Effective Sample Size for the Kaplan-Meier Estimator: A Valuable Measure of Uncertainty?

Abstract

Sample size is an essential indicator of the uncertainty in clinical research results. When studies present time-to-event outcomes with Kaplan-Meier curves, these are often accompanied by the remaining number of patients at risk in a table below the curve. The number at risk at time t informs about uncertainty of the hazard at t, rather than the uncertainty of the estimated survival probability until (Formula presented.). We aim to review the role of the effective sample size of (Formula presented.) to reflect the uncertainty in survival probability estimation. Effective sample size is defined as the size of a hypothetical sample with complete follow-up until time t, that would give the same variance as the variance of the Kaplan-Meier estimate (Formula presented.). We consider hypothetical scenarios and a publicly available dataset with patients treated for colon cancer. These illustrations support that effective sample size provides a readily interpretable measure of uncertainty for survival curves in the presence of censoring. We show that effective sample size can also quantify the loss of information when the reporting for an ongoing study is moved to an earlier time point. In conclusion, effective sample size is a valuable measure of uncertainty in survival analysis.