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. 2019 Jul;24(7):867-871.
doi: 10.1634/theoncologist.2018-0141. Epub 2018 Sep 10.

How Do the Accrual Pattern and Follow-Up Duration Affect the Hazard Ratio Estimate When the Proportional Hazards Assumption Is Violated?

Miki Horiguchi  1 , Michael J Hassett  2 , Hajime Uno  3   4
Affiliations

How Do the Accrual Pattern and Follow-Up Duration Affect the Hazard Ratio Estimate When the Proportional Hazards Assumption Is Violated?

Miki Horiguchi et al. Oncologist. 2019 Jul.

Abstract

In randomized clinical trials, the magnitude of the treatment effect is often reported using the hazard ratio (HR) even when the proportional hazards (PH) assumption is not met. Conducting numerical studies, this commentary illustrates how/why the HR estimate via the standard Cox's procedure is difficult to interpret even as an “average” treatment effect for non‐PH cases.

Keywords: Clinical trials; Cox proportional hazards model; Survival data analysis; Time‐to‐event outcomes.

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Conflict of interest statement

Disclosures of potential conflicts of interest may be found at the end of this article.

Figures

Figure 1.
Figure 1.
Survival functions, hazard functions, and the ratio of two hazard functions. Survival functions (top) and corresponding hazard functions (middle) by group, and the ratio of two hazard functions (time‐specific hazard ratio) (bottom) in a pattern of proportional hazards (A) and one of non‐proportional hazards (B).
Figure 2.
Figure 2.
Four patterns of patient accrual and length of additional follow‐up. Panels (A) through (D) correspond to patterns (a)–(d) in Table 1. Abbreviations: N, total number of patients enrolled; T1, accrual period; T2, additional follow‐up period after the end of the accrual.
Figure 3.
Figure 3.
Overall survival by group with reconstructed data of the CheckMate 057 study. Kaplan‐Meier curves (top) and estimated time‐specific hazard ratio (bottom).
Figure 4.
Figure 4.
Hazard ratio estimated by Cox's procedure as a summary of the difference between two survival time distributions presented in Figure 3 with various scenarios of accrual period (T1) and additional follow‐up period after the end of accrual (T2), where T1 + T2 is the total study duration.
See this image and copyright information in PMC

References

    1. Uno H, Claggett B, Tian L et al. Moving beyond the hazard ratio in quantifying the between‐group difference in survival analysis. J Clin Oncol 2014;32:2380–2385. - PMC - PubMed
    1. Uno H, Wittes J, Fu H et al. Alternatives to hazard ratios for comparing the efficacy or safety of therapies in noninferiority studies. Ann Intern Med 2015;163:127–134. - PMC - PubMed
    1. A'Hern RP. Restricted mean survival time: An obligatory end point for time‐to‐event analysis in cancer trials? J Clin Oncol 2016;34:3474–3476. - PubMed
    1. Chappell R, Zhu X. Describing differences in survival curves. JAMA Oncol 2016;2:906–907. - PubMed
    1. Péron J, Roy P, Ozenne B et al. The net chance of a longer survival as a patient‐oriented measure of treatment benefit in randomized clinical trials. JAMA Oncol 2016;2:901–905. - PubMed

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