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On confidence intervals for the hazard ratio in randomized clinical trials.

ABSTRACT: The log-rank test is widely used to compare two survival distributions in a randomized clinical trial, while partial likelihood (Cox, 1975) is the method of choice for making inference about the hazard ratio under the Cox (1972) proportional hazards model. The Wald 95% confidence interval of the hazard ratio may include the null value of 1 when the p-value of the log-rank test is less than 0.05. Peto et al. (1977) provided an estimator for the hazard ratio based on the log-rank statistic; the corresponding 95% confidence interval excludes the null value of 1 if and only if the p-value of the log-rank test is less than 0.05. However, Peto's estimator is not consistent, and the corresponding confidence interval does not have correct coverage probability. In this article, we construct the confidence interval by inverting the score test under the (possibly stratified) Cox model, and we modify the variance estimator such that the resulting score test for the null hypothesis of no treatment difference is identical to the log-rank test in the possible presence of ties. Like Peto's method, the proposed confidence interval excludes the null value if and only if the log-rank test is significant. Unlike Peto's method, however, this interval has correct coverage probability. An added benefit of the proposed confidence interval is that it tends to be more accurate and narrower than the Wald confidence interval. We demonstrate the advantages of the proposed method through extensive simulation studies and a colon cancer study.

SUBMITTER: Lin DY

PROVIDER: S-EPMC5085885 | biostudies-literature | 2016 Dec

REPOSITORIES: biostudies-literature

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On confidence intervals for the hazard ratio in randomized clinical trials.

Lin Dan-Yu DY Dai Luyan L Cheng Gang G Sailer Martin Oliver MO

Biometrics 20160428 4

The log-rank test is widely used to compare two survival distributions in a randomized clinical trial, while partial likelihood (Cox, 1975) is the method of choice for making inference about the hazard ratio under the Cox (1972) proportional hazards model. The Wald 95% confidence interval of the hazard ratio may include the null value of 1 when the p-value of the log-rank test is less than 0.05. Peto et al. (1977) provided an estimator for the hazard ratio based on the log-rank statistic; the co ...[more]

PMID: 27123760

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Project description:ImportanceImmune checkpoint inhibitors (ICIs) have unique patterns of response and survival that differ from conventional chemotherapies. Novel intermediate end points are urgently required to detect the early signals of ICI activity.ObjectiveTo evaluate milestone rate (Kaplan-Meier estimates of survival probabilities at given time points) and milestone restricted mean survival time (RMST, the area under survival curves up to given time points) as potential intermediate end points for ICI trials.Data sourcesElectronic databases (pre-MEDLINE, MEDLINE, Embase, and the Cochrane Central Register of Controlled Trials) were searched for randomized clinical trials published between January 1, 2000, and December 31, 2017.Study selectionPhase 2 and phase 3 randomized clinical trials evaluating ICIs in advanced solid tumors.Data extraction and synthesisTwo investigators extracted the data and reconstructed individual patient data to estimate the milestone rate or milestone RMST from the published Kaplan-Meier curves.Main outcomes and measuresTrial-level milestone rates or milestone RMSTs were estimated for 6-month and 9-month progression-free survival (PFS) and 9-month and 12-month overall survival (OS). A weighted linear regression model evaluated the correlations of ratios of milestone rates or milestone RMSTs with OS hazard ratios (HRs).ResultsTwenty-six trials examining 8 different tumor types were identified, including 12 892 patients. Overall survival HR was correlated with the ratio of 9-month OS milestone rate (R2 = 0.45; 95% CI, 0.27-0.74), and with the ratio of 12-month OS milestone rate (R2 = 0.40; 95% CI, 0.22-0.70). The ratio of 9-month OS milestone RMST (R2 = 0.60; 95% CI, 0.28-0.74) and ratio of 12-month OS milestone RMST were correlated with OS HR (R2 = 0.64; 95% CI, 0.42-0.78). No correlations were observed between OS HR and the ratio of 6-month or 9-month PFS milestone rates or milestone RMSTs.Conclusions and relevanceRatios of OS milestone RMSTs had a stronger correlation with OS HRs than ratios of OS milestone rates, whereas ratios of PFS milestone rates and ratios of PFS milestone RMSTs were not correlated with OS HRs. The OS milestone RMST could be further studied as an intermediate end point in future ICI trials.

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On confidence intervals for the hazard ratio in randomized clinical trials.

Publications

On confidence intervals for the hazard ratio in randomized clinical trials.

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