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I have multiple questions regarding the best way of estimating the odds ratios after I have calculated a propensity score.

I am using a complex survey sample with single-stage design (sampling unit = hospitals) and stratification. Weights are assigned per sampling unit (a hospital).

I use Stata 14. My matching is 1:1 nearest neighbor done by psmatch2 module.

Preliminary question: when I estimate the propensity score, should I use a mixed model with hospital id as my level-2 intercept, or will a simple regression do? Shall i also use svy- or simple weights or no weights at all?

I want to calculate odds ratios of a specific comorbidity in matched patients predicting a dichotomous outcome.

Main questions:

1) Do i run a svy-model?

2) If I don't run a svy-model, do i still need to incorporate weights? I noticed major differences if i don't include weights and i just run an unweighted regression.

2) Svy or not, do i run a mixed level model with hospital id as level-2 intercept and use _weight (variable created by psmatch2 procedure indicating a matched pair) as the subpopulation (ie, including only matched pairs) or do include the "pair_id" variable as a level-2 (and avoid svy estimation, since weights are don't follow pair levels but hospital levels)?

3) regardless of the type of regression i use above, do i have to include all the confounders together with the treatment again or do i simply run outcome = treatment + error . What about including the actual propensity score (ie "double robust regression").

4) If i don't use mixed models, I will use ordinary logistic regression but I will have to use clustered standard errors using the pair_id as the clustering variable is that right?

5) Regardless of how i do my clustering (mixed model or robust/clustered SEs), is it ok if I have 2 observation (1 control + 1 case) in each cluster/group? The number of groups range between 7000-1000, depending on matching efficiency.

If you have any other suggestions on how to go about it with the best degree of accuracy or any literature with evidence or recommendations for stratified complex survey designs, please advise by all means.

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