Should we still use pointwise confidence intervals for the Kaplan–Meier estimator?

To represent uncertainty in survival analysis, the Kaplan–Meier estimator is frequently presented, along with pointwise confidence intervals, though rarely with confidence bands. Using theoretical reasoning and simulations, this paper investigates the coverage properties and interpretation of pointwise confidence intervals. In addition, we examine the technicalities and potential pitfalls of confidence bands. As both the sample size and the number of events increase, the simultaneous coverage of pointwise confidence intervals decreases. The portion of the survival curve covered by interconnected pointwise confidence intervals corresponds to the nominal coverage of pointwise confidence intervals. Contrary to expectations, most confidence bands cover only a portion of the survival curve. The coverage of confidence bands built for the entire curve may be below the nominal coverage. Despite their limitations, pointwise confidence intervals remain practical and easy to use for illustrating uncertainty in survival estimates. They do not cover a continuous portion of the survival curve but, on average, cover a portion equal to the pointwise nominal confidence level.