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

The American Statistician, vol. 80, pp. 100–108

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 t, Ŝ(t). We aim to review the role of the effective sample size of Ŝ(t) 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 Ŝ(t). 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.

Authors 8

1. Toby Hackmann corresponding Aachen Department of Biomedical Data Sciences

   Leiden University Medical Center

   Affiliation as printed

   Department of Biomedical Data Sciences, Leiden University Medical Center

2. Doranne Thomassen Aachen Department of Biomedical Data Sciences

   Leiden University Medical Center

   Affiliation as printed

   Department of Biomedical Data Sciences, Leiden University Medical Center

3. Anne Margarethe Stiggelbout Aachen Department of Biomedical Data Sciences

   Leiden University Medical Center

   Affiliation as printed

   Department of Biomedical Data Sciences, Leiden University Medical Center

4. Saskia le Cessie Aachen Department of Biomedical Data Sciences Department of Clinical Epidemiology

   Leiden University Medical Center

   Affiliation as printed

   Department of Biomedical Data Sciences, Leiden University Medical Center

   Department of Clinical Epidemiology, Leiden University Medical Center

5. Hein Putter Aachen Department of Biomedical Data Sciences

   Leiden University Medical Center

   Affiliation as printed

   Department of Biomedical Data Sciences, Leiden University Medical Center

6. Liesbeth C. de Wreede Aachen Department of Biomedical Data Sciences

   Leiden University Medical Center

   Affiliation as printed

   Department of Biomedical Data Sciences, Leiden University Medical Center

7. Ewout Willem Steyerberg Aachen Department of Biomedical Data Sciences

   Leiden University Medical Center · University Medical Center Utrecht

   Affiliation as printed

   Department of Biomedical Data Sciences, Leiden University Medical Center

   Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht

8. on behalf of the 4D PICTURE Consortium

   University of Ljubljana · Institute of Oncology Ljubljana

   Affiliation as printed

   Institute of Oncology Ljubljana, Medical faculty Ljubljana, University of Ljubljana