You want adjusted effect sizes to check confounding. It’s not because variables are different for the controls, but because you don’t know if they affected your treatment group. You could stratify by group and take a weighted average of the effect sizes (“effect size” defined as change from baseline, as in the writeup). However, you might not have a large enough sample size for all strata, you can’t adjust for many variables at once, and it’s inferior to regression.
If correlation was your primary method to check confounding, there are two problems: a) confounding depends on the correlations with both the independent and dependent variables, but you only have data for the latter. b) the concept of significance can’t be applied to confounding in a straightforward way. It’s affected by sample size and variance, but confounding isn’t.
The main complication is the missing control group. I’m undecided on how to interpret this study, because I can’t think of any reason to avoid controls and I’m still trying to figure out the implications. If the RCT was done well, this makes the evidence a little bit stronger because it’s a replication. But by itself, I still haven’t thought of any way to draw useful conclusions from these data. There’s some good information, but it’s like two cross-sections, which are usually used only to find hypotheses for new research.
You’ll have to clarify those points. For the first part, M-bias is not confounding. It’s a kind of selection bias, and it happens when there is no causal relation with the independent or dependent variables (not no correlation), specifically when you try to adjust for confounding that doesn’t exist. The collider can be a confounder, but it doesn’t have to be. From the second link, “some authors refer to this type of (M-bias) as confounding...but this extension has no practical consequences”
I don’t think you can get a good control group after the fact, because you need their outcomes at both timepoints, with a year in between. None of the options that come to mind are very good: you could ask them what they would have answered a year ago, you could start collecting data now and ask them in a year’s time, or you could throw out the temporal data and use only a single cross-section.
Yes, M-bias is an example of a situation where a variable depends on treatment and outcome, but is not a confounder. Hence I was confused by your statement:
confounding depends on the correlations with both the independent and dependent variables
I used “depends” informally, so I didn’t mean to say that variables that depend on treatment and outcome are always confounders. I was answering the implication that a variable with no detectable correlation with the outcome is not likely to be a source of confounding. I assumed they were using a correlational definition of confounding, so I answered in that context.
A variable with no detectable correlation with the outcome might still be a confounder, of course, you might have unfaithful things going on, or dependence might be non-linear. “Unlikely” usually implies “with respect to some model” you have in mind. How do you know that model is right? What if the true model is highly unfaithful for some reason? etc. etc.
edit: I don’t mean to jump on you specifically, but it sort of is unfortunate that it somehow is a social norm to say wrong things in statistics “informally.” To me, that’s sort of like saying “don’t worry, when I said 2+2=5, I was being informal.”
We talked about this before. I disagree with wikipedia’s philosophy, and don’t have time to police edits there. Wikipedia doesn’t have a process in place to recognize that the opinion of someone like me on a subject like confounding is worth considerably more than the opinion of a randomly sampled internet person. I like *overflow a lot better.
One somewhat subtle point in that article is that it is titled “confounding” (which is easy to define), but then tries to define “a confounder” which is much harder, and might not be a well-defined concept according to some people.
You want adjusted effect sizes to check confounding. It’s not because variables are different for the controls, but because you don’t know if they affected your treatment group. You could stratify by group and take a weighted average of the effect sizes (“effect size” defined as change from baseline, as in the writeup). However, you might not have a large enough sample size for all strata, you can’t adjust for many variables at once, and it’s inferior to regression.
If correlation was your primary method to check confounding, there are two problems: a) confounding depends on the correlations with both the independent and dependent variables, but you only have data for the latter. b) the concept of significance can’t be applied to confounding in a straightforward way. It’s affected by sample size and variance, but confounding isn’t.
The main complication is the missing control group. I’m undecided on how to interpret this study, because I can’t think of any reason to avoid controls and I’m still trying to figure out the implications. If the RCT was done well, this makes the evidence a little bit stronger because it’s a replication. But by itself, I still haven’t thought of any way to draw useful conclusions from these data. There’s some good information, but it’s like two cross-sections, which are usually used only to find hypotheses for new research.
That’s not the correct definition of confounding (standard counterexample: M-bias).
Re: missing controls, can try to find similar people who didn’t take the course, and match on something sensible.
Not sure what this means, people have been using bootstrap CIs for the ACE for ages.
You’ll have to clarify those points. For the first part, M-bias is not confounding. It’s a kind of selection bias, and it happens when there is no causal relation with the independent or dependent variables (not no correlation), specifically when you try to adjust for confounding that doesn’t exist. The collider can be a confounder, but it doesn’t have to be. From the second link, “some authors refer to this type of (M-bias) as confounding...but this extension has no practical consequences”
I don’t think you can get a good control group after the fact, because you need their outcomes at both timepoints, with a year in between. None of the options that come to mind are very good: you could ask them what they would have answered a year ago, you could start collecting data now and ask them in a year’s time, or you could throw out the temporal data and use only a single cross-section.
Yes, M-bias is an example of a situation where a variable depends on treatment and outcome, but is not a confounder. Hence I was confused by your statement:
Confounding is not about that at all.
I used “depends” informally, so I didn’t mean to say that variables that depend on treatment and outcome are always confounders. I was answering the implication that a variable with no detectable correlation with the outcome is not likely to be a source of confounding. I assumed they were using a correlational definition of confounding, so I answered in that context.
Should be careful with that, might confuse people, see also:
https://en.wikipedia.org/wiki/Confounding
which gets it wrong.
A variable with no detectable correlation with the outcome might still be a confounder, of course, you might have unfaithful things going on, or dependence might be non-linear. “Unlikely” usually implies “with respect to some model” you have in mind. How do you know that model is right? What if the true model is highly unfaithful for some reason? etc. etc.
edit: I don’t mean to jump on you specifically, but it sort of is unfortunate that it somehow is a social norm to say wrong things in statistics “informally.” To me, that’s sort of like saying “don’t worry, when I said 2+2=5, I was being informal.”
Very true. This is something I’ll try to change.
Cheers! If you know what M-bias is, we must have hung out in similar circles. Where did you learn “the causal view of epi”?
If Wikipedia get’s it wrong it might be high leverage to correct it.
We talked about this before. I disagree with wikipedia’s philosophy, and don’t have time to police edits there. Wikipedia doesn’t have a process in place to recognize that the opinion of someone like me on a subject like confounding is worth considerably more than the opinion of a randomly sampled internet person. I like *overflow a lot better.
One somewhat subtle point in that article is that it is titled “confounding” (which is easy to define), but then tries to define “a confounder” which is much harder, and might not be a well-defined concept according to some people.