Visualizing Time-Varying Effect in Survival Analysis: 5 Complementary Plots to Kaplan-Meier Curve

Abstract

Background. Kaplan-Meier (KM) curve has been widely used in the field of oxidative medicine and cellular longevity. However, time-varying effect might be presented in KM curve and cannot be intuitively observed. Complementary plots might promote clear insights in time-varying effect from KM curve. Methods. Three KM curves were identified from published randomized control trials: (a) curves diverged immediately; (b) intersected curves with statistical significance; and (c) intersected curves without statistical significance. We reconstructed individual patient data, and plotted 5 complementary plots (difference in survival probability and risk difference, difference in restricted mean survival time, landmark analyses, and hazard ratio over time), along with KM curve. Results. Entanglement and intersection of two KM curves would make the 5 complementary plots to fluctuate over time intuitively. Absolute effects were presented in the 3 plots of difference in survival probability, risk, and restricted mean survival time. Changed $P$ values from landmark analyses were used to inspect conditional treatment effect; the turning points could be identified for further landmark analysis. When proportional hazard assumption was not met, estimated hazard ratio from traditional Cox regression was not appropriate, and time-varying hazard ratios could be presented instead of an average and single value. Conclusions. The 5 complementary plots with KM curve give a broad and straightforward picture of potential time-varying effect. They will provide clear insight in treatment effect and assist clinicians to make decision comprehensively.