# Can exact tests compare groups from case-cohort studies?

I have reviewed several helpful threads most related to my question and many thanks to the authors. The first thread suggests odds ratio is valid for cohort studies, but risk ratios or hazard ratios are more desirable. The second thread suggests that in the case of case-cohort studies, odds ratios can estimate relative risks (reiterated in #3 below). The third thread discusses methods of estimating relative risks, although in a cohort study context.

Odds ratios are inappropriate for a cross-sectional or cohort study

Follow-up updates in case-cohort designs

Poisson regression to estimate relative risk for binary outcomes

About my data: I inherited a case-cohort study dataset but I don't know the size of the total population where the subcohort was drawn to calculate an adjusted weight for Cox PH model (more on that in #2). In addition, my dataset omits the timestamps of cases for privacy protection, therefore I do not have an actual estimate of person-time. I'd like to find out whether there is an elevated risk of outcome given an exposure using the data.

The TL;DR version of my question is (1) are odds ratio appropriate for case-cohort studies; and (2) if so, whether the exposure and non-exposure groups from a case-cohort study are considered independent so that I can use Fisher's exact test.

Apologies in advance if I'm mixing up multiple concepts. Here is what I know that motivated this question. Please correct me if I'm wrong.

1. Case-cohort studies sample subcohort from the population to be the control (baseline) group at t=0. Hence, a subject that may develop a case later can be included in the control group.

2. Case-cohort studies, similar to cohort studies, can address time-variant risks, in that a subject may develop a case at a later point. Hence, measuring hazard ratio at time t is desirable when comparing two groups. Hazard ratio is akin to risk ratio (relative risk) at a given time t. Therefore, a generally acceptable approach of analyzing case-cohort data is a modified Cox proportional hazard regression with reassigned weights to correct for under-representation of the total N. This presentation helped me a lot in understanding the analysis procedure for case-cohort studies. https://www.stata.com/meeting/nordic-and-baltic16/slides/norway16_johansson.pdf

3. Because the control group in a case-cohort study design includes all subjects at risk at t=0, calculating the odds ratio can be a good estimate of relative risk.

4. Fisher's exact test is appropriate for assessing independence between nominal variables when the comparing groups are independent and not correlated. McNemar's exact test can be used for pair groups.

There arises my confusion - are the case and controls groups in a case-cohort study independent? My hunch is no, because per #1 a case may rise out of the control group at a later point. But it is clear that the case and control groups do not suffice as paired, either, under a case-cohort design. Am I wrong? Can Fisher's exact test be used for estimating odds ratio for case-cohort studies?

To take a step back, when you draw up a 2x2 table for a case-cohort study, is a subject that later developed a case counted in the case group or the control group or both?

This paper gives comparisons on different risk ratio calculation for case-cohort studies for those who are interested. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1566546/ At the moment, I'm looking for a conventional approach to test strength of association for a risk factor between groups from case-cohort studies without needing to implement one from scratch, if possible.

Thanks so much.

It's unfortunate that you don't know the subcohort sampling fraction, but you can still calculate odds ratios.

Cases who were subcohort members will need to be treated the same way as cases who were not subcohort members (which is desirable anyway).

The cases are sampled with probability 1.

I'll use the word controls to refer to subcohort members who do not become cases. The controls are part of the subcohort, who were originally sampled randomly with some unknown probability $$p$$, and so they are still a random sample of population members who do not become cases, still with the same unknown probability $$p$$.

This means we have standard case:control sampling, and the unknown sampling probability cancels out of odds ratios, at least for exposures that do not vary over time. Fisher's test works.

For exposures that do vary over time, things are a bit more complicated.

• Thanks so much, @Thomas Lumley. It's helpful to think of the data as a standard case-control situation and that the sampling probability cancels out in odds ratio calculations. While waiting for answers, I started playing with mixed-effect logistic regression models thinking that the same subject can have multiple cases during the course of the study. Although I suspect the numbers aren't going to be that different, methodologically speaking would (unadjusted) odds ratio coming from a mixed-effect logit model better than Fisher's exact test? Jul 3, 2020 at 19:10
• And to your last point about time-variant risk, I am thinking the longer a subject stays in the study, it's probably more likely that we capture a case by chance. However, each occurrence of a case should be independent. In this case, we'd say exposure remains constant over time. Correct? @Thomas Lumley Jul 3, 2020 at 19:16
• I was thinking of the exposure variable, the other variable in the 2x2 table, and whether it was constant over time or time-varying. Jul 3, 2020 at 20:21