I have a propensity score matched data after 1-to-2 matching. Each treatment case is matched to one or two control cases. May I use paired tests to compare the outcomes? The discussion https://www.researchgate.net/post/how_is_paired_t-test_performed_for_21_case_controlled_studies_on_SPSS suggests that if a treatment case is matched to two control cases, the average of the outcomes of these two cases be compared with the treatment case outcome. Are there any other approaches? For instance, instead of the averaging, we may "double" the treatment cases matched to only one control case (and double this control case as well)? Or may be just put into the analysis all matched pairs as different pairs (each treatment case may participate in one or two such pairs)?

Or are there some special tests for one-to-many matching?

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    $\begingroup$ I think the key search term for which you are looking is stratification. Each matched set, in your case one case and two controls, corresponds to one stratum. If you had a binary outcome you would use conditional logistic regression. I do not use SPSS so have no idea what it calls stratified analyses for continuous outcomes. $\endgroup$
    – mdewey
    Oct 2, 2018 at 15:57
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    $\begingroup$ Googling "matching with multiple controls" gives a lot of relevant hits $\endgroup$ Oct 2, 2018 at 19:54
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    $\begingroup$ Not all researchers thinking you need to do a paired t-test, and so a (weighted) t-test/regression of the outcome on treatment may be sufficient. Another possibility is to use a cluster-robust standard error, where pair membership is the clustering variable. $\endgroup$
    – Noah
    Oct 2, 2018 at 20:47
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    $\begingroup$ @Viktor the exact extension would be ordinal logistic regression with cluster-robust standard errors. $\endgroup$ Oct 3, 2018 at 22:06
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    $\begingroup$ @Viktor ordinal regression with the proportional odds assumption is the regression extension of the rank test. See this answer and the comments beneath it stats.stackexchange.com/a/43897/162986 $\endgroup$ Oct 4, 2018 at 11:29


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