Can I use Covariate Balancing Propensity Score method to adjust for confounding in a Cox Regression model with splines?

Question

I would like to use the Covariate Balancing Propensity Score (CBPS) method to adjust for confounding because of its optimization properties.

I am doing a Cox regression model on some observed survival data and I have age as a confounder. However, as expected the age covariate breaks the proportional hazards assumption (risk of death increases with age).

One approach I took was to break age into intervals and stratify the Cox model on those intervals (basically create a new Cox model for each interval). I checked the Cox PH assumption and the non-interaction assumption and it seemed that the stratified model fixed the problems.

I was able to use the CBPS method to calculate weights to then use in my stratified model. However, I am learning from Frank Harrell that this approach is is dangerous for many reasons. His preferred approach on continuous covariates such as age is to approximate it using a spline instead of breaking it up into intervals. If do this I am not sure I can implement the CBPS method anymore.

Should I abandon the CBPS method and calculate the propensity score using a less optimal method where I can incorporate splines? Thank you in advance for any insight!

Answer 1

A couple of remarks: What you call a "covariate balancing propensity score" is simply a "propensity score". Rubin shows the effect of weighting, adjusting, or matching (WAM) by such a score effectively balances covariates, and thus precludes confounding. As far as optimality properties, propensity scores do not boast any clear advantage over covariate adjustment for linear models, however both are optimal in the sense that they provide unbiased inference. Confounding is bias. Confounders must be controlled for to reduce that bias. One must perform either multivariate adjustment or a propensity score WAM to do so.

Bear in mind propensity scores are estimated by modeling exposure risk--or more specifically chance of being included in the sample as an exposed participant. In either case, possible non-linearities can contribute to what is called residual confounding: that is that a covariate was appropriately adjusted in the model, but the shape of its effect was crude or wrong so either the wrong participants are WAMed for the covariate effect on outcome/exposure. Propensity scores are as equally prone to residual confounding as covariate adjustment.

Splines can prevent residual confounding. They provide flexible non-linear predictions that interpolate trends. Splines can be included in either exposure-risk (propensity score) models, or in the final model. The cost of splines is a large number of model parameters and possible overfitting. Crossvalidation can aid in evaluating a bias/variance tradeoff and a sparse but flexible non-linear interpolation of either outcome via splines. By all means you can hybridize the approaches (splines in the exposure model or splines in the outcome model), but be mindful of power and sample size issues.