A Method for Reconstructing Individual Patient Data From Kaplan-Meier Survival Curves That Incorporate Marked Censoring Times

Abstract

Introduction. Access to individual patient data (IPD) can be advantageous when conducting cost-effectiveness analyses or indirect treatment comparisons. While exact times of censoring are often marked on published Kaplan-Meier (KM) curves, an algorithm for reconstructing IPD from such curves that allows for their incorporation is presently unavailable. Methods. An algorithm capable of incorporating marked censoring times was developed to reconstruct IPD from KM curves, taking as additional inputs the total patient count and coordinates of the drops in survival. The reliability of the algorithm was evaluated via a simulation exercise, in which survival curves were simulated, digitized, and then reconstructed. To assess the reliability of the reconstructed curves, hazard ratios (HRs) and quantiles of survival were compared between the original and reconstructed curves, and the reconstructed curves were visually inspected. Results. No systematic differences were found in HRs and quantiles in the original versus reconstructed curves. Upon visual inspection, the reconstructed IPD provided a close fit to the digitized data from the published KM curves. Inherent to the algorithm, censoring times were incorporated into the reconstructed data exactly as specified. Conclusion. This new algorithm can reliably be used to reconstruct IPD from reported KM survival curves in the presence of extractable censoring times. Use of the algorithm will allow health researchers to reconstruct IPD more closely by incorporating censoring times exactly as marked, requiring as additional inputs the total patient count and coordinates of the drops in survival.

Keywords: Kaplan-Meier; algorithm; data recovery; individual patient data; survival analysis.

Graphical Abstract

This is a visual representation of the abstract.

Figure 1

Algorithm flowchart.

Figure 2

Example of published Kaplan-Meier survival curves. Takahashi M, Takahashi S, Araki N, et al. Efficacy of trabectedin in patients with advanced translocation-related sarcomas: pooled analysis of two phase ii studies. Oncologist. 2017;22(8):979–988. https://doi.org/10.1634/theoncologist.2016-0064. Creative Commons Attribution-NonCommercial-NoDerivs: https://creativecommons.org/licenses/by-ncnd/4.0/

Figure 3

Example of points to digitize to obtain coordinates of drops in survival required for the algorithm. Solid gray circles indicate required points to digitize.

Figure 4

Example of reconstructed Kaplan-Meier survival curves.

Figure 5

Example of checking the fit of reconstructed Kaplan-Meier survival curves through digitized points.

Figure 6

Kaplan-Meier survival curves reconstructed based on digitized survival data from various distributions and sample sizes. Black points mark digitized survival times and probabilities. Original and reconstructed hazard ratios are reported for comparison. Abbreviations: Orig., original; Recons., reconstructed.