# Using propensity scores as continuous variable in Cox model to estimate treatment effect

I am exploring various methods of covariate adjustment to estimate treatment effects. These include - matching, weighting (IPTW) and use of propensity scores as a continuous variable in the cox model.

Here is a fully reproducible R script

library("survival")
library("survminer")
library("MatchIt")
data("ovarian")

summary(as.factor(ovarian$$rx)) ovarian$$rx <- ifelse(ovarian\$rx==1, 1, 0)
ps <- matchit(rx ~ age + resid.ds + ecog.ps, data = ovarian, method="nearest")

propensity_scores <- ps$$distance ovarian$$ps <- propensity_scores

cox_model <- coxph(Surv(futime, fustat) ~ rx + ps, data = ovarian)
summary(cox_model)
Call:
coxph(formula = Surv(futime, fustat) ~ rx + ps, data = ovarian)

n= 26, number of events= 12

coef exp(coef) se(coef)      z Pr(>|z|)
rx  0.6105    1.8414   0.5908  1.033    0.301
ps -1.1348    0.3215   5.3374 -0.213    0.832

exp(coef) exp(-coef)   lower .95 upper .95
rx    1.8414     0.5431 0.578463044     5.862
ps    0.3215     3.1104 0.000009204 11230.137

Concordance= 0.624  (se = 0.082 )
Likelihood ratio test= 1.1  on 2 df,   p=0.6
Wald test            = 1.08  on 2 df,   p=0.6
Score (logrank) test = 1.11  on 2 df,   p=0.6


As you can see, I have used the propensity scores from the logistic regression model as a continuous variable to estimate treatment effect. I did this without matching or weighting.

This means that the Cox regression model has been adjusted with the propensity of being assigned to treatment for each patient. This way, I do not intend to include all the covariates in the Cox model. Instead I just used the propensity score as a continuous variable in the model.

Questions:

1. Can we compare the hazard ratios from such a Cox model with those of Cox models who are generated by using only the matched patients (propensity score matching like 1:1 nearest neighbor matching) and Cox models weighted by IPTW weights.
2. How do I generate adjusted Cox survival curves for the two treatment groups from the Cox model?
• Check out my answer here, which is about the difference between matching and covariate-adjusted Cox regression. It applies to weighting and PS-adjusted Cox regression.
– Noah
Commented Jul 30, 2020 at 6:14
• @Noah Thanks. I see that the difference would be that if I use matching or weighting, the estimated HR from a Cox model which only uses the treatment variable as the independent variable would be a marginal adjusted HR. Now, if I use the propensity scores as continuous variable in addition to the treatment variable, the estimated HR would be a conditional adjusted HR. Would the survival curves be different then between the methods for the same data? Commented Jul 30, 2020 at 7:16
• Yes, though probably only slightly. There is probably more uncertainty around the survival curves in each method than there are differences among methods.
– Noah
Commented Jul 30, 2020 at 8:04