Measures of follow-up in time-to-event studies: Why provide them and what should they be?

Abstract

Background/aims: There is some consensus among authors of reports of clinical studies that a measure of follow-up time is informative for the interpretation of the Kaplan-Meier estimate of the survivor function of the event time of interest. Previous authors have suggested that length of follow-up is important to report because the findings of a study should be extracted from the time frame in which most of the subjects have had the event or have remained under observation. This time frame is where the Kaplan-Meier estimate is most stable. This concept of stability is relative to the potential maximum information about the event time distribution contained in the sample; it is not relative to the true, population survivor function. A measure of stability is useful for the interpretation of an interim analysis in which an immature survivor function is presented. Our interest in this article lies in characterizing the unobserved, complete follow-up Kaplan-Meier estimate based on the observed, partial follow-up estimate. Our focus is not on characterizing the true event time distribution relative to its estimate. The concept of stability has not been well-defined in the literature, which has led to inconsistency and lack of transparency across trials in their attempts to capture it through a variety of measures of follow-up.

Methods: We report the results of a survey of recent literature on cancer clinical trials and summarize whether follow-up is reported and if so, whether it is well-defined. We define commonly used measures of follow-up in clinical studies.

Results: We explain how each measure should be assessed to evaluate the stability of the Kaplan-Meier estimate for the event, and we identify relationships among measures. We propose a new measure that better conveys the desired information about the stability of the current Kaplan-Meier estimate relative to one based on complete follow-up. We apply the proposed measure to a meningioma study for illustration.

Conclusion: It is useful for reports of clinical studies to supplement Kaplan-Meier estimates with quantitative assessments of the stability of those estimates relative to the potential follow-up of study participants. We justify the use of one commonly used measure, and we propose a new measure that most directly accomplishes this goal.

Keywords: Censoring; clinical trials; observation time.

Figure 1

Kaplan Meier estimate of survivor function for overall survival, X, with 95% confidence intervals and numbers at risk.

Figure 2

Proposed upper and lower limits for Kaplan Meier.

Figure 3

Kaplan Meier estimates of survivor functions for time to censoring, C, observation time, T, and time to censoring among those who are censored, C|C

Figure 4

Difference curve between upper and lower limits of Kaplan Meier and partial difference curves between Kaplan Meier and upper and lower limits.