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I am not sure about the best design in this case.

I have a representative sample (N=15,000) of individuals with a moderately rare condition and I want to match them to controls who do not have this condition. I want to compare rates of fatal and non-fatal vascular events and all-cause mortality between cases and controls controlling for confounders (demographic, SES, and clinical characteristics). As for controls I can extract them from a random sample (N=1,000,000) which is also state representative.

In summary I want to match case and controls and follow them up for 10 years to compare rates of different outcomes.

My first thought was to perform a propensity score 1:m kernel matching (including for the matching estimator age, sex, but also vascular risk factors considering I am going to look at vascular outcomes) and compare incident outcomes. However, I read it does not perform well when you try to match selected cases to a random sample of control. Any good reference that might support the opposite?

I also thought about a nested case control design matching by age and sex and controlling in the conditional logistic regression for the baseline cardiovascular risk factor. However, in my case I would match at baseline and then follow-up my two groups over time to compare rates (or probability as in the conditional logistic regression). Would this design still be appropriate? Normally NCC look retrospectively at outcomes. Also, I am considering multiple outcomes, would it be suitable for that?

I also thought about the inverse probability weighting but I guess this approach shares majority of the weakness and strengths with the first. correct?

Any good reference would also be appreciated.

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What you have described is not a case-control study, and it is very important to know that because the methods you would use to analyze a case-control study are different form what you would use to analyze a cohort study, which is what this is. In a case-control study, you perform selection on the outcome, which in your case is vascular events and mortality, and see how they differ with respect to the exposure, which in your case is whether they have the condition or not. What you described is a cohort study, in which you examine those with and without the exposure and see how they differ with respect to the outcome. A cohort study is more straightforward to analyze; you need to eliminate confounding and approximate a randomized control trial (or similar randomized design). To this end, matching, weighting, or regression-based methods work well.

With a sample this large, if possible, you should include all control units that bear any resemblance to the exposed units. You have the opportunity to perform an advanced statistical technique for causal effect estimation; in this case I would recommend targeted maximum likelihood estimation (TMLE), which combines regression and weighting and is easy to implement. You could also try Bayesian additive regression trees (BART), which has also proven to be highly effective and fairly easy to implement, but I'm not sure how it fares for survival outcomes.

If you do matching, make sure you try to retain as many control units as possible; throwing away a large percentage of your 1m control units would be disastrous. Kernel matching is popular but isn't prima facie better than other matching methods that optimize a criterion; check out other sophisticated methods such as FLAME (Fast Large-scale Almost Matching Exactly) and Zubizarreta's designmatch.

Weighting (i.e., with entropy balancing or similar optimization-based approaches)would also be effective. Whatever you do, make sure you include as many pre-exposure covariates as possible and incorporate highly flexible models that attempt to balance on many functions of the covariates. With sample sizes that large, the effect of bias will be larger than most decreases in precision.

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