title: Moving beyond the hazard ratio in quantifying the between-group difference in survival analysis.
abstract: In a longitudinal clinical study to compare two groups, the primary end point is often the time to a specific event (eg, disease progression, death). The hazard ratio estimate is routinely used to empirically quantify the between-group difference under the assumption that the ratio of the two hazard functions is approximately constant over time. When this assumption is plausible, such a ratio estimate may capture the relative difference between two survival curves. However, the clinical meaning of such a ratio estimate is difficult, if not impossible, to interpret when the underlying proportional hazards assumption is violated (ie, the hazard ratio is not constant over time). Although this issue has been studied extensively and various alternatives to the hazard ratio estimator have been discussed in the statistical literature, such crucial information does not seem to have reached the broader community of health science researchers. In this article, we summarize several critical concerns regarding this conventional practice and discuss various well-known alternatives for quantifying the underlying differences between groups with respect to a time-to-event end point. The data from three recent cancer clinical trials, which reflect a variety of scenarios, are used throughout to illustrate our discussions. When there is not sufficient information about the profile of the between-group difference at the design stage of the study, we encourage practitioners to consider a prespecified, clinically meaningful, model-free measure for quantifying the difference and to use robust estimation procedures to draw primary inferences.
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Hajime
authors: H
authors: Uno
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Brian
authors: B
authors: Claggett
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Lu
authors: L
authors: Tian
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Eisuke
authors: E
authors: Inoue
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Paul
authors: P
authors: Gallo
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Toshio
authors: T
authors: Miyata
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Deborah
authors: D
authors: Schrag
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Masahiro
authors: M
authors: Takeuchi
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Yoshiaki
authors: Y
authors: Uyama
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Lihui
authors: L
authors: Zhao
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Hicham
authors: H
authors: Skali
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Scott
authors: S
authors: Solomon
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Susanna
authors: S
authors: Jacobus
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Michael
authors: M
authors: Hughes
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX.
authors: Milton
authors: M
authors: Packer
authors: Hajime Uno, Deborah Schrag, and Susanna Jacobus, Dana-Farber Cancer Institute; Brian Claggett, Hicham Skali, and Scott Solomon, Harvard Medical School, Brigham and Women's Hospital; Michael Hughes and Lee-Jen Wei, Harvard School of Public Health, Boston, MA; Lu Tian, Stanford University School of Medicine, Palo Alto, CA; Eisuke Inoue and Masahiro Takeuchi, Kitasato University; Toshio Miyata, Health and Global Policy Institute; Yoshiaki Uyama, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan; Paul Gallo, Novartis Pharmaceuticals, East Hanover, NJ; Lihui Zhao, Northwestern University Feinberg School of Medicine, Chicago, IL; and Milton Packer, University of Texas Southwestern Medical Center, Dallas, TX. wei@hsph.harvard.edu.
authors: Lee-Jen
authors: LJ
authors: Wei
mesh_terms: D006801:Humans; D008137:Longitudinal Studies; D016016:Proportional Hazards Models; D016019:Survival Analysis