Adjusted Survival Curves

Suppose we want to investigate to what extent some factor influences survival, as an example we might compare the experience of diabetic patients who are using metformin versus those on injected insulin as their primary treatment modality. There is some evidence that metformin has a positive influence, particularly in cancers, but the ascertainment is confounded by the fact that it is a first line therapy: the patients on metformin will on average be younger and have had a diabetes diagnosis for a shorter amount of time than those using insulin. “Young people live longer” is not a particularly novel observation. The ideal way to test this is with a controlled clinical trial. This is of course not always possible, and assessments using available data that includes and adjusts for such confounders is also needed. There is extensive literature — and debate — on this topic in the areas of modeling and testing. The subtopic of how to create honest survival curve estimates in the presence of confounders is less well known, and is the focus of this note. Assume that we have an effect of interest x and a set of possible confounding variables c. There are two main approaches to adjustment. The first approach, sometimes known as marginal analysis, modifies the data so that the confounders c are balanced across the factor of interest x, we can then proceed with simple analysis of survival versus x using the reformulated data, ignoring the confounders. The second approach seeks to understand and model the effect of each confounder, with this we can then correct for them. This is often called the conditional approach since we are examining the conditional survivals given x and c. From these conditional survivals average curves are created that balance on the confounder. As shown below, these differ essentially in the order in which the two necessary operations are done, balancing and survival curve creation.