Thread by @ihtanboga

PS is the probability of tx assignment based on baseline covariates. b/c PS idea mimics an RCT, researchers've extensively used.
used PS with caution instead of banning is a solution. In the next tweets, I’m going to specify some critics on PS methods.1/

https://twitter.com/CMichaelGibson/status/1120299514575900672

@CMichaelGibson @KalayciArzu @venkmurthy @raj_mehta @MaartenvSmeden @ADAlthousePhD @drjohnm @SABOURETCardio @bogdienache @boback

A PS is defined as the probability of a patient being assigned to an intervention, given a set of covariates. PS summarizes all patient characteristics into a single covariate. Then, all patients have calculated PS using covariates.2/

All variables related to the outcome and/or the tx decision should be included to estimate PS.However, variables that largely associated with the tx decision but not outcome should not be included.Lets not forget, PS is not magical, it is only as good as included covariates.3/

After generating PS, one can choose following PS methods; #1 and #2 dont use whole dataset, however, #3 and #4 use whole dataset.

1) PS matching
2) Stratification
3) Inverse probability weighting
4) Multivariable regression using PS as a covariate 4/

PS Matching tries to find pts with similiar PS in treatment groups then gave good measured covariates balance (!!). The main problem is that TOO MANY pts excluded (reduced effective sample size). This results in a loss of both precision, power and generalizability. 5/

Even after well balanced (!!) PS matched population, covariate adjustment for strong prognostic factors must be used to get the more precise tx effects, due to non-collapsibility of odds and hazards ratios.
Does anyone see a paper use cov adj after PSM? (I never saw) 6/

Why PS matching may not useful ( or should not be used) ?
1-PS deal with confounding not outcome heterogeneity
2-matching algorithm is possibly arbitrary and not reproducible
(7/)

3-PSM exclude many of pts >> reduce effective sample size, power
4-many PSM user do not take interaction/non-linearity into account
5-many PSM user ignore the non-collapsability of OR/HR (8/)

@stephensenn’s paper; PS methods (stratification for the PS in their paper) is inefficient/illogical/inferior to good traditional regression model. (9/)

In obs studies, need to adjust for non-random tx selection. Sometimes no confounders can be too many. To reduce the risk of overfitting, @f2harrell’s paper; If we have too many covariates and too few case, a general approach is to use penalized MLE over PS (10/)

#pocock and @GreggWStone reported in their paper that 4 common PS methods (mathc, stratif., IPW and PS adjusted MV model) IS NOT superior to conventional regression modeling (11/)

Using PS adjusted multivariable regression may useful for prediction and for data reduction. I think it is the most useful PS based methods, but care should be taken to build the proper model.
1-Select large list of potential confounder variables to generate PS (gray).
(12/)

2-Include spline of logit PS in relating propensity to outcome (yellow).
3-finally, include pre-specified important prognostic factors in the model to account for the majority of outcome heterogeneity(green).
4-We may also assess an interaction with logit PS and real tx (13/)

PS based methods are not magical tools and none of the PS methods (PSM, IPWT) is superior to traditional regression. (14/)

Finally, traditional/modern regression methods are more useful than PS based methods, b/c preserving the effective sample size, allowing to test interaction, capture non-linearity. In addition, IMO, PS adjusted MV regression may be useful to use for data reduction (15/)