Estimate hazard ratios in small clinical trials without reported hazard ratios

Abstract

Abstract Background For survival studies, pooling hazard ratios (HRs) across multiple clinical trials through meta-analysis is commonly performed to achieve widely accepted and robust conclusions. However, clinical trials sometimes do not report HRs. Methods We developed a new, simple approach to estimate HRs by reconstructing life tables from Kaplan–Meier (KM) curves, particularly for small clinical trials. First, we extracted the time points and survival rates from the published KM curves. Then, we reconstructed the life table by reverse derivation of its parameters, using time points and survival rates extracted from the KM curves. Finally, we replotted the KM curves using the Kaplan–Meier method and estimated the HRs via the Cox regression method by SPSS software, using the survival data from the reconstructed life table. Results The estimated HRs of 3 examples were 0.510 (95% CI 0.272–0.958, P = 0.036), 2.472 (95% CI 1.548–3.949, P < 0.001), and 0.591 (95% CI 0.291–1.199, P = 0.145), compared with the original HRs of 0.51 (95% CI 0.27–0.96, P = 0.04), 2.33 (95% CI 1.45–3.73, P < 0.001), and 0.62 (95% CI 0.31–1.26, P = 0.18), respectively. Conclusions This simple approach allows for the estimate of HRs from published KM curves in small survival studies without reported HRs, facilitating their inclusion in meta-analyses. This increases the overall sample size and enhances the reliability of synthesized clinical evidence.

Keywords

• Hazard ratio
• Kaplan–Meier curve
• Life table
• Survival analysis
• Clinical trial