Understanding Kaplan-Meier and Survival Statistics

Purpose: This paper aims to explore the mathematics of Kaplan-Meier and survival statistics, explain how the mathematics are relevant for prosthodontic treatment planning, and provide advice for future presentation of such data. Materials and Methods: The mathematics of the Kaplan-Meier and related survival statistic formulas were explored with hypothetical data consisting of 100 prostheses, reviewed yearly for 10 years. The hypothetical impact of failures (n = 1, 2, 9, or 0) and censored data (n = 5, 9, or 10) were reviewed across three life tables and survival curves. Actual published data of 304 porcelain veneers, reviewed regularly for 16 years, were similarly utilized. The impact of changing the number of failures and censored data on the estimated cumulative survival (ECS) and the standard error (SE) was reviewed across two life tables and survival curves. Results: The ECS and SE are calculated from two data figures: the number of failures that occurred during an interval and the number of prostheses at risk during that same interval. The ECS reduces and its SE enlarges when prostheses fail. These results can also change if prostheses are lost from the study (censored). However, the number of failures is in the numerator of the equation. Therefore, if no failures occur, loss of prostheses from the study cannot change the ECS or the SE. This can dramatically affect the calculated ECS and SE if a prosthesis becomes lost to follow-up rather than presenting as a failure. The hypothetical and actual data were used to explore these concepts. Conclusion: Current techniques for analysis of time-to-event data are imperfect and can be misleading. It therefore behooves authors to strive to improve reporting transparency, journals to support such industry, and readers to remain mindful that the cumulative survival is an estimate, ie, a reflection of reality.