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I study school grades in children with brain tumors (=cases), using databases. Every case in the database has five healthy controls, matched on sex, birth year and residency. The hypothesis is that cases have worse school grades than controls (this is of course already known, but I will also look at other covariates here).

I am not starting by looking at grades, and then trying to determine whether or not the children with low grades were exposed (=had a brain tumor or not) - which would make it a case-control study. No, instead, I look at whether or not a child is a case (=brain tumor) or a control (=no brain tumor), and then find out what grades they have - this makes it a retrospective cohort study.

So I do exposure first, then look at outcome = retrospective cohort study. Not outcome first, then look at exposure = not a case-control study.

This took me quite some time to realize, and also my statisticians got this wrong, because if you have cases and controls, people (including myself) easily think it is a case-control study.

So, my questions here are:

  1. Do you agree with me that this is a retrospective cohort study, and not a case-control study (even though it uses the terms "case" and "control")?

  2. Since the controls are matched against the cases (on at least some variables that are known to influence school grades, i.e. sex and residency), I have been told to use conditional logistic regression (clogit) when investigating the relationship between being a case (yes/no) and failing a school subject (yes/no). Any thoughts on this, as opposed to using ordinary logistic regression models?

  3. When I read more on this, it is usually assumed that clogit is used mainly in case-control studies. Is it not valid in retrospective cohort studies?

Specifically, this quote from the following article (https://www-ncbi-nlm-nih-gov.proxy.kib.ki.se/pmc/articles/PMC9188848/) gets me thinking:

"Matching in case–control studies can also have other counterintuitive effects because the matching is across outcome groups rather than exposure groups, and thus does not necessarily result in balancing the matching factors across exposure groups. "

I would argue that the matching in my study is not "across outcome groups" - the controls are not selected based on school grades - but rather "across exposure groups" - the controls ARE selected based on that they DO NOT have brain tumors, and also based on sex, birth year, and residency.

I have asked different statisticians to clarify the above for me, and get mumbling or unclear answers only, or otherwise answers that later turn out to be incorrect. PLEASE, can someone shed a light on this?

Or, to put it in more succintly: IS there really a statistical dependency between cases and controls in my particular study, such that I cannot use Chi-square (for simple proportion comparisons between cases and controls), or that I have to use clogit?

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    $\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$
    – Community Bot
    Commented Sep 26, 2023 at 13:53

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This analysis is not a case-control analysis, and using the words "case" and "control" will only muddy things and make them confusing. In your case, children with brain tumors are exposed, and those without brain tumors are unexposed. All the causal inference methods that are used with cohort studies, which examine the effect of an exposure on an outcome without selecting on the outcome, are applicable here. So all the literature on, e.g., propensity score matching is useful; all the literature on matching for case-control studies is not. I can understand why this would be confusing for your analysts; typically, diseases are outcomes, not exposures.

You should consider your population as children you have access to and do an analysis that targets the part of that population most relevant for you. This refers to the estimand, the quantity you are trying to estimate. Performing the analysis you had planned to perform (finding unexposed children with similar backgrounds to exposed children) allows you to estimate the "ATT", which compares the observed outcomes for the exposed children with the counterfactual outcomes for these children had they not been exposed (i.e., had they not developed the tumor). See this paper for an explanation of this and other estimands.

Note the kind of study you are running is not too dissimilar from one of the foundational studies done to examine the effectiveness of causal inference methods. Lalonde compared the treated units in a randomized trial to untreated units collected from a public survey. He used matching to estimate the ATT by finding untreated units similar to his treated units.

After propensity score matching, you should run a regular (generalized) linear outcome model and use a cluster-robust standard error with pair membership as the cluster variable. This is explained the MatchIt vignette on estimating effects, which should be your guide here.

Note that it is inappropriate to look at the relationship between covariates and the outcome when treatment and other covariates are included in the outcome model or when adjusting for a consequence of that covariate. To do so is to commit the table 2 fallacy. You can examine moderation by the covariates, but this requires you to match on the covariates as well. The same vignette above explains how to do moderation analysis with matching.

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  • $\begingroup$ Thank you! I will look into the suggested papers. $\endgroup$
    – Gus Hell
    Commented Oct 2, 2023 at 20:02
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The analysis is not a case-control analysis, but neither is it exactly a retrospective cohort study. I am in a very similar situation with a study I have in hand and I will try to explain my thoughts on the subject.

The point is that the distribution of your outcome is not the real one in the population, and that makes your estimators may be biased. I understand that the first idea is to think that this does not have to be true, since the only thing we know for sure is that the distribution of your exposure, brain cancer, is not the one in the general population, as cases are over represented. The truth is that if we assume that there really is a relationship between brain cancer and the outcome, school grades, by taking a subset of the population that has a different distribution in the brain cancer variable, the distribution of school grades will not be the real one either, therefore your population is not representative, since you are over representing the population with bad grades.

If I understood correctly, you took 5 controls randomly from all the children free of brain cancer of the same age, sex and residency. If this is the case I believe the best option for you is to use a Weighted Logistic Regression, i.e., to do a logistic regression but using inverse probability weighting to balance the sample.

The general idea is to use a weight on each observation. For the brain cancer cases this weight would be $1$, as you have observed all. For people without brain cancer this weight will be $1/p_i$ with $p_i$ being the probability of the subject $i$ of having been selected for the study. This $p_i$ could be easily calculated using the matching variables if you have the real population information.

For example, imagine that you had $1$ case from residency $X$ who was $10$ years old and who is a male. You have taken $5$ controls with these characteristics. Imagine that the real population with these characteristics is $2000$ children. To each of these $5$ controls you would have to put a weight of $2000/5 = 400$, and to your control $1$.

Weighting all your controls would solve your problem, since you would have a "complete cohort".

In this Chapter of the book Modeling Binary Correlated Responses using SAS, SPSS and R you can find more information about Weighted Logistic Regression.

Another reference that could help you is Logistic Regression in Rare Events Data by King, G., & Zeng, L. (2001). Find it here.

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