Are you asking whether one would still include covariates in a regression or ANCOVA even if the intervention groups to be compared on the outcome variable (pain) were previously created based on propensity score matching? I'd say probably not because the relevant covariates (confounders) would typically be included in the propensity score matching phase to create groups that are as "comparable" as possible. However, if later on other potential confounders become apparent, it would probably not hurt to include them in the statistical analysis of group differences (i.e., regression or ANCOVA).

uh, use matching only for reinsertion. usual regression works for the efect of the treatment indepent of scores. in the case you have a score of rehabilitate the person vs others that not so much the proponesity score is useuful. but this method has a problem, you need to ensure the study is relevant to the patient. in other case it will be bias and thats dangerous for the patient good day.

You cannot use simple or multiple regression when the outcome is binary. You might consider using logistic regression for a binary outcome if its assumptions are met. Related to your question, in regression analysis, one would like to estimate the individual effect of each covariate on the outcome variable controlling for other variables (one of the covariate can be the treatment condition). Regression is an analysis technique, it does not account for the design effect: for example, let's say, people in treatment group may have higher socioeconomic status compared to the ones in control group, they are not comparable so the resulting statistics may be biased. More unbalanced covariates may bias the results more. In propensity score matching, your goal is to account for the design effect (eliminating selection bias, endogeneity issue) when a treatment exist. You mimic randomized controlled trials by using propensity scores that ideally gives you equitable probability of subjects being included in the control or treatment group so that you can estimate treatment effect between comparable/balanced groups. So, through a correctly specified PSM model, the scores of covariates are almost equally distributed across treatment and control groups, because in PSM you are not interested in their individual effect on the outcome, you want to make sure that statistics for the covariates are almost equal for both treatment and control groups. Recalling the previous example, you use propensity scores to find individuals in control group that look like the individuals in treatment group but one gets the treatment and the other does not (or both treatment and control groups have almost equal average SES, or equal statistics of other covariates that you matched).

Jochen Wilhelm, Thanks for your comments.

Regarding your first comment, yes, a regression model adjusts for the average effect of SES on the outcome if the functional form of SES is correctly specified in the model (e.g., higher-order non-linear relationships, complex interactions etc.). However, ignoring such relationships or its relationships with other covariates may introduce bias and harm the precision of estimating model. Including too many functional forms of a covariate might make the model too complex and make the interpretation more difficult. Also, in regression, if treatment and control groups differ significantly in terms of an important covariate (let's say SES), regression model uses information from incomparable/unbalanced units, which is a form of extrapolation. So, in terms of precision, interpretability, and extrapolation and model-mispecification bias, there are differences: regression is more efficient if modeled correctly, but PSM estimates are more robust to these biases (of course, PSM model should also be modeled correctly). Their estimates wouldn't differ drastically; however, PSM discards some non-matched samples but provides more robust and precise estimates on observed&balanced data, mimicking randomization process.

Second, propensity scores used in PSM procedure are obtained through logit or probit models, but the main purpose is to obtain a balanced treatment and control samples in which the distribution of confounders (such as SES) is almost equal (to obtain samples that have a very much smaller bias) across treatment and control groups. These confounding variables are used in logit model to balance the samples through weights obtained by their probabilities, and we are interested in whether a very large portion of bias in these confounders is eliminated post-matching. We make sure that the average treatment effect is calculated on the treatment and control subjects that have similar characteristics prior to the treatment condition. So, these confounders are not used directly to estimate average treatment effects; they are only used to match the groups and eliminate sampling bias as much as possible; logit/probit models are conducted prior to estimating average treatment effect; the use of these models is for the design, not the analysis for treatment effects. [Note: IPTW weights are used in logit or regression models but they are not part of the discussion about PSM].

I hope these answers clarify my first comments.

Jochen Wilhelm, thank you for your kind words.

I recently conducted a PSM analysis. I understand a single vector sounds simplistic, I felt the same then; but PSM modeling procedure includes the introduction of theoretically justified interaction terms or higher-order terms when post-matching biases (the difference in standardized means of confounders between treatment and control groups) are not minimized. Model adjustments continue until a balanced sample is obtained (when each confounders has a standardized bias less then 10% or 5%, but preferably much less).

So, the modeling process continues if the assumptions of PSM (Guo & Frazer, 2014) are met and the evidence for the treatment effects are deemed valid if and only if these assumptions are met, which is more easily satisfied when theoretically justified model specifications are established (statistical balance of covariates is one of the assumptions). Guo & Frazer (2014) explains the procedure and assumptions in more details.

Rosenbaum & Rubin's (1983) article is a little technical to me, which statistically explains the method, but I interpret the PSM procedure as that the logistic (or probit) regression compresses all the predictive information about covariates into a single vector of propensity scores (roughly, individuals' odds of being in the treatment group conditional on specified covariates), which is just one of the combination of many propensity scores, that changes with model adjustments until the balance between treatment and control group is observed. It is a bit counterintuitive. In summary, the goal of PSM analysis is to obtain the propensity scores of a balanced treatment and control groups and to interpret only the ATE/ATT of that balanced sample.

References:

Guo, S., & Fraser, M. W. (2014). Propensity score analysis: Statistical methods and applications (Vol. 11). SAGE publications.

Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1), 41-55.

Personally, my opinion is that propensity score analysis is more advantageous in my field, because regression analysis assume that each variable is measured correctly without error. For laboratory studies and some suitable fields, this can be achieved. However, for social sciences including psychology or education, it is practically very hard to measure a variable/construct without error (beside sampling bias). Both models should be specified with theoretical justifications with a comprehensive literature review, but in my opinion, matching techniques has more advantage to make more correct and precise inferences (of course except for randomized controlled trials).