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Open accessJournal ArticleDOI: 10.1080/19466315.2021.1874507

Robust Design and Analysis of Clinical Trials With Nonproportional Hazards: A Straw Man Guidance From a Cross-Pharma Working Group

04 Mar 2021-Statistics in Biopharmaceutical Research (Informa UK Limited)-pp 1-15
Abstract: Loss of power and clear description of treatment differences are key issues in designing and analyzing a clinical trial where nonproportional hazard (NPH) is a possibility. A log-rank test may be i...

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Topics: Clinical study design (51%)
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Open accessJournal ArticleDOI: 10.1080/19466315.2019.1697738
Ray S. Lin1, Ji Lin, Satrajit Roychoudhury2, Keaven M. Anderson3  +14 moreInstitutions (8)
Abstract: The log-rank test is most powerful under proportional hazards (PH). In practice, non-PH patterns are often observed in clinical trials, such as in immuno-oncology; therefore, alternative methods ar...

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28 Citations


Open accessJournal ArticleDOI: 10.1177/0962280220907355
Malka Gorfine1, Matan Schlesinger1, Li Hsu2Institutions (2)
Abstract: This work presents novel and powerful tests for comparing non-proportional hazard functions, based on sample–space partitions. Right censoring introduces two major difficulties, which make the exis...

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9 Citations


Open accessJournal ArticleDOI: 10.1080/19466315.2020.1825522
Ray S. Lin1, Ji Lin, Satrajit Roychoudhury2, Keaven M. Anderson3  +14 moreInstitutions (8)
Abstract: We would like to thank the authors of the letter (Bartlett et al. 2020) for sharing their concerns regarding reporting treatment effect under nonproportional hazards (NPH), and we respect their pos...

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4 Citations


Open accessPosted Content
Dominic Magirr1Institutions (1)
Abstract: A fundamental concept in two-arm non-parametric survival analysis is the comparison of observed versus expected numbers of events on one of the treatment arms (the choice of which arm is arbitrary), where the expectation is taken assuming that the true survival curves in the two arms are identical. This concept is at the heart of the counting-process theory that provides a rigorous basis for methods such as the log-rank test. It is natural, therefore, to maintain this perspective when extending the log-rank test to deal with non-proportional hazards, for example by considering a weighted sum of the "observed - expected" terms, where larger weights are given to time periods where the hazard ratio is expected to favour the experimental treatment. In doing so, however, one may stumble across some rather subtle issues, related to the difficulty in ascribing a causal interpretation to hazard ratios, that may lead to strange conclusions. An alternative approach is to view non-parametric survival comparisons as permutation tests. With this perspective, one can easily improve on the efficiency of the log-rank test, whilst thoroughly controlling the false positive rate. In particular, for the field of immuno-oncology, where researchers often anticipate a delayed treatment effect, sample sizes could be substantially reduced without loss of power.

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Topics: Hazard ratio (52%)

3 Citations


Open accessPosted Content
19 May 2020-arXiv: Methodology
Abstract: In confirmatory cancer clinical trials, overall survival (OS) is normally a primary endpoint in the intention-to-treat (ITT) analysis under regulatory standards. After the tumor progresses, it is common that patients allocated to the control group switch to the experimental treatment, or another drug in the same class. Such treatment switching may dilute the relative efficacy of the new drug compared to the control group, leading to lower statistical power. It would be possible to decrease the estimation bias by shortening the follow-up period but this may lead to a loss of information and power. Instead we propose a modified weighted log-rank test (mWLR) that aims at balancing these factors by down-weighting events occurring when many patients have switched treatment. As the weighting should be pre-specified and the impact of treatment switching is unknown, we predict the hazard ratio function and use it to compute the weights of the mWLR. The method may incorporate information from previous trials regarding the potential hazard ratio function over time. We are motivated by the RECORD-1 trial of everolimus against placebo in patients with metastatic renal-cell carcinoma where almost 80\% of the patients in the placebo group received everolimus after disease progression. Extensive simulations show that the new test gives considerably higher efficiency than the standard log-rank test in realistic scenarios.

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Topics: Log-rank test (57%), Hazard ratio (56%), Clinical endpoint (52%)

2 Citations


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Book ChapterDOI: 10.1007/978-1-4612-4380-9_25
Edward L. Kaplan1, Paul Meier2Institutions (2)
Abstract: In lifetesting, medical follow-up, and other fields the observation of the time of occurrence of the event of interest (called a death) may be prevented for some of the items of the sample by the previous occurrence of some other event (called a loss). Losses may be either accidental or controlled, the latter resulting from a decision to terminate certain observations. In either case it is usually assumed in this paper that the lifetime (age at death) is independent of the potential loss time; in practice this assumption deserves careful scrutiny. Despite the resulting incompleteness of the data, it is desired to estimate the proportion P(t) of items in the population whose lifetimes would exceed t (in the absence of such losses), without making any assumption about the form of the function P(t). The observation for each item of a suitable initial event, marking the beginning of its lifetime, is presupposed. For random samples of size N the product-limit (PL) estimate can be defined as follows: L...

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Topics: Kaplan-Meier Estimate (54%), Population (52%)

51,084 Citations


Book ChapterDOI: 10.1007/978-1-4612-4380-9_37
David Cox1Institutions (1)
Abstract: The analysis of censored failure times is considered. It is assumed that on each individual arc available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations are outlined.

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Topics: Regression analysis (61%), Linear regression (61%), Accelerated failure time model (55%) ... read more

28,225 Citations


Open accessJournal ArticleDOI: 10.1056/NEJMOA1507643
Hossein Borghaei1, Luis Paz-Ares1, Leora Horn1, D. R. Spigel1  +24 moreInstitutions (1)
Abstract: BackgroundNivolumab, a fully human IgG4 programmed death 1 (PD-1) immune-checkpoint–inhibitor antibody, disrupts PD-1–mediated signaling and may restore antitumor immunity. MethodsIn this randomized, open-label, international phase 3 study, we assigned patients with nonsquamous non–small-cell lung cancer (NSCLC) that had progressed during or after platinum-based doublet chemotherapy to receive nivolumab at a dose of 3 mg per kilogram of body weight every 2 weeks or docetaxel at a dose of 75 mg per square meter of body-surface area every 3 weeks. The primary end point was overall survival. ResultsOverall survival was longer with nivolumab than with docetaxel. The median overall survival was 12.2 months (95% confidence interval [CI], 9.7 to 15.0) among 292 patients in the nivolumab group and 9.4 months (95% CI, 8.1 to 10.7) among 290 patients in the docetaxel group (hazard ratio for death, 0.73; 96% CI, 0.59 to 0.89; P=0.002). At 1 year, the overall survival rate was 51% (95% CI, 45 to 56) with nivolumab ve...

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Topics: Docetaxel (57%), Nivolumab (57%), Lung cancer (51%)

6,111 Citations


Open accessBook
11 Aug 2000-
Abstract: Introduction.- Estimating the Survival and Hazard Functions.- The Cox Model.- Residuals.- Functional Form.- Testing Proportional Hazards.- Influence.- Multiple Events per Subject.- Frailty Models.- Expected Survival.

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4,565 Citations


Journal ArticleDOI: 10.1093/BIOMET/81.3.515
Patricia Grambsch1, Terry M. Therneau2Institutions (2)
01 Sep 1994-Biometrika
Abstract: SUMMARY Nonproportional hazards can often be expressed by extending the Cox model to include time varying coefficients; e.g., for a single covariate, the hazard function for subject i is modelled as exp { fl(t)Zi(t)}. A common example is a treatment effect that decreases with time. We show that the function /3(t) can be directly visualized by smoothing an appropriate residual plot. Also, many tests of proportional hazards, including those of Cox (1972), Gill & Schumacher (1987), Harrell (1986), Lin (1991), Moreau, O'Quigley & Mesbah (1985), Nagelkerke, Oosting & Hart (1984), O'Quigley & Pessione (1989), Schoenfeld (1980) and Wei (1984) are related to time-weighted score tests of the proportional hazards hypothesis, and can be visualized as a weighted least-squares line fitted to the residual plot.

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4,183 Citations