What is the difference between the average treatment effect obtained from Propensity Score Matching and the Hazard Ratios?

I performed a moderation analysis according to the point "moderation analysis" https://cran.r-project.org/web/packages/MatchIt/vignettes/estimating-effects.html

Now, I have found that my three subgroups that are evident in TG as well as CG apparently do not act as a moderator for my outcome as the pairwise comparison was insignificant for all of the combinations of the three subgroups that I have.

I am wondering what this means.

Propensity scores hide outcome heterogeneity and result in effect estimates that may apply to no one and are very hard to interpret. See this chapter in my BBR notes for more details. One example helps to illustrate the problem. Suppose that a person's sex is a major predictor of outcome. Then the response variable's distribution is a mixture of two distributions and may be bi-modal. This mixing may lead to the proportional hazards assumption being violated for a non-sex variable. On the other hand conditioning on covariates recognizes outcome heterogeneity, and this has the side benefit of increasing power.

You didn't explain why the less-problem-prone ordinary covariate adjustment approach didn't work for your problem.

You never tested the moderation hypothesis on the hazard ratio, only on the censoring event. It's certainly possible for there still to be moderation of the hazard ratio.

That said, what you are asking about is standardizing the hazard ratio. There is no obvious way to do this, which is why the guide does not provide any examples of adjusting for covariates in the Cox model. If you use an additive hazards model you might be able to standardize, but not with a Cox model. The most straightforward way to get a marginal hazard ratio is to ignore subgroup membership in the Cox model, as you have done. As Frank mentions, this means the Cox model is certainly misspecified and the proportional hazards assumption is violated. In addition, marginal hazard ratios provide little useful interpretation and are confounded even in a randomized trial. If you can avoid using a Cox model, you should.

• I mean standardization in the epidemiological sense, as described here. Essentially estimating the effect within each level of another variable and averaging the effects across the variables to arrive at a single estimate. That is what we do with g-computation for the risk difference/risk ratio. But for the hazard ratio there is no obvious way to do that. So there is no clear way to get a marginal hazard ratio from a Cox regression that has covariates in it.
– Noah
Jul 13, 2023 at 18:03
• I don't understand what acg_comparisons() computes, which is the average difference in the linear predictor of the survival model, and which is quite divorced from the hazard ratio. The hazard ratio is a ratio of two (conditional) probabilities. The linear predictor of the Cox model is on an uninterpretable scale and cannot easily be used to compute the marginal hazards.
– Noah
Jul 19, 2023 at 4:52
• I can't tell you which estimand is most useful for you; you need to decide that. I can tell you how to estimate it. The usual estimand is the hazard ratio, which is estimated using a Cox regression with no covariates after matching/weighting. If you don't have censoring, the risk difference at a given time point is also useful and can be estimated as the AME of treatment in a logistic regression, which can include covariates.
– Noah
Jul 19, 2023 at 15:28
• Yes, doing a subgroup analysis (i.e., using by) is the same as doing the main analysis, just in a subgroup, so you need to use the same code in addition to supplying by.
– Noah
Jul 20, 2023 at 16:34