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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.

Project description:In the analysis of networks we frequently require the statistical significance of some network statistic, such as measures of similarity for the properties of interacting nodes. The structure of the network may introduce dependencies among the nodes and it will in general be necessary to account for these dependencies in the statistical analysis. To this end we require some form of Null model of the network: generally rewired replicates of the network are generated which preserve only the degree (number of interactions) of each node. We show that this can fail to capture important features of network structure, and may result in unrealistic significance levels, when potentially confounding additional information is available.We present a new network resampling Null model which takes into account the degree sequence as well as available biological annotations. Using gene ontology information as an illustration we show how this information can be accounted for in the resampling approach, and the impact such information has on the assessment of statistical significance of correlations and motif-abundances in the Saccharomyces cerevisiae protein interaction network. An algorithm, GOcardShuffle, is introduced to allow for the efficient construction of an improved Null model for network data.We use the protein interaction network of S. cerevisiae; correlations between the evolutionary rates and expression levels of interacting proteins and their statistical significance were assessed for Null models which condition on different aspects of the available data. The novel GOcardShuffle approach results in a Null model for annotated network data which appears better to describe the properties of real biological networks.An improved statistical approach for the statistical analysis of biological network data, which conditions on the available biological information, leads to qualitatively different results compared to approaches which ignore such annotations. In particular we demonstrate the effects of the biological organization of the network can be sufficient to explain the observed similarity of interacting proteins.

Dataset Information

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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