Abstract
Evaluation of treatment effect durability over time cannot be based on analyses that examine the first of many events. Here, it is explained how misinterpretation of survival curves led to wrong conclusions in a recent ERJ editorial. http://bit.ly/2K3amgQ
To the Editor:
Great care should be taken when assessing the consistency of treatment effect over time based on a survival curve plot, and even more so when a treatment affects a repeating event end-point, such as exacerbations, rather than an event that can occur only once, like death.
In their recent editorial in the European Respiratory Journal, Suissa and Ariel [1] make the assertation that survival functions plotted from Kaplan–Meier estimates from figure 1b in the IMPACT study [2] “clearly show that the difference in the rate of exacerbation between LAMA/LABA/ICS and LAMA/LABA over follow-up is due to the first month's surge, with practically no differences in the subsequent rates between the two groups”. However, this statement is based on a misunderstanding of the survival analyses presented.
Hypothetical example of a cumulative event plot, survival curve and gradient of survival curve presented on the same data.
The events plotted on the figure are the first moderate or severe COPD exacerbations experienced by a patient in the IMPACT study. The statements made by Suissa and Ariel [1] about exacerbation rates refer to the rate of first exacerbations only, and not to the rate of all exacerbations during the study.
Their conclusion that the rates of first exacerbations, and ratio between those rates changes over time is correct. However, this is entirely in line with statistical theory for repeated events with overall constant rates. It cannot be used to support any conclusion that the difference in the rate of exacerbation is due to a “first month's surge”. The “digitised” curve of first events behaves entirely consistently with constant rate events. Drawing any conclusions about the durability of the treatment effect on all exacerbations from this digitised plot, which shows only first exacerbations, is methodologically incorrect.
Consider a repeating event end-point (such as exacerbations) in two treatment groups, A (low constant rate) and B (high constant rate). Initially the gradient of the survival curve for the first event for treatment B (high rate) will be very steep, because all patients are “at risk” of an event. As fewer and fewer patients are left available to have a first event, the gradient will necessarily diminish. The gradient of the survival curve for the first event for treatment A (low rate) will eventually become steeper. Eventually the two survival curves for time to first event will converge despite event rates being different in both arms, as illustrated in the figure, which is described by the equations below.
Suppose that in treatment arm A events occur at a constant annual rate of 1.0, and in treatment arm B events occur with a constant annual rate of 1.5. The exponential survival functions (i.e. the functions that describe survival for events with constant hazard rates) are given by:
where t is the time in years [3]. The resulting survival curves can be plotted and it is also possible to differentiate with respect to t, to obtain the gradient 
of the survival curves, which corresponds to the digitised plot presented by Suissa and Ariel [1].
These survival curves converge, and the gradient of both curves start to diminish, with the gradient functions crossing exactly as shown in the real data (figure 1). It is important to understand this phenomenon occurs for constant rate events, and therefore its presence should not be taken as evidence that the rates are not constant.
This can be understood in the following way: the cumulative incidence or survival curve only describes the first event experienced by each patient. If treatment A consistently reduces the rate of events, then these first events will be delayed but they will still occur. While patients on treatment A are experiencing their first events there are simply fewer patients on the treatment B arm who are still “at risk” of a first event, these events having already occurred. By this point patients on treatment B are having second or third events, which are not captured by a time to first event analysis, thus the rate of their first events has diminished.
This illustrates that conclusions about the durability of the treatment effect over time cannot be based on analyses restricted to looking at only the first event of many. To imply that the treatment effect diminishes because one survival curve catches up with another is inappropriate and risks propagating incorrect information, which could lead to harm to patients if treatment is withdrawn or not used.
Shareable PDF
Supplementary Material
This one-page PDF can be shared freely online.
Shareable PDF ERJ-00634-2019.Shareable
Footnotes
Conflict of interest: B. Hartley reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; B. Hartley is a contingent worker on assignment at GlaxoSmithKline, and holds shares in GlaxoSmithKline, outside the submitted work.
Conflict of interest: G.J. Criner reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; personal fees from Almirall, AstraZeneca, Boehringer Ingelheim, Chiesi, CSA Medical, Eolo, GlaxoSmithKline, HGE Technologies, Novartis, Nuvaira, Olympus, Pulmonx, Verona and NGM Bio, outside the submitted work.
Conflict of interest: M.T. Dransfield reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; grants from Department of Defense and NIH, has received personal fees for consultancy from and undertaken clinical trials for Boehringer Ingelheim, AstraZeneca, PneumRx/BTG, Boston Scientific and GlaxoSmithKline, undertaken clinical trials for Novartis, Yungjin and Pulmonx, personal fees for consultancy from Genentech and Quark Pharmaceuticals, outside the submitted work.
Conflict of interest: D.M.G. Halpin reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; personal fees from AstraZeneca, Chiesi, GlaxoSmithKline and Pfizer, personal fees and non-financial support from Boehringer Ingelheim and Novartis, outside the submitted work.
Conflict of interest: M.K. Han reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; personal fees from AstraZeneca and Boehringer Ingelheim, grant support from Novartis and Sunovion, outside the submitted work.
Conflict of interest: C.E. Jones reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; C.E. Jones is an employee of and holds shares/options in GlaxoSmithKline, outside the submitted work.
Conflict of interest: S. Kilbride reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; S. Kilbride is an employee of and holds shares/options in GlaxoSmithKline, outside the submitted work.
Conflict of interest: P. Lange reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; personal fees from GlaxoSmithKline, AstraZeneca, Boehringer Ingelheim and Chiesi, outside the submitted work.
Conflict of interest: D.A. Lipson reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; D.A. Lipson is an employee of and holds shares/options in GlaxoSmithKline, outside the submitted work.
Conflict of interest: D.A. Lomas reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; grants, personal fees for consultancy and honoraria from GlaxoSmithKline, personal fees for consultancy from Grifols, outside the submitted work.
Conflict of interest: N. Martin reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; N. Martin is an employee of and holds shares/options in GlaxoSmithKline, outside the submitted work.
Conflict of interest: F.J. Martinez reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; personal fees and travel support for educational activities from American College of Chest Physicians, Inova Fairfax Health System, MD Magazine, Miller Communications, National Association for Continuing Education, PeerView Communications, Prime Communications, Puerto Rican Respiratory Society, Potomac, University of Alabama Birmingham, Physicians Education Resource, Canadian Respiratory Network and Dartmouth, personal fees for advisory board work, steering committee work and lectures, and travel support from AstraZeneca, personal fees for advisory board work, data monitoring committee work and lectures, and travel support from Boehringer Ingelheim and Genentech, non-financial support for advisory board work from ProterrixBio, personal fees for educational activities from Columbia University, Integritas, Methodist Hospital Brooklyn, New York University, UpToDate, WebMD/MedScape, Western Connecticut Health Network, PlatformIQ, Rockpointe, Rare Disease Healthcare Communications and France Foundation, personal fees for advisory board work and travel support from ConCert, Sunovion, Theravance and Teva, personal fees for advisory board work and non-financial support for travel, lecturing, steering committee work and data monitoring committee work from GlaxoSmithKline, personal fees for advisory board work and lectures, and travel support from Novartis, personal fees for advisory board work and non-financial support for steering committee work from Pearl Pharmaceuticals, personal fees for advisory board work and educational activites, and travel support from Chiesi, non-financial support for steering committee work from Afferent/Merck, Gilead, Nitto, Veracyte, Prometic, Bayer and ProMedior, personal fees for consultancy and steering committee work from Patara/Respivant, non-financial support for data monitoring committee and steering committee work from Biogen, non-financial support for lecturing and advisory board work from Zambon, personal fees for journal editorship from American Thoracic Society, grants from NIH, non-financial support for consultancy from Bridge Biotherapeutics, outside the submitted work.
Conflict of interest: D. Singh reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; personal fees from GlaxoSmithKline, Cipla, Genentech and Peptinnovate, grants and personal fees from AstraZeneca, Boehringer Ingleheim, Chiesi, Glenmark, Menarini, Mundipharma, Novartis, Pfizer, Pulmatrix, Therevance and Verona, outside the submitted work.
Conflict of interest: R.A. Wise reports grant support and medical writing support funded by GlaxoSmithKline, personal fees for data monitoring committee and advisory board work from GlaxoSmithKline, during the conduct of the study; grants and personal fees for data monitoring committee and consultancy work from AstraZeneca/Medimmune and GSK, grants and personal fees for data monitoring and steering committee work from Boehringer Ingelheim, personal fees for clinical end-point committee work from Contrafect, personal fees for data monitoring committee work from Pulmonx, Roche, Merck and AbbVie, personal fees for steering committee work from Spiration, personal fees for workshops and consultancy from Sunovion, grants from Pearl Therapeutics and Sanofi-Aventis, personal fees for consultancy from Circassia, Pneuma, Verona, Denali, Aradigm, Mylan/Theravance and Propelloer Health, personal fees for safety review committee work from Bonti, outside the submitted work.
Conflict of interest: S. Lettis reports grant support and medical writing support funded by GlaxoSmithKline, during the conduct of the study; S. Lettis is an employee of and holds shares/options in GlaxoSmithKline, outside the submitted work.
Support statement: Editorial support (in the form of assembling figures, collating author comments, grammatical editing and referencing) was provided by Chrystelle Rasamison, at Fishawack Indicia Ltd, UK, and was funded by GSK. This study was funded by GSK (study number CTT116855). The funders of the study had a role in the study design, data analysis, data interpretation, and writing of the report. Funding information for this article has been deposited with the Crossref Funder Registry.
- Received March 29, 2019.
- Accepted May 30, 2019.
- Copyright ©ERS 2019
