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Sun S, Nešlehová JG, Moodie EEM. Principal stratification for quantile causal effects under partial compliance. Stat Med 2024; 43:34-48. [PMID: 37926675 DOI: 10.1002/sim.9940] [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: 09/28/2022] [Revised: 08/21/2023] [Accepted: 09/29/2023] [Indexed: 11/07/2023]
Abstract
Within the principal stratification framework in causal inference, the majority of the literature has focused on binary compliance with an intervention and modelling means. Yet in some research areas, compliance is partial, and research questions-and hence analyses-are concerned with causal effects on (possibly high) quantiles rather than on shifts in average outcomes. Modelling partial compliance is challenging because it can suffer from lack of identifiability. We develop an approach to estimate quantile causal effects within a principal stratification framework, where principal strata are defined by the bivariate vector of (partial) compliance to the two levels of a binary intervention. We propose a conditional copula approach to impute the missing potential compliance and estimate the principal quantile treatment effect surface at high quantiles, allowing the copula association parameter to vary with the covariates. A bootstrap procedure is used to estimate the parameter to account for inflation due to imputation of missing compliance. Moreover, we describe precise assumptions on which the proposed approach is based, and investigate the finite sample behavior of our method by a simulation study. The proposed approach is used to study the 90th principal quantile treatment effect of executive stay-at-home orders on mitigating the risk of COVID-19 transmission in the United States.
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Affiliation(s)
- Shuo Sun
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts, USA
- Department of Epidemiology and Biostatistics, McGill University, Montréal, Québec, Canada
| | - Johanna G Nešlehová
- Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada
| | - Erica E M Moodie
- Department of Epidemiology and Biostatistics, McGill University, Montréal, Québec, Canada
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Hans N, Klein N, Faschingbauer F, Schneider M, Mayr A. Boosting distributional copula regression. Biometrics 2023; 79:2298-2310. [PMID: 36165288 DOI: 10.1111/biom.13765] [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: 03/21/2022] [Accepted: 09/15/2022] [Indexed: 11/28/2022]
Abstract
Capturing complex dependence structures between outcome variables (e.g., study endpoints) is of high relevance in contemporary biomedical data problems and medical research. Distributional copula regression provides a flexible tool to model the joint distribution of multiple outcome variables by disentangling the marginal response distributions and their dependence structure. In a regression setup, each parameter of the copula model, that is, the marginal distribution parameters and the copula dependence parameters, can be related to covariates via structured additive predictors. We propose a framework to fit distributional copula regression via model-based boosting, which is a modern estimation technique that incorporates useful features like an intrinsic variable selection mechanism, parameter shrinkage and the capability to fit regression models in high-dimensional data setting, that is, situations with more covariates than observations. Thus, model-based boosting does not only complement existing Bayesian and maximum-likelihood based estimation frameworks for this model class but rather enables unique intrinsic mechanisms that can be helpful in many applied problems. The performance of our boosting algorithm for copula regression models with continuous margins is evaluated in simulation studies that cover low- and high-dimensional data settings and situations with and without dependence between the responses. Moreover, distributional copula boosting is used to jointly analyze and predict the length and the weight of newborns conditional on sonographic measurements of the fetus before delivery together with other clinical variables.
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Affiliation(s)
- Nicolai Hans
- Chair of Statistics and Data Science, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Nadja Klein
- Chair of Statistics and Data Science, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Florian Faschingbauer
- Department of Obstetrics and Gynecology, University Hospital of Erlangen, Erlangen, Germany
| | - Michael Schneider
- Department of Obstetrics and Gynecology, University Hospital of Erlangen, Erlangen, Germany
| | - Andreas Mayr
- Department of Medical Biometrics, Informatics and Epidemiology, Faculty of Medicine, University of Bonn, Bonn, Germany
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Klein N, Hothorn T, Barbanti L, Kneib T. Multivariate conditional transformation models. Scand Stat Theory Appl 2020. [DOI: 10.1111/sjos.12501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Nadja Klein
- Humboldt‐Universität zu Berlin Berlin Germany
| | | | | | - Thomas Kneib
- Georg‐August‐Universität Göttingen Göttingen Germany
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Espasandín‐Domínguez J, Cadarso‐Suárez C, Kneib T, Marra G, Klein N, Radice R, Lado‐Baleato O, González‐Quintela A, Gude F. Assessing the relationship between markers of glycemic control through flexible copula regression models. Stat Med 2019; 38:5161-5181. [DOI: 10.1002/sim.8358] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2018] [Revised: 07/29/2019] [Accepted: 08/06/2019] [Indexed: 01/30/2023]
Affiliation(s)
- J. Espasandín‐Domínguez
- Department of Statistics, Mathematical Analysis, and OptimizationUniversidade de Santiago de Compostela Santiago de Compostela Spain
| | - C. Cadarso‐Suárez
- Department of Statistics, Mathematical Analysis, and OptimizationUniversidade de Santiago de Compostela Santiago de Compostela Spain
| | - T. Kneib
- Chair of StatisticsGeorg‐August‐Universität Göttingen Göttingen Germany
| | - G. Marra
- Department of Statistical ScienceUniversity College London London UK
| | - N. Klein
- Humboldt‐Universitat zu Berlin Berlin Germany
| | - R. Radice
- Cass Business SchoolCity, University of London London UK
| | - O. Lado‐Baleato
- Department of Statistics, Mathematical Analysis, and OptimizationUniversidade de Santiago de Compostela Santiago de Compostela Spain
| | - A. González‐Quintela
- Department of Internal MedicineComplejo Hospitalario Universitario de Santiago de Compostela Santiago de Compostela Spain
| | - F. Gude
- Clinical Epidemiology UnitComplejo Hospitalario Universitario de Santiago de Compostela Santiago de Compostela Spain
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Stander J, Dalla Valle L, Taglioni C, Liseo B, Wade A, Cortina-Borja M. Analysis of paediatric visual acuity using Bayesian copula models with sinh-arcsinh marginal densities. Stat Med 2019; 38:3421-3443. [PMID: 31144351 DOI: 10.1002/sim.8176] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2017] [Revised: 03/04/2019] [Accepted: 03/20/2019] [Indexed: 11/10/2022]
Abstract
We analyse paediatric ophthalmic data from a large sample of children aged between 3 and 8 years. We use a Bayesian additive conditional bivariate copula regression model with sinh-arcsinh marginal densities with location, scale, and shape parameters that depend smoothly on a covariate. We perform Bayesian inference about the unknown quantities of our model using a specially tailored Markov chain Monte Carlo algorithm. We gain new insights about the processes, which determine transformations in visual acuity with respect to age, including the nature of joint changes in both eyes as modelled with the age-related copula dependence parameter. We analyse posterior predictive distributions to identify children with unusual sight characteristics, distinguishing those who are bivariate, but not univariate outliers. In this way, we provide an innovative tool that enables clinicians to identify children with unusual sight who may otherwise be missed. We compare our simultaneous Bayesian method with a two-step frequentist generalised additive modelling approach.
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Affiliation(s)
- Julian Stander
- School of Computing, Electronics and Mathematics, University of Plymouth, Plymouth, UK
| | - Luciana Dalla Valle
- School of Computing, Electronics and Mathematics, University of Plymouth, Plymouth, UK
| | | | - Brunero Liseo
- Department of Methods and Models for Territories, Economy and Finance, University of Rome La Sapienza, Rome, Italy
| | - Angie Wade
- Great Ormond Street Institute of Child Health, University College London, London, UK
| | - Mario Cortina-Borja
- Great Ormond Street Institute of Child Health, University College London, London, UK
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Klein N, Kneib T, Marra G, Radice R, Rokicki S, McGovern ME. Mixed binary-continuous copula regression models with application to adverse birth outcomes. Stat Med 2018; 38:413-436. [DOI: 10.1002/sim.7985] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2018] [Revised: 06/01/2018] [Accepted: 09/06/2018] [Indexed: 11/06/2022]
Affiliation(s)
- Nadja Klein
- Applied Statistics; Humboldt University of Berlin; Berlin Germany
| | - Thomas Kneib
- Chair of Statistics; Georg-August Universität Göttingen; Göttingen Germany
| | - Giampiero Marra
- Department of Statistical Science; University College London; London UK
| | - Rosalba Radice
- Cass Business School; City, University of London; 106 Bunhill Row, EC1Y 8TZ London UK
| | - Slawa Rokicki
- Geary Institute for Public Policy; University College Dublin; Dublin Ireland
| | - Mark E. McGovern
- CHARMS - Centre for Health Research at the Management School; Queen's University Belfast; Belfast UK
- Centre of Excellence for Public Health (Northern Ireland); Belfast UK
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Donat F, Marra G. Simultaneous equation penalized likelihood estimation of vehicle accident injury severity. J R Stat Soc Ser C Appl Stat 2018. [DOI: 10.1111/rssc.12267] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Affiliation(s)
| | - Thomas Nagler
- Lehrstuhl für Mathematische Statistik, Technische Universität München, Boltzmannstraße 3, 85748 Garching b. München, Germany
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Levi E, Craiu RV. Bayesian inference for conditional copulas using Gaussian Process single index models. Comput Stat Data Anal 2018. [DOI: 10.1016/j.csda.2018.01.013] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Vatter T, Chavez-Demoulin V. Generalized additive models for conditional dependence structures. J MULTIVARIATE ANAL 2015. [DOI: 10.1016/j.jmva.2015.07.003] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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