Crossing Survival Curves

A Chance To Live Longer

The ad above is based on results from the CheckMate 227 trial comparing the two immunotherapy's Optivo (Nivolumab) and Yervoy (ipilimumab) to chemo for non-small cell lung cancer. At two years, 40% of patients in immunology arm are still alive, while only 33% of chemo patients are alive.

Results May Vary

But look carefully at the chart above. Look at the curves at the 3 month mark. The ordering is reversed. About 92% of patients on chemo are alive while only 87% of the immunotherapy patients are alive. At 3 months, chemo has a five percentage point advantage of immunotherapy, but at 2 years immunotherapy has a seven percentage point advantage. So which treatment is better?

What is Going On?

To understand the problem, consider you are a doctor and you have a patient with non-small cell lung cancer. Which treatment do you recommend? There are two sets of potential outcomes. Number of months of survival with immunotherapy and number of months of survival with chemotherapy. We are interested in the difference. Which treatment leads to longer survival for that patient?

Unfortunately, this is something we cannot know.

Unlike George Bailey we cannot observe different possible futures. We cannot observe the treatment effect of each individual. We cannot even estimate the distribution of individual treatment effect. We can however, measure the distribution of outcomes for each treatment separately.

Kolmogorov Bounds