# Propensity score and Cox regression

I have a retrospective dataset of patients treated with a certain drug (treatment, $n=46$) or with placebo (control $n=96$). The stored variables are age, sex, stage of disease. I want to assess the effect of treatment on overall survival with propensity score. Here are the steps I followed:

1. I calculated propensity score with a binary logistic regression model using treatment as dependent variable and age, sex, stage as covariates.
2. I used fuzzy matching to create a 1:1 matching with 0.05 tolerance.
3. I deleted the unmatched cases and obtained a dataset of 46*2 cases (46 treated, 46 controls).
4. I used a Cox proportional regression model using propensity score and treatment as covariates.

Is my procedure correct? I'm using SPSSv19.

• Seems sensible to me – Peter Flom - Reinstate Monica Oct 16 '13 at 13:21
• You are assuming that the hazard ratio associated with treatment does not substantially depend on the propensity score (i.e. on the variables used for matching). – Michael M Oct 16 '13 at 15:38
• Actually, the HR may substantially depend on age: older people have more comorbidities and this could influence treatment they had been given. How should I proceed? I thought to add the variable age as a covariate in the Cox regression. Correct? – Andrea Oct 16 '13 at 18:01
• @MichaelMayer Shouldn't including those variables within the propensity score model cancel out the association if modeled correctly - that's my understanding of the whole point of propensity scores. Andrea, you could include the variables as well in a "doubly robust" analysis. See: aje.oxfordjournals.org/content/early/2011/03/08/aje.kwq439.full – Fomite Apr 28 '14 at 7:53
• You could (I think) also use propensity score subclasses instead of 1:n matching, and then use subclasses as strata in Cox regression. This way one does not need to discard observations, which might be good if you have 'only' 150 observ. – Adam Robinsson Nov 2 '14 at 20:17