Solved – Propensity score weighting in Cox PH analysis and covariate selection

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Regarding propensity score weighting (IPTW) when doing Cox proportional hazard modeling of time-to-event survival data:

I have prospective registry data where we're interested in looking at treatment effect of a medication that in most cases the patients were already taking at baseline. I'm therefore not sure how to best analyze the data. Potentially, some of the baseline variables are to a substantial degree influenced by the treatment and not the other way around (e.g. certain biomarkers). I'm a bit lost as to which covariates I should include in the propensity score model for estimating weights and which covariates I should include as covariates in the coxph model (if any at all). Any hints in the right direction would be helpful! I haven't been able to find any literature regarding this in CoxPh modeling as of yet.

I'm thinking that covariates that represent treatments instituted at baseline that (might) influence the outcome should be included as Cox PH covariates, but I'm not sure of this.

How do I determine which variables should be included as covariates in the Cox model instead of being used in calculating the propensity score weights?

Follow-up question:

I understand the inherit problem of evaluating a treatment effect of a certain intervention that has already begun – i.e. is prevalent among the patients, prior to start of observation. Both in regards to introducing bias related to time-variation of the risk (e.g. adverse side effects more common the first year of therapy) and covariates being affected by treatment. If I'm not mistaken – this has been proposed as a cause of discrepancy between observational and randomized that in regards to cardiovascular endpoints and hormon replacement therapy. In my dataset on the other hand, we're interested in looking at an possible adverse effect of the treatment.

If I use propensity score adjustment to investigate the treatment effect among prevalent users, i.e. already using the medication before observation starts, in cohort data and we observe an adverse effect of a pharmacological therapy (and this is what we were looking for). Can I rule out the possibilty of overestimating the risk associated with the treatment? I.e. as long as the risk is significantly elevated, it's most "definitely" not protective?

I can't quite picture an example where this kind of bias can introduce an overestimation of risk of falsy risk association in this context.

Best Answer

In theory, every variable you select as part of the propensity score weight need not be included as covariates in the model, because the weighting has already controlled for their potential confounding. With a proper weighting model you can, quite literally, just model the effect of the exposure.

That being said, there are reasons you may wish to include terms in the model:

  • "Doubly robust" estimates. There is no reason, save for a loss in precision, that you cannot use variables both in the weighting model and as covariates. In theory, you are protecting yourself against confounding two ways (hence this technique being referred to as "doubly robust"). Keep in mind this only protects you against either the PS model or the covariate model being misspecified by giving you a "second chance" to specify the correct model, it isn't a magic fix-all.
  • Multiple estimates of interest. Weighting makes the effect estimates from the covariates disappear - if you want a regression coefficient for the variable, you're going to want to include it as a covariate in the CoxPH step and not in the PS model.

Try searching for "Doubly robust" and similar terms in journals like Epidemiology or The American Journal of Epidemiology as well as the biostatistical literature and you should uncover some useful sources.

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