Average Probability of Survival Effect

In a previous post, I claimed that it was not possible to estimate the average causal effect on survival for treatments in cancer.  It is not possible because average survival is not observed.  

Moertel et al (1990)

In another post, I pointed that the widely reported median difference in survival has no content.  This is because it is easy to come up with examples in which treatment A has higher median survival than treatment B, and yet almost all patients would live longer on treatment B.

Is there some information that can be garnered from a randomized control trial in cancer that is both measurable and would provide information to regulators, patients and doctors on the likely effect of a treatment?

There is.  It is the "average probability of survival effect".

Consider the figure to the right.  It presents survival probabilities (Kaplan-Meier plots) for the effect of adjuvant chemotherapy for stage III colon cancer patients.  The study was interested in determining whether adjuvant chemotherapy would increase survival for colon cancer patients.  Consider the 4 year mark.  At that point in time approximately 50% of the standard of care arm (observation) had survived, while approximately 70% of patients in the combination with 5-FU arm had survived.

If there is no biased attrition and no biased selection into the study, then we have unbiased estimates of the average probability of surviving to 4 years when given no chemo after surgery (50%) and the average probability of surviving to 4 years when given 5-FU after surgery (70%).  As the difference in averages is equal to the average difference we know that for the average stage III patient, taking a 5-FU based adjuvant chemotherapy increases the 4 year survival probability by twenty percentage points.

Of course, we may not be average and the policy implications of the measure are not clear, but those are discussions for another time.