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Janvin M, Young JG, Ryalen PC, Stensrud MJ. Causal inference with recurrent and competing events. LIFETIME DATA ANALYSIS 2024; 30:59-118. [PMID: 37173588 PMCID: PMC10764453 DOI: 10.1007/s10985-023-09594-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2021] [Accepted: 02/14/2023] [Indexed: 05/15/2023]
Abstract
Many research questions concern treatment effects on outcomes that can recur several times in the same individual. For example, medical researchers are interested in treatment effects on hospitalizations in heart failure patients and sports injuries in athletes. Competing events, such as death, complicate causal inference in studies of recurrent events because once a competing event occurs, an individual cannot have more recurrent events. Several statistical estimands have been studied in recurrent event settings, with and without competing events. However, the causal interpretations of these estimands, and the conditions that are required to identify these estimands from observed data, have yet to be formalized. Here we use a formal framework for causal inference to formulate several causal estimands in recurrent event settings, with and without competing events. When competing events exist, we clarify when commonly used classical statistical estimands can be interpreted as causal quantities from the causal mediation literature, such as (controlled) direct effects and total effects. Furthermore, we show that recent results on interventionist mediation estimands allow us to define new causal estimands with recurrent and competing events that may be of particular clinical relevance in many subject matter settings. We use causal directed acyclic graphs and single world intervention graphs to illustrate how to reason about identification conditions for the various causal estimands based on subject matter knowledge. Furthermore, using results on counting processes, we show that our causal estimands and their identification conditions, which are articulated in discrete time, converge to classical continuous time counterparts in the limit of fine discretizations of time. We propose estimators and establish their consistency for the various identifying functionals. Finally, we use the proposed estimators to compute the effect of blood pressure lowering treatment on the recurrence of acute kidney injury using data from the Systolic Blood Pressure Intervention Trial.
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Affiliation(s)
- Matias Janvin
- Department of Mathematics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.
| | - Jessica G Young
- Department of Population Medicine, Harvard Medical School and Harvard Pilgrim Health Care Institute, Boston, USA
- Department of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, USA
- CAUSALab, Harvard T.H. Chan School of Public Health, Boston, USA
| | - Pål C Ryalen
- Department of Biostatistics, University of Oslo, Oslo, Norway
| | - Mats J Stensrud
- Department of Mathematics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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2
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Mao L. Nonparametric inference of general while-alive estimands for recurrent events. Biometrics 2023; 79:1749-1760. [PMID: 35731993 PMCID: PMC9772359 DOI: 10.1111/biom.13709] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Accepted: 06/16/2022] [Indexed: 12/24/2022]
Abstract
Measuring the treatment effect on recurrent events like hospitalization in the presence of death has long challenged statisticians and clinicians alike. Traditional inference on the cumulative frequency unjustly penalizes survivorship as longer survivors also tend to experience more adverse events. Expanding a recently suggested idea of the "while-alive" event rate, we consider a general class of such estimands that adjust for the length of survival without losing causal interpretation. Given a user-specified loss function that allows for arbitrary weighting, we define as estimand the average loss experienced per unit time alive within a target period and use the ratio of this loss rate to measure the effect size. Scaling the loss rate by the width of the corresponding time window gives us an alternative, and sometimes more photogenic, way of showing the data. To make inferences, we construct a nonparametric estimator for the loss rate through the cumulative loss and the restricted mean survival time and derive its influence function in closed form for variance estimation and testing. As simulations and analysis of real data from a heart failure trial both show, the while-alive approach corrects for the false attenuation of treatment effect due to patients living longer under treatment, with increased statistical power as a result. The proposed methods are implemented in the R-package WA, which is publicly available from the Comprehensive R Archive Network (CRAN).
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Affiliation(s)
- Lu Mao
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, 53792, USA
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3
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Claggett BL, McCaw ZR, Tian L, McMurray JJV, Jhund PS, Uno H, Pfeffer MA, Solomon SD, Wei LJ. Quantifying Treatment Effects in Trials with Multiple Event-Time Outcomes. NEJM EVIDENCE 2022; 1:10.1056/evidoa2200047. [PMID: 37645407 PMCID: PMC10465123 DOI: 10.1056/evidoa2200047] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
BACKGROUND Data on the occurrence times of multiple outcomes, reflecting the temporal profile of disease burden/progression, have been used to estimate treatment effects in various recent randomized trials. Most procedures for analyzing these data require specific model assumptions. When the assumptions are not met, the results may be misleading. Robust, model-free procedures for study design and analysis that enable clinically meaningful interpretations are warranted. METHODS For each treatment group, we constructed and summarized the estimated mean cumulative count of events over time by the area under the curve (AUC), which can be interpreted as the mean total event-free time lost from multiple undesirable outcomes. A higher curve, and resulting larger AUC, implies a worse treatment. The treatment effect is quantified by the ratio and/or difference of AUCs. The timing and occurrence of recurrent heart failure hospitalizations (HFHs) and cardiovascular (CV) death from Prospective Comparison of ARNI with ARB Global Outcomes in HF with Preserved Ejection Fraction (PARAGON-HF), comparing sacubitril/valsartan with valsartan, are presented for illustration. We also discuss the design of future studies on the basis of the proposed method. RESULTS With 48 months of follow-up, estimated AUCs, representing the total event-free time lost to HFHs and CV death, were 11.3 and 13.1 event-months for sacubitril/valsartan and valsartan, respectively. The ratio of these AUCs was 0.86 (95% confidence interval, 0.75 to 1.00; P=0.049), a 14% reduction of disease burden favoring combination therapy. A future study, similar to PARAGON-HF, designed using the new proposal would require fewer patients would than a conventional time-to-first-event analysis. CONCLUSIONS The proposed method is robust and model-free and provides a clinically interpretable, time-scale summary of the treatment effect. (Funded by National Institutes of Health.).
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Affiliation(s)
- Brian Lee Claggett
- Cardiovascular Division, Brigham and Women's Hospital, Harvard Medical School, Boston
| | | | - Lu Tian
- Department of Biomedical Data Science, Stanford University, Stanford, CA
| | - John J V McMurray
- British Heart Foundation Glasgow Cardiovascular Research Center, Institute of Cardiovascular and Medical Sciences, University of Glasgow, Glasgow, Scotland
| | - Pardeep S Jhund
- British Heart Foundation Glasgow Cardiovascular Research Center, Institute of Cardiovascular and Medical Sciences, University of Glasgow, Glasgow, Scotland
| | - Hajime Uno
- Department of Data Science, Dana-Farber Cancer Institute, Boston
| | - Marc A Pfeffer
- Cardiovascular Division, Brigham and Women's Hospital, Harvard Medical School, Boston
| | - Scott D Solomon
- Cardiovascular Division, Brigham and Women's Hospital, Harvard Medical School, Boston
| | - Lee-Jen Wei
- Harvard T.H. Chan School of Public Health, Boston
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McCaw ZR, Tian L, Wei J, Claggett BL, Bretz F, Fitzmaurice G, Wei LJ. Choosing clinically interpretable summary measures and robust analytic procedures for quantifying the treatment difference in comparative clinical studies. Stat Med 2021; 40:6235-6242. [PMID: 34783094 PMCID: PMC8687139 DOI: 10.1002/sim.8971] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2020] [Revised: 02/20/2021] [Accepted: 03/16/2021] [Indexed: 12/11/2022]
Affiliation(s)
| | - Lu Tian
- Department of Biomedical Data Science, Stanford University, Stanford, California
| | - Jiawei Wei
- Novartis Institutes for Biomedical Research Co., Shanghai, China
| | - Brian Lee Claggett
- Cardiovascular Division, Brigham and Women’s Hospital, Boston, Massachusetts
| | - Frank Bretz
- Novartis Pharma AG, Basel, Switzerland
- Section for Medical Statistics, Medical University of Vienna, Vienna, Austria
| | - Garrett Fitzmaurice
- Laboratory for Psychiatric Biostatistics, McLean Hospital, Belmont, Massachusetts
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Harvard University, Boston, Massachusetts
| | - Lee-Jen Wei
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Harvard University, Boston, Massachusetts
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Mao L, Kim K. Statistical models for composite endpoints of death and non-fatal events: a review. Stat Biopharm Res 2021; 13:260-269. [PMID: 34540133 DOI: 10.1080/19466315.2021.1927824] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
The proper analysis of composite endpoints consisting of both death and non-fatal events is an intriguing and sometimes contentious topic. The current practice of analyzing time to the first event often draws criticisms for ignoring the unequal importance between component events and for leaving recurrent-event data unused. Novel methods that address these limitations have recently been proposed. To compare the novel versus traditional approaches, we review three typical models for composite endpoints based on time to the first event, composite event process, and pairwise hierarchical comparisons. The pros and cons of these models are discussed with reference to the relevant regulatory guidelines, such as the recently released ICH-E9(R1) Addendum "Estimands and Sensitivity Analysis in Clinical Trials". We also discuss the impact of censoring when the model assumptions are violated and explore sensitivity analysis strategies. Simulation studies are conducted to assess the performance of the reviewed methods under different settings. As demonstration, we use publicly available R-packages to analyze real data from a major cardiovascular trial.
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Affiliation(s)
- Lu Mao
- Department of Biostatistics and Medical Informatics, School of Medicine and Public Health, University of Wisconsin-Madison
| | - KyungMann Kim
- Department of Biostatistics and Medical Informatics, School of Medicine and Public Health, University of Wisconsin-Madison
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Lopez-Sendon JL, Cyr DD, Mark DB, Bangalore S, Huang Z, White HD, Alexander KP, Li J, Nair RG, Demkow M, Peteiro J, Wander GS, Demchenko EA, Gamma R, Gadkari M, Poh KK, Nageh T, Stone PH, Keltai M, Sidhu M, Newman JD, Boden WE, Reynolds HR, Chaitman BR, Hochman JS, Maron DJ, O'Brien SM. Effects of initial invasive vs. initial conservative treatment strategies on recurrent and total cardiovascular events in the ISCHEMIA trial. Eur Heart J 2021; 43:148-149. [PMID: 34514494 DOI: 10.1093/eurheartj/ehab509] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 12/30/2020] [Revised: 04/26/2021] [Accepted: 08/16/2021] [Indexed: 12/24/2022] Open
Abstract
AIMS The International Study of Comparative Health Effectiveness with Medical and Invasive Approaches (ISCHEMIA) trial prespecified an analysis to determine whether accounting for recurrent cardiovascular events in addition to first events modified understanding of the treatment effects. METHODS AND RESULTS Patients with stable coronary artery disease (CAD) and moderate or severe ischaemia on stress testing were randomized to either initial invasive (INV) or initial conservative (CON) management. The primary outcome was a composite of cardiovascular death, myocardial infarction (MI), and hospitalization for unstable angina, heart failure, or cardiac arrest. The Ghosh-Lin method was used to estimate mean cumulative incidence of total events with death as a competing risk. The 5179 ISCHEMIA patients experienced 670 index events (318 INV, 352 CON) and 203 recurrent events (102 INV, 101 CON). A single primary event was observed in 9.8% of INV and 10.8% of CON patients while ≥2 primary events were observed in 2.5% and 2.8%, respectively. Patients with recurrent events were older; had more frequent hypertension, diabetes, prior MI, or cerebrovascular disease; and had more multivessel CAD. The average number of primary endpoint events per 100 patients over 4 years was 18.2 in INV [95% confidence interval (CI) 15.8-20.9] and 19.7 in CON (95% CI 17.5-22.2), difference -1.5 (95% CI -5.0 to 2.0, P = 0.398). Comparable results were obtained when all-cause death was substituted for cardiovascular death and when stroke was added as an event. CONCLUSIONS In stable CAD patients with moderate or severe myocardial ischaemia enrolled in ISCHEMIA, an initial INV treatment strategy did not prevent either net recurrent events or net total events more effectively than an initial CON strategy. CLINICAL TRIAL REGISTRATION ISCHEMIA ClinicalTrials.gov number, NCT01471522, https://clinicaltrials.gov/ct2/show/NCT01471522.
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Affiliation(s)
- Jose L Lopez-Sendon
- Cardiology department, Hospital Universitario La Paz, Idipaz, UAM, CIBER-CV, Paseo de la Castellana 261, Madrid 28046, Spain
| | - Derek D Cyr
- Duke Clinical Research Institute and Duke University, 300 W. Morgan Street, Durham, NC, USA
| | - Daniel B Mark
- Duke Clinical Research Institute and Duke University, 300 W. Morgan Street, Durham, NC, USA
| | - Sripal Bangalore
- NYU Grossman School of Medicine, 530 First Avenue, New York, NY, USA
| | - Zhen Huang
- Duke Clinical Research Institute and Duke University, 300 W. Morgan Street, Durham, NC, USA
| | - Harvey D White
- Auckland City Hospital Green Lane Cardiovascular Services and University of Auckland, 2 Park Road, Grafton, Auckland 1023, New Zealand
| | - Karen P Alexander
- Duke Clinical Research Institute and Duke University, 300 W. Morgan Street, Durham, NC, USA
| | - Jianghao Li
- Duke Clinical Research Institute and Duke University, 300 W. Morgan Street, Durham, NC, USA
| | - Rajesh Goplan Nair
- Government Medical College, 48/584, Subhag Sastrinagar, Thiruvananthapuram, Kerala 695002, India
| | - Marcin Demkow
- Department of Coronary and Structural Heart Diseases, National Institute of Cardiology, Alpejska 42, Warsaw 04-628, Poland
| | - Jesus Peteiro
- CHUAC, Universidad de A Coruña, CIBER-CV, As Xubias, 84, A Coruna 15006, Spain
| | - Gurpreet S Wander
- Dayanand Medical College & Hospital, Civil Lines, Tagore Nagar, Ludhiana, Punjab 141001, India
| | - Elena A Demchenko
- Almazov National Medical Research Centre, Ulitsa Akkuratova, 2, Saint-Petersburg 197341, Russia
| | - Reto Gamma
- Broomfield Hospital, Court Rd, Broomfield, Chelmsford CM1 7ET, UK
| | - Milind Gadkari
- Kem Hospital Maharashtra, 489, Mudaliar Rd, Rasta Peth, Pune, Maharashtra 411011, India
| | - Kian Keong Poh
- National University Heart Center Singapore, Singapore, Singapore.,Yong Loo Lin School of Medicine, National University of Singapore, 10 Medical Dr, Singapore, Singapore
| | - Thuraia Nageh
- Southend University Hospital, Prittlewell Chase, Westcliff-on-Sea, Southend-on-Sea, Westcliff-on-Sea SS0 0RY, Southend, England, UK
| | - Peter H Stone
- Brigham and Women's Hospital, 75 Francis St, Boston, MA, USA
| | - Matyas Keltai
- Semmelweis University, Budapest, Üllői út 26, 1085 Hungary
| | - Mandeep Sidhu
- Albany Medical College, 47 New Scotland Avenue, Physicians Pavilion, 2nd Floor, Albany, NY 12208, USA
| | - Jonathan D Newman
- NYU Grossman School of Medicine, 530 First Avenue, New York, NY, USA
| | - William E Boden
- VA New England Healthcare System, Boston University School of Medicine, 150 South Huntington Avenue, Boston, MA, USA
| | | | - Bernard R Chaitman
- St Louis University School of Medicine Center for Comprehensive Cardiovascular Care, 1034 S. Brentwood Blvd., Suite 1120, St. Louis, MO, USA
| | - Judith S Hochman
- NYU Grossman School of Medicine, 530 First Avenue, New York, NY, USA
| | - David J Maron
- Department of Medicine, Stanford University, 300 Pasteur Drive, Falk CVRC 265, Stanford, CA 94305-5406, USA
| | - Sean M O'Brien
- Duke Clinical Research Institute and Duke University, 300 W. Morgan Street, Durham, NC, USA
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Fritsch A, Schlömer P, Mendolia F, Mütze T, Jahn-Eimermacher A. Efficiency Comparison of Analysis Methods for Recurrent Event and Time-to-First Event Endpoints in the Presence of Terminal Events—Application to Clinical Trials in Chronic Heart Failure. Stat Biopharm Res 2021. [DOI: 10.1080/19466315.2021.1945488] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
| | | | | | | | - Antje Jahn-Eimermacher
- Department of Mathematics and Natural Sciences, Darmstadt University of Applied Sciences, Darmstadt, Germany
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8
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Schmidli H, Roger JH, Akacha M. Estimands for Recurrent Event Endpoints in the Presence of a Terminal Event. Stat Biopharm Res 2021. [DOI: 10.1080/19466315.2021.1895883] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Affiliation(s)
| | - James H. Roger
- Medical Statistics Department, London School of Hygiene & Tropical Medicine, London, UK
| | - Mouna Akacha
- Statistical Methodology, Novartis, Basel, Switzerland, on behalf of the Recurrent Event Qualification Opinion Consortium
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9
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Qiu J, Zhou D, Hung HMJ, Lawrence J, Bai S. Estimation on conditional restricted mean survival time with counting process. J Biopharm Stat 2020; 31:141-155. [PMID: 32892707 DOI: 10.1080/10543406.2020.1814799] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Abstract
In a comparative longitudinal clinical study, multiple clinical events of interest are typically collected in timing and occurrence during the follow-up period. These clinical events are often indicative of disease burden over the study period and provide overall evidence of benefit/risk of one treatment relative to another. While these clinical events are usually used to form a composite endpoint, only the first occurrence of the composite endpoint event is considered in primary efficacy analysis. This type of analysis is commonly performed but it may not be ideal. Most of the existing methods for analyzing multiple event-time data were developed, relying on certain model assumptions. However, the assumptions may greatly affect the inferences for treatment effect. In this paper, we propose a simple, non-parametric estimator of conditional mean survival time for multiple events to quantify treatment effect which has clinically meaningful interpretation. We use simulation studies to evaluate the performance of the new method. Further, we apply this method to analyze the data from a cardiovascular clinical trial as an illustration.
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Affiliation(s)
- Junshan Qiu
- Division of Pharmacometrics, OCP/OTS/CDER, US FDA
| | - Dali Zhou
- Division of Biometrics II, OB/OTS/CDER, US FDA
| | | | | | - Steven Bai
- Division of Biometrics II, OB/OTS/CDER, US FDA
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10
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Claggett B, Pocock S, Wei LJ, Pfeffer MA, McMurray JJV, Solomon SD. Response by Claggett et al to Letter Regarding Article, "Comparison of Time-to-First Event and Recurrent-Event Methods in Randomized Clinical Trials". Circulation 2019; 139:422-423. [PMID: 30640547 DOI: 10.1161/circulationaha.118.038478] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Affiliation(s)
- Brian Claggett
- Cardiovascular Division, Brigham and Women's Hospital, Boston, MA (B.C., M.A.P., S.D.S.)
| | - Stuart Pocock
- Department of Medical Statistics, London School of Hygiene, UK (S.P.)
| | - L J Wei
- Department of Biostatistics, Harvard School of Public Health, Boston, MA (L.J.W.)
| | - Marc A Pfeffer
- Cardiovascular Division, Brigham and Women's Hospital, Boston, MA (B.C., M.A.P., S.D.S.)
| | - John J V McMurray
- British Heart Foundation Cardiovascular Research Centre, University of Glasgow, UK (J.J.V.M.)
| | - Scott D Solomon
- Cardiovascular Division, Brigham and Women's Hospital, Boston, MA (B.C., M.A.P., S.D.S.)
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