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Karim ME, Hossain MB, Ng HS, Zhu F, Frank HA, Tremlett H. Evaluating the Role of High-Dimensional Proxy Data in Confounding Adjustment in Multiple Sclerosis Research: A Case Study. Pharmacoepidemiol Drug Saf 2025; 34:e70112. [PMID: 39901338 PMCID: PMC11791124 DOI: 10.1002/pds.70112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2024] [Revised: 01/18/2025] [Accepted: 01/22/2025] [Indexed: 02/05/2025]
Abstract
PURPOSE Given the historical use of limited confounders in multiple sclerosis (MS) studies utilizing administrative health data, this brief report evaluates the impact of incorporating high-dimensional proxy information on confounder adjustment in MS research. We have implemented high-dimensional propensity score (hdPS) and high-dimensional disease risk score (hdDRS) methods to assess changes in effect estimates for the association between disease-modifying drugs (DMDs) and all-cause mortality in an MS cohort from British Columbia (BC), Canada. METHODS We conducted a population-based retrospective study using linked administrative databases from BC, including health insurance registries, demographics, physician visits, hospitalizations, prescriptions, and vital statistics. The cohort comprised 19 360 individuals with MS, followed from January 1, 1996, to December 31, 2017. DMD exposure was defined as at least 180 days of use for beta-interferon or glatiramer acetate, or at least 90 days for other DMDs. The outcome was time to all-cause mortality. We compared Cox proportional hazards models adjusting for investigator-specified covariates with those incorporating additional empirical covariates using hdPS and hdDRS methods. RESULTS In the unadjusted analysis, DMD exposure was associated with a 69% lower risk of mortality (HR 0.31; 95% CI: 0.27-0.36). Adjusting for investigator-specified covariates, the adjusted hazard ratio (aHR) was 0.76 (95% CI: 0.65-0.89). HdPS analyses showed a 20%-23% lower mortality risk (aHRs: 0.77 to 0.80), while hdDRS analyses indicated a 19%-21% reduction (aHRs: 0.79 to 0.81). CONCLUSIONS Incorporating high-dimensional proxy information resulted in minor variations in effect estimates compared to traditional covariate adjustment. These findings suggest that the impact of residual confounding in the question under consideration may be modest. Further research should explore additional data dimensions and replicate these findings across different datasets.
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Affiliation(s)
- Mohammad Ehsanul Karim
- School of Population and Public HealthUniversity of British ColumbiaVancouverBritish ColumbiaCanada
- Centre for Advancing Health Outcomes, University of British ColumbiaVancouverBritish ColumbiaCanada
| | - Md. Belal Hossain
- School of Population and Public HealthUniversity of British ColumbiaVancouverBritish ColumbiaCanada
- Centre for Advancing Health Outcomes, University of British ColumbiaVancouverBritish ColumbiaCanada
| | - Huah Shin Ng
- Flinders Health and Medical Research Institute, College of Medicine and Public HealthFlinders UniversityAdelaideAustralia
- SA PharmacySA HealthAdelaideAustralia
| | - Feng Zhu
- Division of Neurology, Department of MedicineThe Djavad Mowafaghian Centre for Brain Health, University of British ColumbiaVancouverBritish ColumbiaCanada
| | - Hanna A. Frank
- School of Population and Public HealthUniversity of British ColumbiaVancouverBritish ColumbiaCanada
| | - Helen Tremlett
- Division of Neurology, Department of MedicineThe Djavad Mowafaghian Centre for Brain Health, University of British ColumbiaVancouverBritish ColumbiaCanada
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Wang Z, Matthewman J, Tazare J, Yu Q, Cheung KS, Chui CSL, Chan EWY, Bhaskaran K, Smeeth L, Wong ICK, Douglas IJ, Wong AYS. Risk of mortality between warfarin and direct oral anticoagulants: population-based cohort studies. BMC Med 2024; 22:597. [PMID: 39710653 DOI: 10.1186/s12916-024-03808-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/12/2024] [Accepted: 12/02/2024] [Indexed: 12/24/2024] Open
Abstract
BACKGROUND Direct oral anticoagulants (DOACs) have been reported to be associated with a higher risk of mortality compared with an older alternative, warfarin using primary care data in the United Kingdom (UK). However, other studies observed contradictory findings. We therefore aimed to investigate the association between mortality and warfarin, compared with DOACs. METHODS We conducted cohort studies using UK Clinical Practice Research Datalink (CPRD) Aurum and Hong Kong Clinical Data Analysis and Reporting System (CDARS) to identify the association between warfarin and hazard of mortality, compared to DOACs. Individuals with non-valvular atrial fibrillation aged ≥ 18 years who had first anticoagulant therapy (warfarin or DOAC) during 1/1/2011-31/12/2019 were included. RESULTS Compared with DOAC use, a lower hazard of all-cause mortality was found in warfarin users (hazard ratio (HR) = 0.81, 95% confidence interval (CI) = 0.77-0.86) in CPRD; while a higher hazard was observed in warfarin users (HR = 1.31, 95% CI = 1.24-1.39) in CDARS, versus DOAC users. In our exploratory analysis, consistent results were seen in both databases when stratified warfarin users by time in therapeutic range (TTR) using post-baseline measurements: a lower hazard of all-cause mortality in warfarin users with TTR ≥ 65% (CPRD: HR = 0.68, 95% CI = 0.65-0.72; CDARS: HR = 0.86, 95% CI = 0.77-0.96) and increased hazard in warfarin users with TTR < 65% (CPRD: HR = 1.14, 95% CI = 1.05-1.23; CDARS: HR = 1.59, 95% CI = 1.50-1.69), versus DOAC users. CONCLUSIONS The differences in hazard of all-cause mortality associated with warfarin compared with DOAC, in part may depend on anticoagulation control in warfarin users. Notably, this study is unable to establish a causal relationship between warfarin and mortality stratified by TTR, versus DOACs, requiring future studies for further investigation.
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Affiliation(s)
- Zixuan Wang
- Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology & Population Health, London, School of Hygiene and Tropical Medicine , London, UK.
- Laboratory of Data Discovery for Health (D24H), Hong Kong, China.
- School of Pharmacy, School of Health Sciences, College of Medicine and Health, University of Birmingham, Birmingham, UK.
| | - Julian Matthewman
- Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology & Population Health, London, School of Hygiene and Tropical Medicine , London, UK
| | - John Tazare
- Department of Medical Statistics, Faculty of Epidemiology & Population Health, London, School of Hygiene and Tropical Medicine , London, UK
| | - Qiuyan Yu
- Laboratory of Data Discovery for Health (D24H), Hong Kong, China
- Centre for Safe Medication Practice and Research, Department of Pharmacology and Pharmacy, The University of Hong Kong, Hong Kong, China
| | - Ka Shing Cheung
- Department of Medicine, School of Clinical Medicine, Queen Mary Hospital, The University of Hong Kong, Hong Kong, China
- Department of Medicine, The University of Hong Kong-Shenzhen Hospital, Shenzhen, China
| | - Celine S L Chui
- Laboratory of Data Discovery for Health (D24H), Hong Kong, China
- School of Nursing, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong, China
- School of Public Health, Li Ka Shing, Faculty of Medicine, The University of Hong Kong, Hong Kong, China
| | - Esther W Y Chan
- Laboratory of Data Discovery for Health (D24H), Hong Kong, China
- Centre for Safe Medication Practice and Research, Department of Pharmacology and Pharmacy, The University of Hong Kong, Hong Kong, China
| | - Krishnan Bhaskaran
- Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology & Population Health, London, School of Hygiene and Tropical Medicine , London, UK
| | - Liam Smeeth
- Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology & Population Health, London, School of Hygiene and Tropical Medicine , London, UK
| | - Ian C K Wong
- Laboratory of Data Discovery for Health (D24H), Hong Kong, China
- Centre for Safe Medication Practice and Research, Department of Pharmacology and Pharmacy, The University of Hong Kong, Hong Kong, China
- Aston School of Pharmacy, Aston University, Birmingham, UK
| | - Ian J Douglas
- Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology & Population Health, London, School of Hygiene and Tropical Medicine , London, UK
| | - Angel Y S Wong
- Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology & Population Health, London, School of Hygiene and Tropical Medicine , London, UK
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Hamedani AG, Pham Nguyen TP, Willis AW, Tazare JR. Application of High-Dimensional Propensity Score Methods to the National Health and Aging Trends Study. J Gerontol A Biol Sci Med Sci 2024; 79:glae178. [PMID: 39022830 PMCID: PMC11341984 DOI: 10.1093/gerona/glae178] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2024] [Indexed: 07/20/2024] Open
Abstract
BACKGROUND High-dimensional propensity scoring (HDPS) is a method for empirically identifying potential confounders within large healthcare databases such as administrative claims data. However, this method has not yet been applied to large national health surveys such as the National Health and Aging Trends Study (NHATS), an ongoing nationally representative survey of older adults in the United States and important resource in gerontology research. METHODS In this Research Practice article, we present an overview of HDPS and describe the specific data transformation steps and analytic considerations needed to apply it to national health surveys. We applied HDPS within NHATS to investigate the association between self-reported visual difficulty and incident dementia, comparing HDPS to conventional confounder selection methods. RESULTS Among 7 207 dementia-free NHATS Wave 1 respondents, 528 (7.3%) had self-reported visual difficulty. In an unadjusted discrete time proportional hazards model accounting for the complex survey design of NHATS, self-reported visual difficulty was strongly associated with incident dementia (odds ratio [OR] 2.34, 95% confidence interval [CI]: 1.95-2.81). After adjustment for standard investigator-selected covariates via inverse probability weighting, the magnitude of this association decreased, but evidence of an association remained (OR 1.44, 95% CI: 1.11-1.85). Adding 75 HDPS-prioritized variables to the investigator-selected propensity score model resulted in further attenuation of the association between visual impairment and dementia (OR 0.94, 95% CI: 0.70-1.23). CONCLUSIONS HDPS can be successfully applied to national health surveys such as NHATS and may improve confounder adjustment. We hope developing this framework will encourage future consideration of HDPS in this setting.
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Affiliation(s)
- Ali G Hamedani
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, USA
- Department of Biostatistics, Epidemiology, and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, USA
| | - Thanh Phuong Pham Nguyen
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, USA
- Department of Biostatistics, Epidemiology, and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, USA
| | - Allison W Willis
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, USA
- Department of Biostatistics, Epidemiology, and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, USA
| | - John R Tazare
- Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, UK
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Martin GL, Petri C, Rozenberg J, Simon N, Hajage D, Kirchgesner J, Tubach F, Létinier L, Dechartres A. A methodological review of the high-dimensional propensity score in comparative-effectiveness and safety-of-interventions research finds incomplete reporting relative to algorithm development and robustness. J Clin Epidemiol 2024; 169:111305. [PMID: 38417583 DOI: 10.1016/j.jclinepi.2024.111305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2023] [Revised: 02/14/2024] [Accepted: 02/20/2024] [Indexed: 03/01/2024]
Abstract
OBJECTIVES The use of secondary databases has become popular for evaluating the effectiveness and safety of interventions in real-life settings. However, the absence of important confounders in these databases is challenging. To address this issue, the high-dimensional propensity score (hdPS) algorithm was developed in 2009. This algorithm uses proxy variables for mitigating confounding by combining information available across several healthcare dimensions. This study assessed the methodology and reporting of the hdPS in comparative effectiveness and safety research. STUDY DESIGN AND SETTING In this methodological review, we searched PubMed and Google Scholar from July 2009 to May 2022 for studies that used the hdPS for evaluating the effectiveness or safety of healthcare interventions. Two reviewers independently extracted study characteristics and assessed how the hdPS was applied and reported. Risk of bias was evaluated with the Risk Of Bias In Non-randomised Studies - of Interventions (ROBINS-I) tool. RESULTS In total, 136 studies met the inclusion criteria; the median publication year was 2018 (Q1-Q3 2016-2020). The studies included 192 datasets, mostly North American databases (n = 132, 69%). The hdPS was used in primary analysis in 120 studies (88%). Dimensions were defined in 101 studies (74%), with a median of 5 (Q1-Q3 4-6) dimensions included. A median of 500 (Q1-Q3 200-500) empirically identified covariates were selected. Regarding hdPS reporting, only 11 studies (8%) reported all recommended items. Most studies (n = 81, 60%) had a moderate overall risk of bias. CONCLUSION There is room for improvement in the reporting of hdPS studies, especially regarding the transparency of methodological choices that underpin the construction of the hdPS.
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Affiliation(s)
- Guillaume Louis Martin
- Sorbonne Université, INSERM, Institut Pierre Louis d'Epidémiologie et de Santé Publique, AP-HP, Hôpital Pitié Salpêtrière, Département de Santé Publique, Paris, France; Synapse Medicine, Bordeaux, France.
| | - Camille Petri
- UKRI Centre for Doctoral Training in AI for Healthcare, Imperial College London, London, UK; National Heart and Lung Institute, Imperial College London, London, UK
| | | | - Noémie Simon
- Sorbonne Université, INSERM, Institut Pierre Louis d'Epidémiologie et de Santé Publique, AP-HP, Hôpital Pitié Salpêtrière, Département de Santé Publique, Paris, France
| | - David Hajage
- Sorbonne Université, INSERM, Institut Pierre Louis d'Epidémiologie et de Santé Publique, AP-HP, Hôpital Pitié Salpêtrière, Département de Santé Publique, Paris, France
| | - Julien Kirchgesner
- Sorbonne Université, INSERM, Institut Pierre Louis d'Epidémiologie et de Santé Publique, AP-HP, Hôpital Saint-Antoine, Département de Gastroentérologie et Nutrition, Paris, France
| | - Florence Tubach
- Sorbonne Université, INSERM, Institut Pierre Louis d'Epidémiologie et de Santé Publique, AP-HP, Hôpital Pitié Salpêtrière, Département de Santé Publique, Paris, France
| | | | - Agnès Dechartres
- Sorbonne Université, INSERM, Institut Pierre Louis d'Epidémiologie et de Santé Publique, AP-HP, Hôpital Pitié Salpêtrière, Département de Santé Publique, Paris, France
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Simon V, Vadel J. Evaluating the Performance of High-Dimensional Propensity Scores Compared with Standard Propensity Scores for Comparing Antihypertensive Therapies in the CPRD GOLD Database. Cardiol Ther 2023; 12:393-408. [PMID: 37145352 DOI: 10.1007/s40119-023-00316-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2023] [Accepted: 03/30/2023] [Indexed: 05/06/2023] Open
Abstract
INTRODUCTION Propensity score (PS) matching is widely used in medical record studies to create balanced treatment groups, but relies on prior knowledge of confounding factors. High-dimensional PS (hdPS) is a semi-automated algorithm that selects variables with the highest potential for confounding from medical databases. The objective of this study was to evaluate performance of hdPS and PS when used to compare antihypertensive therapies in the UK clinical practice research datalink (CPRD) GOLD database. METHODS Patients initiating antihypertensive treatment with either monotherapy or bitherapy were extracted from the CPRD GOLD database. Simulated datasets were generated using plasmode simulations with a marginal hazard ratio (HRm) of 1.29 for bitherapy versus monotherapy for reaching blood pressure control at 3 months. Either 16 or 36 known covariates were forced into the PS and hdPS models, and 200 additional variables were automatically selected for hdPS. Sensitivity analyses were conducted to assess the impact of removing known confounders from the database on hdPS performance. RESULTS With 36 known covariates, the estimated HRm (RMSE) was 1.31 (0.05) for hdPS and 1.30 (0.04) for PS matching; the crude HR was 0.68 (0.61). Using 16 known covariates, the estimated HRm (RMSE) was 1.23 (0.10) and 1.09 (0.20) for hdPS and PS, respectively. Performance of hdPS was not compromised when known confounders were removed from the database. RESULTS ON REAL DATA With 49 investigator-selected covariates, the HR was 1.18 (95% CI 1.10; 1.26) for PS and 1.33 (95% CI 1.22; 1.46) for hdPS. Both methods yielded the same conclusion, suggesting superiority of bitherapy over monotherapy for time to blood pressure control. CONCLUSION HdPS can identify proxies for missing confounders, thereby having an advantage over PS in case of unobserved covariates. Both PS and hdPS showed superiority of bitherapy over monotherapy for reaching blood pressure control.
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Affiliation(s)
- Virginie Simon
- Global Real World Evidence, Institut de Recherches Internationales Servier (IRIS), Suresnes, France.
| | - Jade Vadel
- Global Real World Evidence, Institut de Recherches Internationales Servier (IRIS), Suresnes, France.
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Rassen JA, Blin P, Kloss S, Neugebauer RS, Platt RW, Pottegård A, Schneeweiss S, Toh S. High-dimensional propensity scores for empirical covariate selection in secondary database studies: Planning, implementation, and reporting. Pharmacoepidemiol Drug Saf 2023; 32:93-106. [PMID: 36349471 PMCID: PMC10099872 DOI: 10.1002/pds.5566] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2022] [Revised: 09/14/2022] [Accepted: 10/17/2022] [Indexed: 11/11/2022]
Abstract
Real-world evidence used for regulatory, payer, and clinical decision-making requires principled epidemiology in design and analysis, applying methods to minimize confounding given the lack of randomization. One technique to deal with potential confounding is propensity score (PS) analysis, which allows for the adjustment for measured preexposure covariates. Since its first publication in 2009, the high-dimensional propensity score (hdPS) method has emerged as an approach that extends traditional PS covariate selection to include large numbers of covariates that may reduce confounding bias in the analysis of healthcare databases. hdPS is an automated, data-driven analytic approach for covariate selection that empirically identifies preexposure variables and proxies to include in the PS model. This article provides an overview of the hdPS approach and recommendations on the planning, implementation, and reporting of hdPS used for causal treatment-effect estimations in longitudinal healthcare databases. We supply a checklist with key considerations as a supportive decision tool to aid investigators in the implementation and transparent reporting of hdPS techniques, and to aid decision-makers unfamiliar with hdPS in the understanding and interpretation of studies employing this approach. This article is endorsed by the International Society for Pharmacoepidemiology.
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Affiliation(s)
| | - Patrick Blin
- Bordeaux PharmacoEpi, Bordeaux University, INSERM CIC‐P 1401BordeauxFrance
| | - Sebastian Kloss
- EMEA Real‐World Evidence & Value‐Based HealthcareJanssenBerlinGermany
| | | | - Robert W. Platt
- Professor, Departments of Pediatrics and of Epidemiology, Biostatistics, and Occupational HealthMcGill UniversityMontrealQuebecCanada
| | - Anton Pottegård
- Clinical Pharmacology, Pharmacy and Environmental Medicine, Department of Public HealthUniversity of Southern DenmarkOdenseDenmark
| | - Sebastian Schneeweiss
- Division of Pharmacoepidemiology and PharmacoeconomicsBrigham and Women's Hospital, Harvard Medical SchoolBostonMassachusettsUSA
| | - Sengwee Toh
- Department of Population MedicineHarvard Medical School and Harvard Pilgrim Health Care InstituteBostonMassachusettsUSA
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Tazare J, Wyss R, Franklin JM, Smeeth L, Evans SJW, Wang SV, Schneeweiss S, Douglas IJ, Gagne JJ, Williamson EJ. Transparency of high-dimensional propensity score analyses: guidance for diagnostics and reporting. Pharmacoepidemiol Drug Saf 2022; 31:411-423. [PMID: 35092316 PMCID: PMC9305520 DOI: 10.1002/pds.5412] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2021] [Revised: 01/20/2022] [Accepted: 01/24/2022] [Indexed: 12/03/2022]
Abstract
Purpose The high‐dimensional propensity score (HDPS) is a semi‐automated procedure for confounder identification, prioritisation and adjustment in large healthcare databases that requires investigators to specify data dimensions, prioritisation strategy and tuning parameters. In practice, reporting of these decisions is inconsistent and this can undermine the transparency, and reproducibility of results obtained. We illustrate reporting tools, graphical displays and sensitivity analyses to increase transparency and facilitate evaluation of the robustness of analyses involving HDPS. Methods Using a study from the UK Clinical Practice Research Datalink that implemented HDPS we demonstrate the application of the proposed recommendations. Results We identify seven considerations surrounding the implementation of HDPS, such as the identification of data dimensions, method for code prioritisation and number of variables selected. Graphical diagnostic tools include assessing the balance of key confounders before and after adjusting for empirically selected HDPS covariates and the identification of potentially influential covariates. Sensitivity analyses include varying the number of covariates selected and assessing the impact of covariates behaving empirically as instrumental variables. In our example, results were robust to both the number of covariates selected and the inclusion of potentially influential covariates. Furthermore, our HDPS models achieved good balance in key confounders. Conclusions The data‐adaptive approach of HDPS and the resulting benefits have led to its popularity as a method for confounder adjustment in pharmacoepidemiological studies. Reporting of HDPS analyses in practice may be improved by the considerations and tools proposed here to increase the transparency and reproducibility of study results.
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Affiliation(s)
- John Tazare
- Faculty of Epidemiology and Population HealthLondon School of Hygiene and Tropical MedicineLondonUK
| | - Richard Wyss
- Division of Pharmacoepidemiology and PharmacoeconomicsBrigham and Women's Hospital and Harvard Medical SchoolBostonMassachusettsUSA
| | - Jessica M. Franklin
- Division of Pharmacoepidemiology and PharmacoeconomicsBrigham and Women's Hospital and Harvard Medical SchoolBostonMassachusettsUSA
| | - Liam Smeeth
- Faculty of Epidemiology and Population HealthLondon School of Hygiene and Tropical MedicineLondonUK
- Health Data Research (HDR) UKLondonUK
| | - Stephen J. W. Evans
- Faculty of Epidemiology and Population HealthLondon School of Hygiene and Tropical MedicineLondonUK
| | - Shirley V. Wang
- Division of Pharmacoepidemiology and PharmacoeconomicsBrigham and Women's Hospital and Harvard Medical SchoolBostonMassachusettsUSA
| | - Sebastian Schneeweiss
- Division of Pharmacoepidemiology and PharmacoeconomicsBrigham and Women's Hospital and Harvard Medical SchoolBostonMassachusettsUSA
| | - Ian J. Douglas
- Faculty of Epidemiology and Population HealthLondon School of Hygiene and Tropical MedicineLondonUK
- Health Data Research (HDR) UKLondonUK
| | - Joshua J. Gagne
- Division of Pharmacoepidemiology and PharmacoeconomicsBrigham and Women's Hospital and Harvard Medical SchoolBostonMassachusettsUSA
| | - Elizabeth J. Williamson
- Faculty of Epidemiology and Population HealthLondon School of Hygiene and Tropical MedicineLondonUK
- Health Data Research (HDR) UKLondonUK
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