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Pelgrims I, Devleesschauwer B, Vandevijvere S, De Clercq EM, Van der Heyden J, Vansteelandt S. The potential impact fraction of population weight reduction scenarios on non-communicable diseases in Belgium: application of the g-computation approach. BMC Med Res Methodol 2024; 24:87. [PMID: 38616261 PMCID: PMC11016220 DOI: 10.1186/s12874-024-02212-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2023] [Accepted: 04/04/2024] [Indexed: 04/16/2024] Open
Abstract
BACKGROUND Overweight is a major risk factor for non-communicable diseases (NCDs) in Europe, affecting almost 60% of all adults. Tackling obesity is therefore a key long-term health challenge and is vital to reduce premature mortality from NCDs. Methodological challenges remain however, to provide actionable evidence on the potential health benefits of population weight reduction interventions. This study aims to use a g-computation approach to assess the impact of hypothetical weight reduction scenarios on NCDs in Belgium in a multi-exposure context. METHODS Belgian health interview survey data (2008/2013/2018, n = 27 536) were linked to environmental data at the residential address. A g-computation approach was used to evaluate the potential impact fraction (PIF) of population weight reduction scenarios on four NCDs: diabetes, hypertension, cardiovascular disease (CVD), and musculoskeletal (MSK) disease. Four scenarios were considered: 1) a distribution shift where, for each individual with overweight, a counterfactual weight was drawn from the distribution of individuals with a "normal" BMI 2) a one-unit reduction of the BMI of individuals with overweight, 3) a modification of the BMI of individuals with overweight based on a weight loss of 10%, 4) a reduction of the waist circumference (WC) to half of the height among all people with a WC:height ratio greater than 0.5. Regression models were adjusted for socio-demographic, lifestyle, and environmental factors. RESULTS The first scenario resulted in preventing a proportion of cases ranging from 32.3% for diabetes to 6% for MSK diseases. The second scenario prevented a proportion of cases ranging from 4.5% for diabetes to 0.8% for MSK diseases. The third scenario prevented a proportion of cases, ranging from 13.6% for diabetes to 2.4% for MSK diseases and the fourth scenario prevented a proportion of cases ranging from 36.4% for diabetes to 7.1% for MSK diseases. CONCLUSION Implementing weight reduction scenarios among individuals with excess weight could lead to a substantial and statistically significant decrease in the prevalence of diabetes, hypertension, cardiovascular disease (CVD), and musculoskeletal (MSK) diseases in Belgium. The g-computation approach to assess PIF of interventions represents a straightforward approach for drawing causal inferences from observational data while providing useful information for policy makers.
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Affiliation(s)
- Ingrid Pelgrims
- Department of Chemical and Physical Health Risks, Sciensano, Rue Juliette Wytsman 14, 1050, Brussels, Belgium.
- Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281, S9, BE-9000, Ghent, Belgium.
- Department of Epidemiology and Public Health, Sciensano, Rue Juliette Wytsman 14, 1050, Brussels, Belgium.
| | - Brecht Devleesschauwer
- Department of Epidemiology and Public Health, Sciensano, Rue Juliette Wytsman 14, 1050, Brussels, Belgium
- Department of Translational Physiology, Infectiology and Public Health, Ghent University, Salisburylaan 133, Hoogbouw, B-9820, Merelbeke, Belgium
| | - Stefanie Vandevijvere
- Department of Epidemiology and Public Health, Sciensano, Rue Juliette Wytsman 14, 1050, Brussels, Belgium
| | - Eva M De Clercq
- Department of Chemical and Physical Health Risks, Sciensano, Rue Juliette Wytsman 14, 1050, Brussels, Belgium
| | - Johan Van der Heyden
- Department of Epidemiology and Public Health, Sciensano, Rue Juliette Wytsman 14, 1050, Brussels, Belgium
| | - Stijn Vansteelandt
- Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281, S9, BE-9000, Ghent, Belgium
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Soohoo M, Arah OA. Investigation of the structure and magnitude of time-varying uncontrolled confounding in simulated cohort data analyzed using g-computation. Int J Epidemiol 2023; 52:1907-1913. [PMID: 37898996 PMCID: PMC10749778 DOI: 10.1093/ije/dyad150] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Accepted: 10/17/2023] [Indexed: 10/31/2023] Open
Abstract
BACKGROUND When estimating the effect of time-varying exposures on longer-term outcomes, the assumption of conditional exchangeability or no uncontrolled confounding extends beyond baseline confounding to include time-varying confounding. We illustrate the structures and magnitude of uncontrolled time-varying confounding in exposure effect estimates obtained from g-computation when sequential conditional exchangeability is violated. METHODS We used directed acyclic graphs (DAGs) to depict time-varying uncontrolled confounding. We performed simulations and used g-computation to quantify the effects of each time-varying exposure for each DAG type. Models adjusting all time-varying confounders were considered the true (bias-adjusted) estimate. The exclusion of time-varying uncontrolled confounders represented the biased effect estimate and an unmet 'no uncontrolled confounding' assumption. True and biased estimates were compared across DAGs, with different magnitudes of uncontrolled confounding. RESULTS Time-varying uncontrolled confounding can present in several scenarios, including relationships into subsequently measured exposure(s), outcome, unmeasured confounder(s) and other measured confounder(s). In simulations, effect estimates obtained from g-computation were more biased in DAGs when the uncontrolled confounders were directly related to the outcome. Complex DAGs that included relationships between uncontrolled confounders and other variables and relationships where exposures caused uncontrolled confounders at the next time point resulted in the most biased effect estimates. In these complex DAGs, excluding uncontrolled confounders affected the multiple effect estimates. CONCLUSIONS Time-varying uncontrolled confounding has the potential to substantially impact observed effect estimates. Given the importance of longitudinal studies in advising public health, the impact of time-varying uncontrolled confounding warrants more recognition and evaluation using quantitative bias analysis.
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Affiliation(s)
- Melissa Soohoo
- Department of Epidemiology, Fielding School of Public Health, University of California, Los Angeles (UCLA), Los Angeles, CA, USA
| | - Onyebuchi A Arah
- Department of Epidemiology, Fielding School of Public Health, University of California, Los Angeles (UCLA), Los Angeles, CA, USA
- Department of Statistics and Data Science, UCLA College, Los Angeles, CA, USA
- Research Unit for Epidemiology, Department of Public Health, Aarhus University, Aarhus, Denmark
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Pear VA, Wintemute GJ, Jewell NP, Cerdá M, Ahern J. Community-Level Risk Factors for Firearm Assault and Homicide: The Role of Local Firearm Dealers and Alcohol Outlets. Epidemiology 2023; 34:798-806. [PMID: 37708491 PMCID: PMC10538383 DOI: 10.1097/ede.0000000000001670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Accepted: 08/30/2023] [Indexed: 09/16/2023]
Abstract
BACKGROUND Identifying community characteristics associated with firearm assault could facilitate prevention. We investigated the effect of community firearm dealer and alcohol outlet densities on individual risk of firearm assault injury. METHODS In this density-sampled case-control study of Californians, January 2005-September 2015, cases comprised all residents with a fatal or nonfatal firearm assault injury. For each month, we sampled controls from the state population in a 4:1 ratio with cases. Exposures were monthly densities of county-level pawn and nonpawn firearm dealers and ZIP code-level off-premises alcohol outlets and bars and pubs ("bars/pubs"). We used case-control-weighted G-computation to estimate risk differences (RD) statewide and among younger Black men, comparing observed exposure densities to hypothetical interventions setting these densities to low. We estimated additive interactions between firearm and alcohol retailer density. Secondary analyses examined interventions targeted to high exposure density or outcome burden areas. RESULTS There were 67,850 cases and 268,122 controls. Observed (vs. low) densities of pawn firearm dealers and off-premises alcohol outlets were individually associated with elevated monthly risk of firearm assault per 100,000 people (RD pawn dealers : 0.06, 95% CI: 0.05, 0.08; RD off-premises outlets : 0.01, 95% CI: 0.01, 0.03), but nonpawn firearm dealer and bar/pub density were not; models targeting only areas with the highest outcome burden were similar. Among younger Black men, estimates were larger. There was no interaction between firearm and alcohol retailer density. CONCLUSIONS Our results are consistent with the hypothesis that limiting pawn firearm dealers and off-premises alcohol outlet densities can reduce interpersonal firearm violence.
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Affiliation(s)
- Veronica A. Pear
- From the Violence Prevention Research Program, Department of Emergency Medicine, University of California, Davis School of Medicine
- Division of Epidemiology, School of Public Health, University of California, Berkeley
| | - Garen J. Wintemute
- From the Violence Prevention Research Program, Department of Emergency Medicine, University of California, Davis School of Medicine
| | - Nicholas P. Jewell
- Department of Medical Statistics, London School of Hygiene and Tropical Medicine
| | - Magdalena Cerdá
- Department of Population Health, New York University Grossman School of Medicine
| | - Jennifer Ahern
- Division of Epidemiology, School of Public Health, University of California, Berkeley
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Daly-Grafstein D, Gustafson P. Combining parametric and nonparametric models to estimate treatment effects in observational studies. Biometrics 2023; 79:1986-1995. [PMID: 36250351 DOI: 10.1111/biom.13776] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2022] [Accepted: 09/29/2022] [Indexed: 11/29/2022]
Abstract
Performing causal inference in observational studies requires we assume confounding variables are correctly adjusted for. In settings with few discrete-valued confounders, standard models can be employed. However, as the number of confounders increases these models become less feasible as there are fewer observations available for each unique combination of confounding variables. In this paper, we propose a new model for estimating treatment effects in observational studies that incorporates both parametric and nonparametric outcome models. By conceptually splitting the data, we can combine these models while maintaining a conjugate framework, allowing us to avoid the use of Markov chain Monte Carlo (MCMC) methods. Approximations using the central limit theorem and random sampling allow our method to be scaled to high-dimensional confounders. Through simulation studies we show our method can be competitive with benchmark models while maintaining efficient computation, and illustrate the method on a large epidemiological health survey.
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Affiliation(s)
- Daniel Daly-Grafstein
- Department of Statistics, University of British Columbia, Vancouver, British Columbia, Canada
| | - Paul Gustafson
- Department of Statistics, University of British Columbia, Vancouver, British Columbia, Canada
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Pavuk M, Rosenbaum PF, Lewin MD, Serio TC, Rago P, Cave MC, Birnbaum LS. Polychlorinated biphenyls, polychlorinated dibenzo-p-dioxins, polychlorinated dibenzofurans, pesticides, and diabetes in the Anniston Community Health Survey follow-up (ACHS II): single exposure and mixture analysis approaches. Sci Total Environ 2023; 877:162920. [PMID: 36934946 DOI: 10.1016/j.scitotenv.2023.162920] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 02/24/2023] [Accepted: 03/13/2023] [Indexed: 05/06/2023]
Abstract
Dioxins and dioxin-like compounds measurements were added to polychlorinated biphenyls (PCBs) and organochlorine pesticides to expand the exposure profile in a follow-up to the Anniston Community Health Survey (ACHS II, 2014) and to study diabetes associations. Participants of ACHS I (2005-2007) still living within the study area were eligible to participate in ACHS II. Diabetes status (type-2) was determined by a doctor's diagnosis, fasting glucose ≥125 mg/dL, or being on any glycemic control medication. Incident diabetes cases were identified in ACHS II among those who did not have diabetes in ACHS I, using the same criteria. Thirty-five ortho-substituted PCBs, 6 pesticides, 7 polychlorinated dibenzo-p-dioxins (PCDD), 10 furans (PCDF), and 3 non-ortho PCBs were measured in 338 ACHS II participants. Dioxin toxic equivalents (TEQs) were calculated for all dioxin-like compounds. Main analyses used logistic regression models to calculate odds ratios (OR) and 95 % confidence intervals (CI). In models adjusted for age, race, sex, BMI, total lipids, family history of diabetes, and taking lipid lowering medication, the highest ORs for diabetes were observed for PCDD TEQ: 3.61 (95 % CI: 1.04, 12.46), dichloro-diphenyl dichloroethylene (p,p'-DDE): 2.07 (95 % CI 1.08, 3.97), and trans-Nonachlor: 2.55 (95 % CI 0.93, 7.02). The OR for sum 35 PCBs was 1.22 (95 % CI: 0.58-2.57). To complement the main analyses, we used BKMR and g-computation models to evaluate 12 mixture components including 4 TEQs, 2 PCB subsets and 6 pesticides; suggestive positive associations for the joint effect of the mixture analyses resulted in ORs of 1.40 (95% CI: -1.13, 3.93) for BKMR and 1.32 (95% CI: -1.12, 3.76) for g-computation. The mixture analyses provide further support to previously observed associations of trans-Nonachlor, p,p'- DDE, PCDD TEQ and some PCB groups with diabetes.
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Affiliation(s)
- M Pavuk
- Agency for Toxic Substances and Disease Registry (ATSDR), Centers for Disease Control and Prevention (CDC), Atlanta, GA, United States of America
| | - P F Rosenbaum
- SUNY Upstate Medical University, Syracuse, NY, United States of America.
| | - M D Lewin
- Agency for Toxic Substances and Disease Registry (ATSDR), Centers for Disease Control and Prevention (CDC), Atlanta, GA, United States of America
| | - T C Serio
- Agency for Toxic Substances and Disease Registry (ATSDR), Centers for Disease Control and Prevention (CDC), Atlanta, GA, United States of America; ATSDR/CDC, Atlanta, GA, United States of America
| | - P Rago
- ATSDR/CDC, Atlanta, GA, United States of America
| | - M C Cave
- University of Louisville, Louisville, KY, United States of America
| | - L S Birnbaum
- NIEHS, Research Triangle Park, NC, United States of America
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Starkopf L, Rajan S, Lange T, Gerds TA. Marginal structural models with monotonicity constraints: A case study in out-of-hospital cardiac arrest patients. Stat Med 2023; 42:603-618. [PMID: 36656059 DOI: 10.1002/sim.9612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Revised: 10/05/2022] [Accepted: 11/09/2022] [Indexed: 01/20/2023]
Abstract
This paper deals with estimating the probability of a binary counterfactual outcome as a function of a continuous covariate under monotonicity constraints. We are motivated by the study of out-of-hospital cardiac arrest patients which aims to estimate the counterfactual 30-day survival probability if either all patients had received, or if none of the patients had received bystander cardiopulmonary resuscitation (CPR), as a function of the ambulance response time. It is natural to assume that the counterfactual 30-day survival probability cannot increase with increasing ambulance response time. We model the monotone relationship with a marginal structural model and B-splines. We then derive an estimating equation for the parameters of interest which however further relies on an auxiliary regression model for the observed 30-day survival probabilities. The predictions of the observed 30-day survival probabilities are used as pseudo-values for the unobserved counterfactual 30-day survival status. The methods are illustrated and contrasted with an unconstrained modeling approach in large-scale Danish registry data.
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Affiliation(s)
- Liis Starkopf
- Section of Biostatistics, University of Copenhagen, Copenhagen, Denmark
| | - Shahzleen Rajan
- Department of Cardiology, Gentofte Hospital, Gentofte, Denmark
| | - Theis Lange
- Section of Biostatistics, University of Copenhagen, Copenhagen, Denmark
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Erdmann A, Loos A, Beyersmann J. A connection between survival multistate models and causal inference for external treatment interruptions. Stat Methods Med Res 2023; 32:267-286. [PMID: 36464917 PMCID: PMC9900139 DOI: 10.1177/09622802221133551] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Recently, treatment interruptions such as a clinical hold in randomized clinical trials have been investigated by using a multistate model approach. The phase III clinical trial START (Stimulating Targeted Antigenic Response To non-small-cell cancer) with primary endpoint overall survival was temporarily placed on hold for enrollment and treatment by the US Food and Drug Administration (FDA). Multistate models provide a flexible framework to account for treatment interruptions induced by a time-dependent external covariate. Extending previous work, we propose a censoring and a filtering approach both aimed at estimating the initial treatment effect on overall survival in the hypothetical situation of no clinical hold. A special focus is on creating a link to causal inference. We show that calculating the matrix of transition probabilities in the multistate model after application of censoring (or filtering) yields the desired causal interpretation. Assumptions in support of the identification of a causal effect by censoring (or filtering) are discussed. Thus, we provide the basis to apply causal censoring (or filtering) in more general settings such as the COVID-19 pandemic. A simulation study demonstrates that both causal censoring and filtering perform favorably compared to a naïve method ignoring the external impact.
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Affiliation(s)
| | - Anja Loos
- Global Biostatistics and Epidemiology, 2792Merck Darmstadt, Darmstadt, Germany
| | - Jan Beyersmann
- Institute of Statistics, 9189University of Ulm, Ulm, Germany
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Vo TT. A cautionary note on the use of G-computation in population adjustment. Res Synth Methods 2023; 14:338-341. [PMID: 36633531 DOI: 10.1002/jrsm.1621] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2022] [Revised: 12/26/2022] [Accepted: 01/03/2023] [Indexed: 01/13/2023]
Abstract
In a recent issue of the Journal; Remiro-Azócar et al. introduce a new method to adjust for population difference between two trials; when the individual patient data (IPD) are only accessible for one study. The proposed method generates the covariate data for the trial without IPD; then using a G-computation approach to transport information about the treatment effect from the other study with IPD to this trial. The authors advocate the use of G-computation over matching-adjusted indirect comparison because (i) the former allows for "useful extrapolation" when there is poor case-mix overlap between populations; and (ii) nonparametric; data-adaptive methods can be used to reduce the risk of (outcome) model misspecification. In this commentary; we provide a different perspective from these arguments. Despite certain disagreements; we believe that the proposed data generation approaches can open new and interesting research directions for population adjustment methodology in the future.
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Affiliation(s)
- Tat-Thang Vo
- Department of Statistics and Data Science, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania, USA
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Sasaki N, Jones LE, Morse GS, Carpenter DO. Mixture Effects of Polychlorinated Biphenyls (PCBs) and Three Organochlorine Pesticides on Cognitive Function in Mohawk Adults at Akwesasne. Int J Environ Res Public Health 2023; 20:1148. [PMID: 36673903 PMCID: PMC9859591 DOI: 10.3390/ijerph20021148] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2022] [Revised: 01/03/2023] [Accepted: 01/04/2023] [Indexed: 05/22/2023]
Abstract
The Mohawks at Akwesasne have been highly exposed to polychlorinated biphenyls (PCBs), via releases from three aluminum foundries located near the reserve. They are also exposed to organochlorine pesticides, namely hexachlorobenzene (HCB), dichlorodiphenyldichloroethylene (DDE), and mirex. Previous studies have demonstrated reduced cognition in relation to total PCBs, but the effects of the mixtures of different PCB congener groups, HCB, DDE, and mirex on cognitive function have not been studied. Therefore, cognitive performance for executive function, scored via the digit symbol substitution test (DSST), in Mohawk adults aged 17-79 years (n = 301), was assessed in relation to serum concentrations of low-chlorinated PCBs, high-chlorinated PCBs, total PCBs, HCB, DDE, and mirex. We used mixture models employing the quantile-based g-computation method. The mixture effects of low-chlorinated PCBs, high-chlorinated PCBs, HCB, DDE, and mirex were significantly associated with 4.01 DSST scores decrements in the oldest age group, 47-79 years old. There were important contributions to mixture effects from low-chlorinated PCBs, high-chlorinated PCBs, and total PCBs, with smaller contributions of HCB and DDE. Our findings indicate that exposures to both low- and high-chlorinated PCBs increase the risk of cognitive decline in older adults, while DDE and HCB have less effect.
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Affiliation(s)
- Nozomi Sasaki
- Institute for Health and the Environment, University at Albany, Rensselaer, NY 12144, USA
| | - Laura E. Jones
- Institute for Health and the Environment, University at Albany, Rensselaer, NY 12144, USA
- Department of Biostatistics and Epidemiology, School of Public Health, University at Albany, Rensselaer, NY 12144, USA
| | - Gayle S. Morse
- Institute for Health and the Environment, University at Albany, Rensselaer, NY 12144, USA
- Department of Psychology, School of Health Sciences, Russell Sage College, Troy, NY 12180, USA
| | - David O. Carpenter
- Institute for Health and the Environment, University at Albany, Rensselaer, NY 12144, USA
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Rudolph JE, Schisterman EF, Naimi AI. A Simulation Study Comparing the Performance of Time-Varying Inverse Probability Weighting and G-Computation in Survival Analysis. Am J Epidemiol 2023; 192:102-110. [PMID: 36124667 PMCID: PMC10144678 DOI: 10.1093/aje/kwac162] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Revised: 08/10/2022] [Accepted: 09/13/2022] [Indexed: 01/11/2023] Open
Abstract
Inverse probability weighting (IPW) and g-computation are commonly used in time-varying analyses. To inform decisions on which to use, we compared these methods using a plasmode simulation based on data from the Effects of Aspirin in Gestation and Reproduction (EAGeR) Trial (June 15, 2007-July 15, 2011). In our main analysis, we simulated a cohort study of 1,226 individuals followed for up to 10 weeks. The exposure was weekly exercise, and the outcome was time to pregnancy. We controlled for 6 confounding factors: 4 baseline confounders (race, ever smoking, age, and body mass index) and 2 time-varying confounders (compliance with assigned treatment and nausea). We sought to estimate the average causal risk difference by 10 weeks, using IPW and g-computation implemented using a Monte Carlo estimator and iterated conditional expectations (ICE). Across 500 simulations, we compared the bias, empirical standard error (ESE), average standard error, standard error ratio, and 95% confidence interval coverage of each approach. IPW (bias = 0.02; ESE = 0.04; coverage = 92.6%) and Monte Carlo g-computation (bias = -0.01; ESE = 0.03; coverage = 94.2%) performed similarly. ICE g-computation was the least biased but least precise estimator (bias = 0.01; ESE = 0.06; coverage = 93.4%). When choosing an estimator, one should consider factors like the research question, the prevalences of the exposure and outcome, and the number of time points being analyzed.
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Affiliation(s)
- Jacqueline E Rudolph
- Correspondence to Dr. Jacqueline E. Rudolph, Department of Epidemiology, Bloomberg School of Public Health, Johns Hopkins University, 615 N. Wolfe Street, Baltimore, MD 21205 (e-mail: )
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Léger M, Chatton A, Le Borgne F, Pirracchio R, Lasocki S, Foucher Y. Causal inference in case of near-violation of positivity: comparison of methods. Biom J 2022; 64:1389-1403. [PMID: 34993990 DOI: 10.1002/bimj.202000323] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Revised: 09/07/2021] [Accepted: 10/24/2021] [Indexed: 12/14/2022]
Abstract
In causal studies, the near-violation of the positivity may occur by chance, because of sample-to-sample fluctuation despite the theoretical veracity of the positivity assumption in the population. It may mostly happen when the exposure prevalence is low or when the sample size is small. We aimed to compare the robustness of g-computation (GC), inverse probability weighting (IPW), truncated IPW, targeted maximum likelihood estimation (TMLE), and truncated TMLE in this situation, using simulations and one real application. We also tested different extrapolation situations for the sub-group with a positivity violation. The results illustrated that the near-violation of the positivity impacted all methods. We demonstrated the robustness of GC and TMLE-based methods. Truncation helped in limiting the bias in near-violation situations, but at the cost of bias in normal conditions. The application illustrated the variability of the results between the methods and the importance of choosing the most appropriate one. In conclusion, compared to propensity score-based methods, methods based on outcome regression should be preferred when suspecting near-violation of the positivity assumption.
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Affiliation(s)
- Maxime Léger
- INSERM UMR 1246 - SPHERE, Université de Nantes, Université de Tours, Nantes, France.,Département d'Anesthésie-Réanimation, Centre Hospitalier Universitaire d'Angers, Angers, France
| | - Arthur Chatton
- INSERM UMR 1246 - SPHERE, Université de Nantes, Université de Tours, Nantes, France.,IDBC-A2COM, Nantes, France
| | - Florent Le Borgne
- INSERM UMR 1246 - SPHERE, Université de Nantes, Université de Tours, Nantes, France.,IDBC-A2COM, Nantes, France
| | - Romain Pirracchio
- Department of Anesthesia and Perioperative Care, University of California, San Francisco, CA, USA
| | - Sigismond Lasocki
- Département d'Anesthésie-Réanimation, Centre Hospitalier Universitaire d'Angers, Angers, France
| | - Yohann Foucher
- INSERM UMR 1246 - SPHERE, Université de Nantes, Université de Tours, Nantes, France.,Centre Hospitalier Universitaire de Nantes, Nantes, France
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Inoue K, Ritz B, Arah OA. Causal Effect of Chronic Pain on Mortality Through Opioid Prescriptions: Application of the Front-Door Formula. Epidemiology 2022; 33:572-580. [PMID: 35384895 PMCID: PMC9148671 DOI: 10.1097/ede.0000000000001490] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2019] [Accepted: 03/24/2022] [Indexed: 11/26/2022]
Abstract
BACKGROUND Chronic pain is the leading cause of disability worldwide and is strongly associated with the epidemic of opioid overdosing events. However, the causal links between chronic pain, opioid prescriptions, and mortality remain unclear. METHODS This study included 13,884 US adults aged ≥20 years who provided data on chronic pain in the National Health and Nutrition Examination Survey 1999-2004 with linkage to mortality databases through 2015. We employed the generalized form of the front-door formula within the structural causal model framework to investigate the causal effect of chronic pain on all-cause mortality mediated by opioid prescriptions. RESULTS We identified a total of 718 participants at 3 years of follow-up and 1260 participants at 5 years as having died from all causes. Opioid prescriptions increased the risk of all-cause mortality with an estimated odds ratio (OR) (95% confidence interval) = 1.5 (1.1, 1.9) at 3 years and 1.3 (1.1, 1.6) at 5 years. The front-door formula revealed that chronic pain increased the risk of all-cause mortality through opioid prescriptions; OR = 1.06 (1.01, 1.11) at 3 years and 1.03 (1.01, 1.06) at 5 years. Our bias analysis showed that our findings based on the front-door formula were likely robust to plausible sources of bias from uncontrolled exposure-mediator or mediator-outcome confounding. CONCLUSIONS Chronic pain increased the risk of all-cause mortality through opioid prescriptions. Our findings highlight the importance of careful guideline-based chronic pain management to prevent death from possibly inappropriate opioid prescriptions driven by chronic pain.
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Affiliation(s)
- Kosuke Inoue
- From the Department of Social Epidemiology, Graduate School of Medicine, Kyoto University, Kyoto, Japan
- Department of Epidemiology, Fielding School of Public Health, University of California, Los Angeles (UCLA), Los Angeles, California, USA
| | - Beate Ritz
- Department of Epidemiology, Fielding School of Public Health, University of California, Los Angeles (UCLA), Los Angeles, California, USA
- Department of Environmental Health Sciences, UCLA Fielding School of Public Health, Los Angeles, California, USA
- Department of Neurology, UCLA David Geffen School of Medicine, Los Angeles, California, USA
| | - Onyebuchi A. Arah
- Department of Epidemiology, Fielding School of Public Health, University of California, Los Angeles (UCLA), Los Angeles, California, USA
- Department of Statistics, UCLA College, Los Angeles, California, USA
- Center for Social Statistics, UCLA, Los Angeles, California, USA
- California Center for Population Research, UCLA Los Angeles, California, USA
- Department of Public Health, Research Unit for Epidemiology, Aarhus University, Aarhus, Denmark
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Graetz N, Boen CE, Esposito MH. Structural Racism and Quantitative Causal Inference: A Life Course Mediation Framework for Decomposing Racial Health Disparities. J Health Soc Behav 2022; 63:232-249. [PMID: 35001689 DOI: 10.1177/00221465211066108] [Citation(s) in RCA: 22] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
Quantitative studies of racial health disparities often use static measures of self-reported race and conventional regression estimators, which critics argue is inconsistent with social-constructivist theories of race, racialization, and racism. We demonstrate an alternative counterfactual approach to explain how multiple racialized systems dynamically shape health over time, examining racial inequities in cardiometabolic risk in the National Longitudinal Study of Adolescent to Adult Health. This framework accounts for the dynamics of time-varying confounding and mediation that is required in operationalizing a "race" variable as part of a social process (racism) rather than a separable, individual characteristic. We decompose the observed disparity into three types of effects: a controlled direct effect ("unobserved racism"), proportions attributable to interaction ("racial discrimination"), and pure indirect effects ("emergent discrimination"). We discuss the limitations of counterfactual approaches while highlighting how they can be combined with critical theories to quantify how interlocking systems produce racial health inequities.
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Affiliation(s)
- Nick Graetz
- Princeton University, Princeton, NJ, USA
- University of Pennsylvania, Philadelphia, PA, USA
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14
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Gennings C, Svensson K, Wolk A, Lindh C, Kiviranta H, Bornehag CG. Using Metrics of a Mixture Effect and Nutrition from an Observational Study for Consideration towards Causal Inference. Int J Environ Res Public Health 2022; 19:2273. [PMID: 35206461 PMCID: PMC8872366 DOI: 10.3390/ijerph19042273] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Revised: 02/07/2022] [Accepted: 02/11/2022] [Indexed: 02/06/2023]
Abstract
Environmental exposures to a myriad of chemicals are associated with adverse health effects in humans, while good nutrition is associated with improved health. Single chemical in vivo and in vitro studies demonstrate causal links between the chemicals and outcomes, but such studies do not represent human exposure to environmental mixtures. One way of summarizing the effect of the joint action of chemical mixtures is through an empirically weighted index using weighted quantile sum (WQS) regression. My Nutrition Index (MNI) is a metric of overall dietary nutrition based on guideline values, including for pregnant women. Our objective is to demonstrate the use of an index as a metric for more causally linking human exposure to health outcomes using observational data. We use both a WQS index of 26 endocrine-disrupting chemicals (EDCs) and MNI using data from the SELMA pregnancy cohort to conduct causal inference using g-computation with counterfactuals for assumed either reduced prenatal EDC exposures or improved prenatal nutrition. Reducing the EDC exposure using the WQS index as a metric or improving dietary nutrition using MNI as a metric, the counterfactuals in a causal inference with one SD change indicate significant improvement in cognitive function. Evaluation of such a strategy may support decision makers for risk management of EDCs and individual choices for improving dietary nutrition.
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Affiliation(s)
- Chris Gennings
- Environmental Medicine and Public Health, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA;
| | - Katherine Svensson
- Department of Health Sciences, Karlstad University, 65188 Karlstad, Sweden;
| | - Alicja Wolk
- Institute of Environmental Medicine, Karolinska Institutet, 17177 Stockholm, Sweden;
- Department of Surgical Sciences, Uppsala University, 75237 Uppsala, Sweden
| | - Christian Lindh
- Division of Occupational and Environmental Medicine, Lund University, 22381 Lund, Sweden;
| | - Hannu Kiviranta
- National Institute for Health and Welfare, FI-00271 Helsinki, Finland;
| | - Carl-Gustaf Bornehag
- Environmental Medicine and Public Health, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA;
- Department of Health Sciences, Karlstad University, 65188 Karlstad, Sweden;
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15
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Rudolph JE, Cartus A, Bodnar LM, Schisterman EF, Naimi AI. The Role of the Natural Course in Causal Analysis. Am J Epidemiol 2022; 191:341-348. [PMID: 34643230 DOI: 10.1093/aje/kwab248] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Accepted: 10/05/2021] [Indexed: 11/13/2022] Open
Abstract
The average causal effect compares counterfactual outcomes if everyone had been exposed versus if everyone had been unexposed, which can be an unrealistic contrast. Alternatively, we can target effects that compare counterfactual outcomes against the factual outcomes observed in the sample (i.e., we can compare against the natural course). Here, we demonstrate how the natural course can be estimated and used in causal analyses for model validation and effect estimation. Our example is an analysis assessing the impact of taking aspirin on pregnancy, 26 weeks after randomization, in the Effects of Aspirin in Gestation and Reproduction trial (United States, 2006-2012). To validate our models, we estimated the natural course using g-computation and then compared that against the observed incidence of pregnancy. We observed good agreement between the observed and model-based natural courses. We then estimated an effect that compared the natural course against the scenario in which participants assigned to aspirin always complied. If participants had always complied, there would have been 5.0 (95% confidence interval: 2.2, 7.8) more pregnancies per 100 women than was observed. It is good practice to estimate the natural course for model validation when using parametric models, but whether one should estimate a natural course contrast depends on the underlying research questions.
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Mooney SJ, Shev AB, Keyes KM, Tracy M, Cerdá M. G-Computation and Agent-Based Modeling for Social Epidemiology: Can Population Interventions Prevent Posttraumatic Stress Disorder? Am J Epidemiol 2022; 191:188-197. [PMID: 34409437 PMCID: PMC8897987 DOI: 10.1093/aje/kwab219] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2020] [Revised: 08/02/2021] [Accepted: 08/11/2021] [Indexed: 11/13/2022] Open
Abstract
Agent-based modeling and g-computation can both be used to estimate impacts of intervening on complex systems. We explored each modeling approach within an applied example: interventions to reduce posttraumatic stress disorder (PTSD). We used data from a cohort of 2,282 adults representative of the adult population of the New York City metropolitan area from 2002-2006, of whom 16.3% developed PTSD over their lifetimes. We built 4 models: g-computation, an agent-based model (ABM) with no between-agent interactions, an ABM with violent-interaction dynamics, and an ABM with neighborhood dynamics. Three interventions were tested: 1) reducing violent victimization by 37.2% (real-world reduction); 2) reducing violent victimization by100%; and 3) supplementing the income of 20% of lower-income participants. The g-computation model estimated population-level PTSD risk reductions of 0.12% (95% confidence interval (CI): -0.16, 0.29), 0.28% (95% CI: -0.30, 0.70), and 1.55% (95% CI: 0.40, 2.12), respectively. The ABM with no interactions replicated the findings from g-computation. Introduction of interaction dynamics modestly decreased estimated intervention effects (income-supplement risk reduction dropped to 1.47%), whereas introduction of neighborhood dynamics modestly increased effectiveness (income-supplement risk reduction increased to 1.58%). Compared with g-computation, agent-based modeling permitted deeper exploration of complex systems dynamics at the cost of further assumptions.
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Affiliation(s)
- Stephen J Mooney
- Correspondence to Dr. Stephen Mooney, 1959 NE Pacific Street, Health Sciences Building F-262, Box 357236, Seattle, WA 98195 (e-mail: )
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17
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Keil AP, Buckley JP, Kalkbrenner AE. Bayesian G-Computation for Estimating Impacts of Interventions on Exposure Mixtures: Demonstration With Metals From Coal-Fired Power Plants and Birth Weight. Am J Epidemiol 2021; 190:2647-2657. [PMID: 33751055 DOI: 10.1093/aje/kwab053] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2019] [Revised: 11/19/2020] [Accepted: 12/03/2020] [Indexed: 02/05/2023] Open
Abstract
The importance of studying the health impacts of exposure mixtures is increasingly being recognized, but such research presents many methodological and interpretation difficulties. We used Bayesian g-computation to estimate effects of a simulated public health action on exposure mixtures and birth weights in Milwaukee, Wisconsin, in 2011-2013. We linked data from birth records with census-tract-level air toxics data from the Environmental Protection Agency's National Air Toxics Assessment model. We estimated the difference between observed and expected birth weights that theoretically would have followed a hypothetical intervention to reduce exposure to 6 airborne metals by decommissioning 3 coal-fired power plants in Milwaukee County prior to 2010. Using Bayesian g-computation, we estimated a 68-g (95% credible interval: 25, 135) increase in birth weight following this hypothetical intervention. This example demonstrates the utility of our approach for using observational data to evaluate and contrast possible public health actions. Additionally, Bayesian g-computation offers a flexible strategy for estimating the effects of highly correlated exposures, addressing statistical issues such as variance inflation, and addressing conceptual issues such as the lack of interpretability of independent effects.
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18
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Eisenberg-Guyot J, Mooney SJ, Barrington WE, Hajat A. Union Burying Ground: Mortality, Mortality Inequities, and Sinking Labor Union Membership in the United States. Epidemiology 2021; 32:721-730. [PMID: 34224470 PMCID: PMC8338895 DOI: 10.1097/ede.0000000000001386] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
BACKGROUND Over the last several decades in the United States, socioeconomic life-expectancy inequities have increased 1-2 years. Declining labor-union density has fueled growing income inequities across classes and exacerbated racial income inequities. Using Panel Study of Income Dynamics (PSID) data, we examined the longitudinal union-mortality relationship and estimated whether declining union density has also exacerbated mortality inequities. METHODS Our sample included respondents ages 25-66 to the 1979-2015 PSID with mortality follow-up through age 68 and year 2017. To address healthy-worker bias, we used the parametric g-formula. First, we estimated how a scenario setting all (versus none) of respondents' employed-person-years to union-member employed-person-years would have affected mortality incidence. Next, we examined gender, racial, and educational effect modification. Finally, we estimated how racial and educational mortality inequities would have changed if union-membership prevalence had remained at 1979 (vs. 2015) levels throughout follow-up. RESULTS In the full sample (respondents = 23,022, observations = 146,681), the union scenario was associated with lower mortality incidence than the nonunion scenario (RR = 0.90, 95% CI = 0.80, 0.99; RD per 1,000 = -19, 95% CI = -37, -1). This protective association generally held across subgroups, although it was stronger among the more-educated. However, we found little evidence mortality inequities would have lessened if union membership had remained at 1979 levels. CONCLUSIONS To our knowledge, this was the first individual-level US-based study with repeated union-membership measurements to analyze the union-mortality relationship. We estimated a protective union-mortality association, but found little evidence declining union density has exacerbated mortality inequities; importantly, we did not incorporate contextual-level effects. See video abstract at, http://links.lww.com/EDE/B839.
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Affiliation(s)
- Jerzy Eisenberg-Guyot
- Department of Epidemiology, Mailman School of Public Health, Columbia University, NY, NY
- Department of Epidemiology, School of Public Health, University of Washington, Seattle, WA
| | - Stephen J. Mooney
- Department of Epidemiology, School of Public Health, University of Washington, Seattle, WA
- Harborview Injury Prevention & Research Center, University of Washington, Seattle, WA
| | - Wendy E. Barrington
- Department of Epidemiology, School of Public Health, University of Washington, Seattle, WA
- Department of Psychosocial and Community Health, School of Nursing, University of Washington, Seattle, WA
| | - Anjum Hajat
- Department of Epidemiology, School of Public Health, University of Washington, Seattle, WA
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Rogawski McQuade ET, Benjamin-Chung J, Westreich D, Arnold BF. Population intervention effects in observational studies to emulate target trial results: reconciling the effects of improved sanitation on child growth. Int J Epidemiol 2021; 51:279-290. [PMID: 34151953 DOI: 10.1093/ije/dyab070] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2020] [Accepted: 03/17/2021] [Indexed: 11/13/2022] Open
Abstract
BACKGROUND Improved sanitation has been associated with improved child growth in observational studies, but multiple randomized trials that delivered improved sanitation found no effect on child growth. We assessed to what extent differences in the effect estimated in the two study designs (the effect of treatment in observational studies and the effect of treatment assignment in trials) could explain the contradictory results. METHODS We used parametric g-computation in five prospective studies (n = 21 524) and 59 cross-sectional Demographic and Health Surveys (DHS; n = 158 439). We compared the average treatment effect (ATE) for improved sanitation on mean length-for-age z-score (LAZ) among children aged <2 years to population intervention effects (PIEs), which are the observational analogue of the effect estimated in trials in which some participants are already exposed. RESULTS The ATE was >0.15 z-scores, a clinically meaningful difference, in most prospective studies but in <20% of DHS surveys. The PIE was always smaller than the ATE, and the magnitude of difference depended on the baseline prevalence of the improved sanitation. Interventions with suboptimal coverage and interventions delivered in populations with higher mean LAZ had a smaller effect on population-level LAZ. CONCLUSIONS Estimates of PIEs corresponding to anticipated trial results were often smaller than clinically meaningful effects. Incongruence between observational associations and null trial results may in part be explained by expected differences between the effects estimated. Using observational ATEs to set expectations for trials may overestimate the impact that sanitation interventions can achieve. PIEs predict realistic effects and should be more routinely estimated.
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Affiliation(s)
- Elizabeth T Rogawski McQuade
- Department of Public Health Sciences, University of Virginia, Charlottesville, VA, USA.,Division of Infectious Diseases and International Health, University of Virginia, Charlottesville, VA, USA
| | - Jade Benjamin-Chung
- Department of Epidemiology & Biostatistics, University of California, Berkeley, CA, USA
| | - Daniel Westreich
- Division of Epidemiology, University of North Carolina-Chapel Hill, NC, USA
| | - Benjamin F Arnold
- Francis I. Proctor Foundation, University of California, San Francisco, CA, USA.,Department of Ophthalmology, University of California, San Francisco, CA, USA
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20
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Eisenberg-Guyot J, Mooney SJ, Barrington WE, Hajat A. Does the Union Make Us Strong? Labor-Union Membership, Self-Rated Health, and Mental Illness: A Parametric G-Formula Approach. Am J Epidemiol 2021; 190:630-641. [PMID: 33047779 PMCID: PMC8024047 DOI: 10.1093/aje/kwaa221] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2020] [Revised: 09/25/2020] [Accepted: 10/08/2020] [Indexed: 11/14/2022] Open
Abstract
Union members enjoy better wages and benefits and greater power than nonmembers, which can improve health. However, the longitudinal union-health relationship remains uncertain, partially because of healthy-worker bias, which cannot be addressed without high-quality data and methods that account for exposure-confounder feedback and structural nonpositivity. Applying one such method, the parametric g-formula, to US-based Panel Study of Income Dynamics data, we analyzed the longitudinal relationships between union membership, poor/fair self-rated health (SRH), and moderate mental illness (Kessler 6-item score of ≥5). The SRH analyses included 16,719 respondents followed from 1985-2017, while the mental-illness analyses included 5,813 respondents followed from 2001-2017. Using the parametric g-formula, we contrasted cumulative incidence of the outcomes under 2 scenarios, one in which we set all employed-person-years to union-member employed-person-years (union scenario), and one in which we set no employed-person-years to union-member employed-person-years (nonunion scenario). We also examined whether the contrast varied by sex, sex and race, and sex and education. Overall, the union scenario was not associated with reduced incidence of poor/fair SRH (relative risk = 1.01, 95% confidence interval (CI): 0.95, 1.09; risk difference = 0.01, 95% CI: -0.03, 0.04) or moderate mental illness (relative risk = 1.02, 95% CI: 0.92, 1.12; risk difference = 0.01, 95% CI: -0.04, 0.06) relative to the nonunion scenario. These associations largely did not vary by subgroup.
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Affiliation(s)
- Jerzy Eisenberg-Guyot
- Correspondence to: Dr. Jerzy Eisenberg-Guyot, Department of Epidemiology, School of Public Health, University of Washington, 3980 15th Avenue NE, Box #351619, Seattle, WA 98195 (e-mail: )
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21
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Oganisian A, Roy JA. A practical introduction to Bayesian estimation of causal effects: Parametric and nonparametric approaches. Stat Med 2021; 40:518-551. [PMID: 33015870 PMCID: PMC8640942 DOI: 10.1002/sim.8761] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2020] [Revised: 09/07/2020] [Accepted: 09/08/2020] [Indexed: 12/27/2022]
Abstract
Substantial advances in Bayesian methods for causal inference have been made in recent years. We provide an introduction to Bayesian inference for causal effects for practicing statisticians who have some familiarity with Bayesian models and would like an overview of what it can add to causal estimation in practical settings. In the paper, we demonstrate how priors can induce shrinkage and sparsity in parametric models and be used to perform probabilistic sensitivity analyses around causal assumptions. We provide an overview of nonparametric Bayesian estimation and survey their applications in the causal inference literature. Inference in the point-treatment and time-varying treatment settings are considered. For the latter, we explore both static and dynamic treatment regimes. Throughout, we illustrate implementation using off-the-shelf open source software. We hope to leave the reader with implementation-level knowledge of Bayesian causal inference using both parametric and nonparametric models. All synthetic examples and code used in the paper are publicly available on a companion GitHub repository.
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Affiliation(s)
- Arman Oganisian
- Department of Biostatistics, Epidemiology, and Informatics, University of Pennsylvania, Pennsylvania, USA
| | - Jason A. Roy
- Department of Biostatistics and Epidemiology, Rutgers University, New Jersey, USA
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Breger TL, Edwards JK, Cole SR, Westreich D, Pence BW, Adimora AA. Two-stage g-computation: Evaluating Treatment and Intervention Impacts in Observational Cohorts When Exposure Information Is Partly Missing. Epidemiology 2020; 31:695-703. [PMID: 32657953 PMCID: PMC8725064 DOI: 10.1097/ede.0000000000001233] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
Illustrations of the g-computation algorithm to evaluate population average treatment and intervention effects have been predominantly implemented in settings with complete exposure information. Thus, worked examples of approaches to handle missing data in this causal framework are needed to facilitate wider use of these estimators. We illustrate two-stage g-computation estimators that leverage partially observed information on the full study sample and complete exposure information on a subset to estimate causal effects. In a hypothetical cohort of 1,623 human immunodeficiency virus (HIV)-positive women with 30% complete opioid prescription information, we illustrate a two-stage extrapolation g-computation estimator for the average treatment effect of shorter or longer duration opioid prescriptions; we further illustrate two-stage inverse probability weighting and imputation g-computation estimators for the average intervention effect of shortening the duration of prescriptions relative to the status quo. Two-stage g-computation estimators approximated the true risk differences for the population average treatment and intervention effects while g-computation fit to the subset of complete cases was biased. In 10,000 Monte Carlo simulations, two-stage approaches considerably reduced bias and mean squared error and improved the coverage of 95% confidence limits. Although missing data threaten validity and precision, two-stage g-computation designs offer principled approaches to handling missing information.
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Affiliation(s)
- Tiffany L. Breger
- Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC
| | - Jessie K. Edwards
- Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC
| | - Stephen R. Cole
- Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC
| | - Daniel Westreich
- Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC
| | - Brian W. Pence
- Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC
| | - Adaora A. Adimora
- Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC
- Department of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, NC
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Okubo Y, Horimukai K, Michihata N, Morita K, Matsui H, Fushimi K, Yasunaga H. Association between early antibiotic treatment and clinical outcomes in children hospitalized for asthma exacerbation. J Allergy Clin Immunol 2020; 147:114-122.e14. [PMID: 32504615 DOI: 10.1016/j.jaci.2020.05.030] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2020] [Revised: 05/17/2020] [Accepted: 05/19/2020] [Indexed: 10/24/2022]
Abstract
BACKGROUND Professional society guidelines recommend against routine early antibiotic use in the treatment of asthma exacerbation without comorbid bacterial infection. However, high antibiotic prescribing rates have been reported in developed countries. OBJECTIVE We sought to assess the effectiveness of this strategy in the routine care of children. METHODS Using data on 48,743 children hospitalized for asthma exacerbation with no indication of bacterial infection during the period 2010 to 2018, we conducted a retrospective cohort study to compare clinical outcomes and resource utilization between children who received early antibiotic treatment and those who did not. RESULTS Overall, 19,866 children (41%) received early antibiotic treatment. According to the propensity score matching analysis, children with early antibiotic treatment had longer hospital stay (mean difference, 0.21 days; 95% CI, 0.18-0.28), higher hospitalization costs (mean difference, $83.5; 95% CI, 62.9-104.0), and higher risk of probiotic use (risk ratio, 2.01; 95% CI, 1.81-2.23) than children who did not receive early antibiotic therapy. Similar results were found from inverse probability of treatment weighting, g-computation, and instrumental variable methods and sensitivity analyses. The risks of mechanical ventilation and 30-day readmission were similar between the groups or slightly higher in the treated group, depending on the statistical models. CONCLUSIONS Antibiotic therapy may be associated with prolonged hospital stay, elevated hospitalization costs, and high risk of probiotic use without improving treatment failure and readmission. Our findings highlight the need for reducing inappropriate antibiotic use among children hospitalized for asthma.
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Affiliation(s)
- Yusuke Okubo
- Department of Epidemiology, University of California, Los Angeles, Fielding School of Public Health, Los Angeles, Calif; Department of Social Medicine, National Center for Child Health and Development, Tokyo, Japan; Department of Clinical Epidemiology and Health Economics, School of Public Health, The University of Tokyo, Tokyo, Japan.
| | - Kenta Horimukai
- Department of Pediatrics, Jikei University Katsushika Medical Center, Tokyo, Japan
| | - Nobuaki Michihata
- Department of Health Services Research, Graduate School of Medicine, The University of Tokyo, Tokyo, Japan
| | - Kojiro Morita
- Department of Clinical Epidemiology and Health Economics, School of Public Health, The University of Tokyo, Tokyo, Japan
| | - Hiroki Matsui
- Department of Clinical Epidemiology and Health Economics, School of Public Health, The University of Tokyo, Tokyo, Japan
| | - Kiyohide Fushimi
- Department of Health Policy and Informatics, Tokyo Medical and Dental University Graduate School of Medicine, Tokyo, Japan
| | - Hideo Yasunaga
- Department of Clinical Epidemiology and Health Economics, School of Public Health, The University of Tokyo, Tokyo, Japan
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Oulhote Y, Coull B, Bind MA, Debes F, Nielsen F, Tamayo I, Weihe P, Grandjean P. Joint and independent neurotoxic effects of early life exposures to a chemical mixture: A multi-pollutant approach combining ensemble learning and g-computation. Environ Epidemiol 2019; 3:e063. [PMID: 32051926 PMCID: PMC7015154 DOI: 10.1097/ee9.0000000000000063] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2019] [Accepted: 07/22/2019] [Indexed: 11/25/2022] Open
Abstract
BACKGROUND Exposure to mercury (Hg) is associated with adverse developmental effects. However, Hg occurs with a multitude of chemicals. We assessed the associations of developmental exposure to multiple pollutants with children's neurodevelopment using a novel approach. METHODS Hg, polychlorinated biphenyls (PCBs), and perfluoroalkyl substances were measured in maternal and children's blood at 5-years (n=449 and 419). At 7-years, children were administered Boston Naming Test (BNT) and the Strengths and Difficulties Questionnaire (SDQ). We used the G-formula combined with SuperLearner to estimate independent and joint effects of chemicals at both ages. We constructed flexible exposure-response relationships and assessed interactions. RESULTS Most chemicals showed negative relationships with BNT scores. An inter-quartile range (IQR) increase in maternal Hg and perfluorooctanoic acid (PFOA) was associated with 0.15 standard deviation [SD] (95% Confidence Interval [CI]: -0.29,-0.03) and 0.14 SD (95%CI: -0.26,-0.05) lower scores in BNT, whereas a joint IQR increase in the mixture of chemicals was associated with 0.48 SD (95%CI: -0.69,-0.25) lower scores in BNT. An IQR increase in PFOA was associated with 0.11 SD (95%CI: 0.02,0.26) higher total SDQ difficulties scores. Maternal ∑PCBs concentrations were associated with lower SDQ scores (β=-0.09 SD; 95%CI: -0.19,0), whereas 5-years ∑PCBs showed a negative association (β=-0.09 SD; 95%CI: -0.21,0). Finally, a joint IQR increase in the mixture was associated with 0.22 SD (95%CI: 0.04,0.4) higher SDQ scores. CONCLUSIONS Using a novel statistical approach, we confirmed associations between prenatal mercury exposure and lower cognitive function. The potential developmental effects of PFASs need additional attention.
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Affiliation(s)
- Youssef Oulhote
- Department of Biostatistics and Epidemiology, School of Public Health and Health Sciences, UMASS- Amherst, Amherst, Massachusetts
- Department of Environmental Health, Harvard T. H. Chan School of Public Health, Boston, Massachusetts
| | - Brent Coull
- Department of Environmental Health, Harvard T. H. Chan School of Public Health, Boston, Massachusetts
- Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, Massachusetts
| | - Marie-Abele Bind
- Department of Statistics, Faculty of Arts and Sciences, Harvard University, Cambridge, Massachusetts
| | - Frodi Debes
- Department of Occupational Medicine and Public Health, Faroese Hospital System, Torshavn, Faroe Islands
| | - Flemming Nielsen
- Institute of Public Health, University of Southern Denmark, Odense, Denmark
| | - Ibon Tamayo
- Department of Statistics, Faculty of Arts and Sciences, Harvard University, Cambridge, Massachusetts
| | - Pal Weihe
- Department of Occupational Medicine and Public Health, Faroese Hospital System, Torshavn, Faroe Islands
| | - Philippe Grandjean
- Department of Environmental Health, Harvard T. H. Chan School of Public Health, Boston, Massachusetts
- Institute of Public Health, University of Southern Denmark, Odense, Denmark
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25
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Abstract
Epidemiologists often wish to estimate quantities that are easy to communicate and correspond to the results of realistic public health interventions. Methods from causal inference can answer these questions. We adopt the language of potential outcomes under Rubin's original Bayesian framework and show that the parametric g-formula is easily amenable to a Bayesian approach. We show that the frequentist properties of the Bayesian g-formula suggest it improves the accuracy of estimates of causal effects in small samples or when data are sparse. We demonstrate an approach to estimate the effect of environmental tobacco smoke on body mass index among children aged 4-9 years who were enrolled in a longitudinal birth cohort in New York, USA. We provide an algorithm and supply SAS and Stan code that can be adopted to implement this computational approach more generally.
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Affiliation(s)
- Alexander P. Keil
- Department of Epidemiology, University of North Carolina, Chapel Hill, USA
| | - Eric J. Daza
- Stanford Prevention Research Center, Stanford University School of Medicine, Palo Alto, USA
| | - Stephanie M. Engel
- Department of Epidemiology, University of North Carolina, Chapel Hill, USA
| | - Jessie P. Buckley
- Department of Epidemiology, University of North Carolina, Chapel Hill, USA
| | - Jessie K. Edwards
- Department of Epidemiology, University of North Carolina, Chapel Hill, USA
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26
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Mooney SJ, Magee C, Dang K, Leonard JC, Yang J, Rivara FP, Ebel BE, Rowhani-Rahbar A, Quistberg DA. "Complete Streets" and Adult Bicyclist Fatalities: Applying G-Computation to Evaluate an Intervention That Affects the Size of a Population at Risk. Am J Epidemiol 2018; 187:2038-2045. [PMID: 29767676 PMCID: PMC6118069 DOI: 10.1093/aje/kwy100] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2017] [Revised: 04/25/2018] [Accepted: 04/27/2018] [Indexed: 11/12/2022] Open
Abstract
"Complete streets" policies require transportation engineers to make provisions for pedestrians, bicyclists, and mass transit users. These policies may make bicycling safer for individual cyclists while increasing the overall number of bicycle fatalities if more people cycle due to improved infrastructure. We merged county-level records of complete streets policies with Fatality Analysis Reporting System counts of cyclist fatalities occurring between January 2000 and December 2015. Because comprehensive county-level estimates of numbers of cyclists were not available, we used bicycle commuter estimates from the American Community Survey and the US Census as a proxy for the cycling population and limited analysis to 183 counties (accounting for over half of the US population) for which cycle commuting estimates were consistently nonzero. We used G-computation to estimate the effect of complete streets policies on overall numbers of cyclist fatalities while also accounting for potential policy effects on the size of the cycling population. Over a period of 16 years, 5,254 cyclists died in these counties, representing 34 fatalities per 100,000 cyclist-years. We estimated that complete streets policies made cycling safer, averting 0.6 fatalities per 100,000 cyclist-years (95% confidence interval: -1.0, -0.3) by encouraging a 2.4% increase in cycling but producing only a 0.7% increase in cyclist fatalities. G-computation is a useful tool for understanding the impact of policy on risk and exposure.
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Affiliation(s)
- Stephen J Mooney
- Harborview Injury Prevention and Research Center, University of Washington, Seattle, Washington
| | | | - Kolena Dang
- University of Washington, Seattle, Washington
| | - Julie C Leonard
- Center for Injury Research and Policy, The Research Institute at Nationwide Children’s Hospital, Columbus, Ohio
| | - Jingzhen Yang
- Center for Injury Research and Policy, The Research Institute at Nationwide Children’s Hospital, Columbus, Ohio
| | - Frederick P Rivara
- Harborview Injury Prevention and Research Center, University of Washington, Seattle, Washington
| | - Beth E Ebel
- Harborview Injury Prevention and Research Center, University of Washington, Seattle, Washington
| | - Ali Rowhani-Rahbar
- Harborview Injury Prevention and Research Center, University of Washington, Seattle, Washington
| | - D Alex Quistberg
- Harborview Injury Prevention and Research Center, University of Washington, Seattle, Washington
- Environmental and Occupational Health, Dornsife School of Public Health, Drexel University, Philadelphia, Pennsylvania
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27
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Keil AP, Edwards JK. A review of time scale fundamentals in the g-formula and insidious selection bias. CURR EPIDEMIOL REP 2018; 5:205-213. [PMID: 30555772 PMCID: PMC6289285] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
PURPOSE OF REVIEW We review recent examples of data analysis with the g-formula, a powerful tool for analyzing longitudinal data and survival analysis. Specifically, we focus on the common choices of time scale and review inferential issues that may arise. RECENT FINDINGS Researchers are increasingly engaged with questions that require time scales subject to left-truncation and right-censoring. The assumptions necessary for allowing right-censoring are well defined in the literature, whereas similar assumptions for left-truncation are not well defined. Policy and biologic considerations sometimes dictate that observational data must be analyzed on time scales that are subject to left-truncation, such as age. SUMMARY Further consideration of left-truncation is needed, especially when biologic or policy considerations dictate that age is the relevant time scale of interest. Methodologic development is needed to reduce potential for bias when left-truncation may occur.
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28
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Abstract
BACKGROUND Respiratory exposure to silica is associated with the risk of death owing to malignant and nonmalignant disease. 2.3 million US workers are exposed to silica. Occupational exposure limits for silica are derived from a number of lines of evidence, including observational studies. Observational studies may be subject to healthy worker survivor bias, which could result in underestimates of silica's impact on worker mortality and, in turn, bias risk estimates for occupational exposure limits. METHODS Using data on 65,999 workers pooled across multiple industries, we estimate the impacts of several hypothetical occupational exposure limits on silica exposure on lung cancer and all-cause mortality. We use the parametric g-formula, which can account for healthy worker survivor bias. RESULTS Assuming we could eliminate occupational exposure, we estimate that there would be 20.7 fewer deaths per 1,000 workers in our pooled study by age 80 (95% confidence interval = 14.5, 26.8), including 3.91 fewer deaths owing to lung cancer (95% CI = 1.53, 6.30). Less restrictive interventions demonstrated smaller but still substantial risk reductions. CONCLUSIONS Our results suggest that occupational exposure limits for silica can be further strengthened to reduce silica-associated mortality and illustrate how current risk analysis for occupational limits can be improved.
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Affiliation(s)
- Alexander P Keil
- From the Department of Epidemiology, University of North Carolina, Chapel Hill, NC
| | - David B Richardson
- From the Department of Epidemiology, University of North Carolina, Chapel Hill, NC
| | - Daniel Westreich
- From the Department of Epidemiology, University of North Carolina, Chapel Hill, NC
| | - Kyle Steenland
- Department of Environmental Health, Rollins School of Public Health, Emory University, Atlanta, GA
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29
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Spieker A, Roy J, Mitra N. Analyzing medical costs with time-dependent treatment: The nested g-formula. Health Econ 2018; 27:1063-1073. [PMID: 29663579 PMCID: PMC8218600 DOI: 10.1002/hec.3651] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2017] [Revised: 01/16/2018] [Accepted: 02/07/2018] [Indexed: 06/08/2023]
Abstract
As medical expenses continue to rise, methods to properly analyze cost outcomes are becoming of increasing relevance when seeking to compare average costs across treatments. Inverse probability weighted regression models have been developed to address the challenge of cost censoring in order to identify intent-to-treat effects (i.e., to compare mean costs between groups on the basis of their initial treatment assignment, irrespective of any subsequent changes to their treatment status). In this paper, we describe a nested g-computation procedure that can be used to compare mean costs between two or more time-varying treatment regimes. We highlight the relative advantages and limitations of this approach when compared with existing regression-based models. We illustrate the utility of this approach as a means to inform public policy by applying it to a simulated data example motivated by costs associated with cancer treatments. Simulations confirm that inference regarding intent-to-treat effects versus the joint causal effects estimated by the nested g-formula can lead to markedly different conclusions regarding differential costs. Therefore, it is essential to prespecify the desired target of inference when choosing between these two frameworks. The nested g-formula should be considered as a useful, complementary tool to existing methods when analyzing cost outcomes.
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Affiliation(s)
- Andrew Spieker
- Department of Biostatistics, Epidemiology, and Informatics, University of Pennsylvania
| | - Jason Roy
- Department of Biostatistics, Epidemiology, and Informatics, University of Pennsylvania
| | - Nandita Mitra
- Department of Biostatistics, Epidemiology, and Informatics, University of Pennsylvania
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30
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Galin J, Abrams B, Leonard SA, Matthay EC, Goin DE, Ahern J. Living in Violent Neighbourhoods is Associated with Gestational Weight Gain Outside the Recommended Range. Paediatr Perinat Epidemiol 2017; 31:37-46. [PMID: 27921300 PMCID: PMC5195875 DOI: 10.1111/ppe.12331] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
BACKGROUND During pregnancy, most women do not meet gestational weight gain (GWG) guidelines, potentially resulting in adverse maternal and infant health consequences. Social environment determinants of GWG have been identified, but evidence on the relationship between neighbourhood violence and GWG is scant. Our study aims to examine the relationship between neighbourhood violence and GWG outside the recommended range. METHODS We used statewide vital statistics and health care utilization data from California for 2006-12 (n = 2 364 793) to examine the relationship of neighbourhood violence (quarters of zip-code rates of homicide and assault) in the first 37 weeks of pregnancy with GWG (categorized using the Institute of Medicine's pregnancy weight gain guidelines). We estimated risk ratios (RR) and marginal risk differences, and analyses were stratified by maternal race/ethnicity and prepregnancy body mass index. RESULTS Residence in neighbourhoods with the highest quartile of violence was associated with more excessive GWG (adjusted RR 1.04, 95% confidence interval CI 1.03, 1.05), compared to the lowest quartile of violence; violence was not associated with inadequate GWG. On the difference scale, this association translates to 2.3% more women gaining weight excessively rather than adequately if all women were exposed to high violence compared to if all women were exposed to low violence. Additionally, associations between neighbourhood violence and excessive GWG were larger in non-white women than in white women. CONCLUSIONS These findings support the hypothesis that violence can affect weight gain during pregnancy, emphasizing the importance of neighbourhood violence as a public health issue.
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Affiliation(s)
- Jessica Galin
- Division of Epidemiology, School of Public Health, University of California, Berkeley, Berkeley, CA, USA
| | - Barbara Abrams
- Division of Epidemiology, School of Public Health, University of California, Berkeley, Berkeley, CA, USA
| | - Stephanie A. Leonard
- Division of Epidemiology, School of Public Health, University of California, Berkeley, Berkeley, CA, USA
| | - Ellicott C. Matthay
- Division of Epidemiology, School of Public Health, University of California, Berkeley, Berkeley, CA, USA
| | - Dana E. Goin
- Division of Epidemiology, School of Public Health, University of California, Berkeley, Berkeley, CA, USA
| | - Jennifer Ahern
- Division of Epidemiology, School of Public Health, University of California, Berkeley, Berkeley, CA, USA
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31
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Lu X, Johnson BA. Direct estimation for adaptive treatment length policies: Methods and application to evaluating the effect of delayed PEG insertion. Biometrics 2016; 73:981-989. [PMID: 28009454 DOI: 10.1111/biom.12639] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2016] [Revised: 11/01/2016] [Accepted: 11/01/2016] [Indexed: 11/25/2022]
Abstract
Dysphagia is a primary cause of death among patients diagnosed with amyotrophic lateral sclerosis (ALS), and percutaneous endoscopic gastrostomy (PEG) is a procedure to insert a tube into the stomach to assist or replace oral feeding. It is believed that PEG is beneficial and, generally, earlier insertion is preferable to later. However, gathering clinical evidence to support these beliefs on the use and timing of PEG is challenging because controlled clinical trials are not feasible and clinical endpoints are confounded with PEG in observational data. Moreover, the confounders are time-varying and time to PEG insertion may be only partially observed. We show how one can view this problem as an adaptive treatment length policy and propose a new estimator via g-computation. We show that our estimator is consistent and asymptotically normal for the causal estimand and explore its finite sample properties in simulation studies. Finally, using more than 10 years of data from Emory ALS clinic registry, we found no evidence to suggest that earlier PEG reduced 4-year mortality; thus, our results do not support the hypothesis and belief that initiating palliative care earlier extends life, on average. At the same, we cannot be certain that all important confounding variables are collected and observed to ensure our modeling assumptions are correct, so more work is needed to address these important end-of-life questions for ALS patients.
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Affiliation(s)
- Xin Lu
- Department of Biostatistics and Programming, Sanofi, Bridgewater, New Jersey 08807, U.S.A
| | - Brent A Johnson
- Department of Biostatistics and Computational Biology, University of Rochester, Rochester, New York 14642, U.S.A
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