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From the abstract of a study that uses propensity score matching to assess the severity of adverse effects of electroconvulsive treatment (ECT):

In propensity score matched analyses, there were 10 016 psychiatric hospitalisation records (6628 women, 3388 men) with mean age 56·6 years (SD 16·3) and no ethnicity data available. 65 818 admissions were eligible for matching and 5008 were matched (1:1) in each exposure group.

I've read the Wikipedia page on propensity score matching, but I fail to understand, based on the abstract only, what this sentence means.

If the total number of hospitalizations equaled 10016, with 5008 receiving ECT and 5008 not receiving ECT, when where did the figure 65818 come from?

Or maybe I do not clearly understand the technique for propensity score matching. In my guessing, it's when a group of patients is found who did not receive the treatment despite being similar to the patients that received the treatment. Maybe I'm getting it wrong.

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    $\begingroup$ If you go to page 5 of the article, you will notice a pretty straightforward flowchart that explains that number. As I understand there was a greater number of eligible records for analysis not only 10016. Maybe 10016 refers to something else in the context of the article. $\endgroup$
    – Nikos H.
    Jul 13, 2021 at 13:16

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In propensity score matching, each exposed unit is paired with an unexposed unit, and the unpaired units are discarded. When matching with a caliper, paired units can only be within some distance of each other, and any treated units without a close enough pair are discarded. Because units are discarded when using matching, the analysis sample size after matching will be smaller than the original sample size. In this case, the hospital database or whatever data source was used contained 65818 eligible patients, but after matching, units were discarded such that only 10016 remained.

A nice, fairly accessible introduction to propensity score analysis is Austin (2011). An introduction to matching methods specifically (of which propensity score matching is one type) is Greifer and Stuart (2021).

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  • $\begingroup$ I wonder if you would consider editing your (excellent and upvoted answer) to state that “the hospital database used to select the 10016 matched pairs (5008 patients who had undergone electroconvulsive therapy and 5008 who had not) contains information on 65818 psychiatric hospitalizations. The outcome measures used a separate database of information on medical hospitalizations.” This abstract is exceptionally poorly written and the Lancet paywall will preclude many readers from accessing the full-text and methods. I think this edit might help such readers. $\endgroup$ Aug 25, 2021 at 21:21
  • $\begingroup$ Thank you for the kind words, but I'm not sure how that addition clarifies anything. There were 65818 records in the original dataset and 10016 were selected by the matching method. That is explained clearly in the excerpt from the OP's post and is the only information needed to interpret this scenario. $\endgroup$
    – Noah
    Aug 26, 2021 at 0:32
  • $\begingroup$ OK. The distinction between psychiatric hospitalizations (used to selected the treated/untreated) and medical hospitalizations (used to define outcomes) is not really a propensity score / statistical issue. More study design/methods. $\endgroup$ Aug 26, 2021 at 14:56

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