significant...

This is because in the model you made, there is no relationship between ME/CFS and niXX, so it is all due to chance. niXX is just a function of age, so there should only be about 5% significant as false positives when testing the association with mecfs_status. If niXX actually depends on...

Several posts about Sjogren's were moved to: Is there a connection between ME/CFS and Sjogren's Syndrome? Discussion and a poll about testing

You replaced model1 <- lm(niirf ~ 1) with model1 <- lm(niirf ~ 0). 1 is the formula for an intercept. 0 means no intercept. From the R docs: So in the first updated code you posted, in the comparison of model1 and model2, it's comparing a model that just predicts 0 for every point with a...

Here is some R code simulating this with random data where NII-RF is correlated to age and to ME/CFS status: Output: To get an idea of what the p-values are, I looked at the ANOVA results for the last trial: When comparing the models without age, the p-value was 0.48. With age, it was 0.03.

In the case of models 3 and 4, we can be more confident about the amount that ME/CFS status improves the model, since the age variable is included and can explain some of the variance. I'm not able to right now, but I might code it with simulated data later. It should be relatively...

I'm not sure what exactly you mean by the p-value of the initial model. The p-value of the ME/CFS status coefficient in a model including all covariates? I think this is the same p-value you would get from an F-test comparing the model with and without ME/CFS status.

Yes, but this is in the case of age being correlated to both ME/CFS status and NII-RF. Age can be correlated to only NII-RF, in which case adding this variable to a model that only had ME/CFS does lead to better predictive ability for NII-RF.

Yeah, decreased standard error for the coefficient of the main exposure on the outcome since some of the noise is accounted for by the covariate. Edit: This goes a bit into it, talking about how controlling for covariates increases precision...

I also wasn't sure why it would be necessary to match group size. Are they saying they excluded ME/CFS participants that didn't have similar metrics to a healthy control? Or they just randomly removed ME/CFS participants to match group size? Either way, I don't really see the reason for doing...