When a caliper is used, two patients with similar but not identical scores can be matched to one another. But if you require an *exact* match of the PS, that can almost only be achieved with patients that have the same covariate values used to compute the PS.
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Replying to @ADAlthousePhD @MarkHoofnagle and
Unless two *covariates* in the PS model have exactly the same regression coefficient (in which case you could match a 67 year old smoker without diabetes to a 67 year old nonsmoker with diabetes - if smoking & DM had **exactly** the same regression coefficient in the PS model)...
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Replying to @ADAlthousePhD @MarkHoofnagle and
...but if each variable included in the PS model has a unique value of the regression coefficient, then the only “exact matches” on the PS will be patients that have exactly the same covariate values.
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Replying to @ADAlthousePhD @MarkHoofnagle and
This paper has plenty of things to critique, but I do not believe this is a copy-paste error nor is it fraudulent (at least, not based on this column of this table). In fact I would be more concerned if *exact matches* on the PS did *not* look like this.
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Replying to @ADAlthousePhD @MarkHoofnagle and
Andrew Althouse Retweeted Eric Weinhandl
As
@eric_weinhandl pointed out here: https://twitter.com/eric_weinhandl/status/1280630034894479360?s=21 …https://twitter.com/eric_weinhandl/status/1280630034894479360 …Andrew Althouse added,
Eric Weinhandl @eric_weinhandlReplying to @eric_weinhandl @SteveJoffeOTOH, maybe that is the explanation? The authors found only 96 (of 1985) HCQ-exposed patients with PS values that were exactly equal to HCQ-unexposed patients. These 192 patients occupied cells with perfectly equal covariate vectors—indeed, all covariates are binary.1 reply 0 retweets 4 likes -
Replying to @ADAlthousePhD @MarkHoofnagle and
I’m literally in the hospital with my wife and a newborn right now, otherwise I would make up a simulated dataset and R code to try and illustrate this. If you want to do it yourself, generate a dataset with a bunch of binary covariates, then...
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Replying to @ADAlthousePhD @MarkHoofnagle and
...run a propensity score matching algorithm with a caliper distance of 0, and examine the matched pairs you end up with. They’ll probably all be perfect matches on every covariate the included in the PS model.
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Replying to @ADAlthousePhD @MarkHoofnagle and
(The fact that the authors did this raises other red flags, most notably that no one really uses propensity score matching this way, just clarifying that the exact match of the two columns is oddly enough consistent with what they said they did)
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Replying to @ADAlthousePhD @MarkHoofnagle and
Agree. They used 21 dichotomized (!) characteristics for propensity score matching. Plus treatment, that yields 2^22 possible combinations. It's extremely unlikely to find 190 perfect matches in a finite real world sample, except when the variables are highly correlated.
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Replying to @jhan2qt @ADAlthousePhD and
By rule of thumb the number of matches would be poisson distributed with a lambda of less than 11.9 (=2500^2/2^19). So 190 matches are unlikely.
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But in this sample, the variables are highly correlated e.g. BMI, cardiovascular complications, age, kidney disease etc. Makes it less unlikely, especially when everything is dichotomized
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Replying to @GidMK @ADAlthousePhD and
Thanks. This gave me more insight into criticism of the PS method. The algorithm finds more matches in certain subgroups, potentially biasing the results.
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Update: I have written a quick and dirty simulation and even for low intra-item correlations 190 or more matches were achieved frequently.
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