Data maturity and follow-up in time-to-event analyses

Abstract

We propose methods to determine the minimum number of subjects remaining at risk after which Kaplan-Meier survival plots for time-to-event outcomes should be curtailed, as, once the number remaining at risk drops below this minimum, the survival estimates are no longer meaningful in the context of the investigation. The size of the decrease of the Kaplan-Meier survival estimate S(t) at time t if one extra event should occur is considered in two ways. In the first approach, the investigator sets a maximum acceptable absolute decrease in S(t) should one extra event occur. In the second, a minimum acceptable number of subjects still at risk is calculated by comparing the size of the decrease in S(t) if an extra event should occur with the variability of the survival estimate had all subjects been followed to that time (confidence interval approach). We recommend calculating both limits for the number still at risk and then making an informed choice in the context of the particular investigation. We explore further how the amount of information actually available can assist in considering issues of data maturity for studies whose outcome of interest is a survival percentage at a particular time point. We illustrate the approaches with a number of published studies having differing sample sizes and censoring issues. In particular, one study was the subject of some controversy regarding how far in time the Kaplan-Meier plot should be extended. The proposed methods allow for limits to be calculated simply using the output provided by most statistical packages.

Keywords: Kaplan-Meier curve; data maturity; data presentation; follow-up; number at risk; percentage of actual information available; sensitivity index; time-to-event.