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Aug 3, 2023 at 20:15 comment added RobertF In special cases where the # of variables selected for a causal inference model exceed the # sample size, can we still obtain an unbiased estimate of the treatment effect using regression (eg, using a variant of Lasso or ridge regression) or is propensity score matching our best option? (See my question here: stats.stackexchange.com/questions/623100/…)
May 1, 2021 at 21:13 comment added robertspierre The topic is also covered in this video at minute 12
May 1, 2021 at 18:14 comment added robertspierre @FrankHarrell Thank you very much for your explanations. They are much appreciated.
May 1, 2021 at 11:13 comment added Frank Harrell Yes under these restrictions: continuous covariates have linear effects (since you didn't mention including nonlinearity), there are no interactions, all covariates meeting your (1) and (2) are included, and the model and distributional assumptions are satisfied. If an important covariate has no distributional overlap between treatment groups the linearity and lack of interaction assumptions are paramount.
Apr 30, 2021 at 22:28 comment added robertspierre So "ordinary covariate adjustment without PS works just fine" means that my OLS model, with dependent variable = outcome, and independent variable = dummy for treatment + any covariate that (1) co-explains the outcome (2) explains the selection into treatment (is correlated with the treatment dummy), works, also if the distribution of those covariates differ between the treatment group and the control group?
Apr 30, 2021 at 18:22 history edited Frank Harrell CC BY-SA 4.0
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Apr 30, 2021 at 17:17 comment added usεr11852 Thank you for clarifying. (Sorry for being pushy but I wanted you to say it because people think that "covariance adjustment" is some magical methodology aside their standard regression modelling - which is of course magical in itself.) :)
Apr 30, 2021 at 17:02 comment added Frank Harrell Yes I meant more standard regression modeling adjusting for covariates including those that would have been in the PS.
Apr 30, 2021 at 13:55 comment added robertspierre @usεr11852 Yes it would be very useful for me to clarify the difference
Apr 30, 2021 at 12:47 comment added usεr11852 +1 but I think ones needs to clarify how "covariate adjustment without PS" is any different from "regression controlling for the covariates" that the OP suggest. Otherwise we are playing with words.
Apr 30, 2021 at 12:20 history answered Frank Harrell CC BY-SA 4.0