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Sewak A, Lodi S, Li X, Shu D, Wen L, Mayer KH, Krakower DS, Young JG, Marcus JL. Causal Effects of Stochastic PrEP Interventions on HIV Incidence Among Men Who Have Sex With Men. Am J Epidemiol 2024; 193:6-16. [PMID: 37073419 PMCID: PMC10773485 DOI: 10.1093/aje/kwad097] [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: 06/14/2022] [Revised: 01/08/2023] [Accepted: 04/13/2023] [Indexed: 04/20/2023] Open
Abstract
Antiretroviral preexposure prophylaxis (PrEP) is highly effective in preventing human immunodeficiency virus (HIV) infection, but uptake has been limited and inequitable. Although interventions to increase PrEP uptake are being evaluated in clinical trials among men who have sex with men (MSM), those trials cannot evaluate effects on HIV incidence. Estimates from observational studies of the causal effects of PrEP-uptake interventions on HIV incidence can inform decisions about intervention scale-up. We used longitudinal electronic health record data from HIV-negative MSM accessing care at Fenway Health, a community health center in Boston, Massachusetts, from January 2012 through February 2018, with 2 years of follow-up. We considered stochastic interventions that increased the chance of initiating PrEP in several high-priority subgroups. We estimated the effects of these interventions on population-level HIV incidence using a novel inverse-probability weighted estimator of the generalized g-formula, adjusting for baseline and time-varying confounders. Our results suggest that even modest increases in PrEP initiation in high-priority subgroups of MSM could meaningfully reduce HIV incidence in the overall population of MSM. Interventions tailored to Black and Latino MSM should be prioritized to maximize equity and impact.
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Affiliation(s)
| | | | | | | | | | | | | | | | - Julia L Marcus
- Correspondence to Dr. Julia L. Marcus, Harvard Medical School and Harvard Pilgrim Health Care Institute Boston, MA 02215 (e-mail: )
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Rytgaard HCW, van der Laan MJ. Targeted maximum likelihood estimation for causal inference in survival and competing risks analysis. LIFETIME DATA ANALYSIS 2024; 30:4-33. [PMID: 36336732 DOI: 10.1007/s10985-022-09576-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Accepted: 09/05/2022] [Indexed: 06/16/2023]
Abstract
Targeted maximum likelihood estimation (TMLE) provides a general methodology for estimation of causal parameters in presence of high-dimensional nuisance parameters. Generally, TMLE consists of a two-step procedure that combines data-adaptive nuisance parameter estimation with semiparametric efficiency and rigorous statistical inference obtained via a targeted update step. In this paper, we demonstrate the practical applicability of TMLE based causal inference in survival and competing risks settings where event times are not confined to take place on a discrete and finite grid. We focus on estimation of causal effects of time-fixed treatment decisions on survival and absolute risk probabilities, considering different univariate and multidimensional parameters. Besides providing a general guidance to using TMLE for survival and competing risks analysis, we further describe how the previous work can be extended with the use of loss-based cross-validated estimation, also known as super learning, of the conditional hazards. We illustrate the usage of the considered methods using publicly available data from a trial on adjuvant chemotherapy for colon cancer. R software code to implement all considered algorithms and to reproduce all analyses is available in an accompanying online appendix on Github.
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Rytgaard HCW, Eriksson F, van der Laan MJ. Estimation of time-specific intervention effects on continuously distributed time-to-event outcomes by targeted maximum likelihood estimation. Biometrics 2023; 79:3038-3049. [PMID: 36988158 DOI: 10.1111/biom.13856] [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: 11/23/2021] [Accepted: 02/22/2023] [Indexed: 03/30/2023]
Abstract
This work considers targeted maximum likelihood estimation (TMLE) of treatment effects on absolute risk and survival probabilities in classical time-to-event settings characterized by right-censoring and competing risks. TMLE is a general methodology combining flexible ensemble learning and semiparametric efficiency theory in a two-step procedure for substitution estimation of causal parameters. We specialize and extend the continuous-time TMLE methods for competing risks settings, proposing a targeting algorithm that iteratively updates cause-specific hazards to solve the efficient influence curve equation for the target parameter. As part of the work, we further detail and implement the recently proposed highly adaptive lasso estimator for continuous-time conditional hazards with L1 -penalized Poisson regression. The resulting estimation procedure benefits from relying solely on very mild nonparametric restrictions on the statistical model, thus providing a novel tool for machine-learning-based semiparametric causal inference for continuous-time time-to-event data. We apply the methods to a publicly available dataset on follicular cell lymphoma where subjects are followed over time until disease relapse or death without relapse. The data display important time-varying effects that can be captured by the highly adaptive lasso. In our simulations that are designed to imitate the data, we compare our methods to a similar approach based on random survival forests and to the discrete-time TMLE.
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Affiliation(s)
| | - Frank Eriksson
- Section of Biostatistics, University of Copenhagen, Copenhagen, Denmark
| | - Mark J van der Laan
- Division of Biostatistics, University of California, Berkeley, California, USA
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Smith MJ, Phillips RV, Luque-Fernandez MA, Maringe C. Application of targeted maximum likelihood estimation in public health and epidemiological studies: a systematic review. Ann Epidemiol 2023; 86:34-48.e28. [PMID: 37343734 DOI: 10.1016/j.annepidem.2023.06.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2023] [Revised: 05/24/2023] [Accepted: 06/06/2023] [Indexed: 06/23/2023]
Abstract
PURPOSE The targeted maximum likelihood estimation (TMLE) statistical data analysis framework integrates machine learning, statistical theory, and statistical inference to provide a least biased, efficient, and robust strategy for estimation and inference of a variety of statistical and causal parameters. We describe and evaluate the epidemiological applications that have benefited from recent methodological developments. METHODS We conducted a systematic literature review in PubMed for articles that applied any form of TMLE in observational studies. We summarized the epidemiological discipline, geographical location, expertize of the authors, and TMLE methods over time. We used the Roadmap of Targeted Learning and Causal Inference to extract key methodological aspects of the publications. We showcase the contributions to the literature of these TMLE results. RESULTS Of the 89 publications included, 33% originated from the University of California at Berkeley, where the framework was first developed by Professor Mark van der Laan. By 2022, 59% of the publications originated from outside the United States and explored up to seven different epidemiological disciplines in 2021-2022. Double-robustness, bias reduction, and model misspecification were the main motivations that drew researchers toward the TMLE framework. Through time, a wide variety of methodological, tutorial, and software-specific articles were cited, owing to the constant growth of methodological developments around TMLE. CONCLUSIONS There is a clear dissemination trend of the TMLE framework to various epidemiological disciplines and to increasing numbers of geographical areas. The availability of R packages, publication of tutorial papers, and involvement of methodological experts in applied publications have contributed to an exponential increase in the number of studies that understood the benefits and adoption of TMLE.
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Affiliation(s)
- Matthew J Smith
- Inequalities in Cancer Outcomes Network, London School of Hygiene and Tropical Medicine, London, UK.
| | - Rachael V Phillips
- Division of Biostatistics, School of Public Health, University of California at Berkeley, Berkeley, CA
| | - Miguel Angel Luque-Fernandez
- Inequalities in Cancer Outcomes Network, London School of Hygiene and Tropical Medicine, London, UK; Department of Statistics and Operations Research, University of Granada, Granada, Spain
| | - Camille Maringe
- Inequalities in Cancer Outcomes Network, London School of Hygiene and Tropical Medicine, London, UK
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5
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Denz R, Timmesfeld N. Visualizing the (Causal) Effect of a Continuous Variable on a Time-To-Event Outcome. Epidemiology 2023; 34:652-660. [PMID: 37462467 PMCID: PMC10392888 DOI: 10.1097/ede.0000000000001630] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/03/2023]
Abstract
Visualization is a key aspect of communicating the results of any study aiming to estimate causal effects. In studies with time-to-event outcomes, the most popular visualization approach is depicting survival curves stratified by the variable of interest. This approach cannot be used when the variable of interest is continuous. Simple workarounds, such as categorizing the continuous covariate and plotting survival curves for each category, can result in misleading depictions of the main effects. Instead, we propose a new graphic, the survival area plot, to directly depict the survival probability over time and as a function of a continuous covariate simultaneously. This plot utilizes g-computation based on a suitable time-to-event model to obtain the relevant estimates. Through the use of g-computation, those estimates can be adjusted for confounding without additional effort, allowing a causal interpretation under the standard causal identifiability assumptions. If those assumptions are not met, the proposed plot may still be used to depict noncausal associations. We illustrate and compare the proposed graphics to simpler alternatives using data from a large German observational study investigating the effect of the Ankle-Brachial Index on survival. To facilitate the usage of these plots, we additionally developed the contsurvplot R-package, which includes all methods discussed in this paper.
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Affiliation(s)
- Robin Denz
- From the Department of Medical Informatics, Biometry, and Epidemiology, Ruhr-University Bochum, Germany
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Montoya LM, Kosorok MR, Geng EH, Schwab J, Odeny TA, Petersen ML. Efficient and robust approaches for analysis of sequential multiple assignment randomized trials: Illustration using the ADAPT-R trial. Biometrics 2023; 79:2577-2591. [PMID: 36493463 PMCID: PMC10424093 DOI: 10.1111/biom.13808] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Accepted: 11/25/2022] [Indexed: 12/13/2022]
Abstract
Personalized intervention strategies, in particular those that modify treatment based on a participant's own response, are a core component of precision medicine approaches. Sequential multiple assignment randomized trials (SMARTs) are growing in popularity and are specifically designed to facilitate the evaluation of sequential adaptive strategies, in particular those embedded within the SMART. Advances in efficient estimation approaches that are able to incorporate machine learning while retaining valid inference can allow for more precise estimates of the effectiveness of these embedded regimes. However, to the best of our knowledge, such approaches have not yet been applied as the primary analysis in SMART trials. In this paper, we present a robust and efficient approach using targeted maximum likelihood estimation (TMLE) for estimating and contrasting expected outcomes under the dynamic regimes embedded in a SMART, together with generating simultaneous confidence intervals for the resulting estimates. We contrast this method with two alternatives (G-computation and inverse probability weighting estimators). The precision gains and robust inference achievable through the use of TMLE to evaluate the effects of embedded regimes are illustrated using both outcome-blind simulations and a real-data analysis from the Adaptive Strategies for Preventing and Treating Lapses of Retention in Human Immunodeficiency Virus (HIV) Care (ADAPT-R) trial (NCT02338739), a SMART with a primary aim of identifying strategies to improve retention in HIV care among people living with HIV in sub-Saharan Africa.
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Affiliation(s)
- Lina M. Montoya
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA
| | - Michael R. Kosorok
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA
- Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA
| | - Elvin H. Geng
- Division of Infectious Diseases, Washington University in St. Louis, St. Louis, Missouri, USA
| | - Joshua Schwab
- Division of Biostatistics, School of Public Health, University of California, Berkeley, California, USA
| | - Thomas A. Odeny
- Center for Microbiology Research, Kenya Medical Research Institute, Nairobi, Kenya
- Division of Oncology, Department of Medicine, Washington University in St. Louis, St. Louis, Missouri, USA
| | - Maya L. Petersen
- Division of Biostatistics, School of Public Health, University of California, Berkeley, California, USA
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7
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van der Laan L, Zhang W, Gilbert PB. Nonparametric estimation of the causal effect of a stochastic threshold-based intervention. Biometrics 2023; 79:1014-1028. [PMID: 35526218 PMCID: PMC10024462 DOI: 10.1111/biom.13690] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Accepted: 03/22/2022] [Indexed: 12/01/2022]
Abstract
Identifying a biomarker or treatment-dose threshold that marks a specified level of risk is an important problem, especially in clinical trials. In view of this goal, we consider a covariate-adjusted threshold-based interventional estimand, which happens to equal the binary treatment-specific mean estimand from the causal inference literature obtained by dichotomizing the continuous biomarker or treatment as above or below a threshold. The unadjusted version of this estimand was considered in Donovan et al.. Expanding upon Stitelman et al., we show that this estimand, under conditions, identifies the expected outcome of a stochastic intervention that sets the treatment dose of all participants above the threshold. We propose a novel nonparametric efficient estimator for the covariate-adjusted threshold-response function for the case of informative outcome missingness, which utilizes machine learning and targeted minimum-loss estimation (TMLE). We prove the estimator is efficient and characterize its asymptotic distribution and robustness properties. Construction of simultaneous 95% confidence bands for the threshold-specific estimand across a set of thresholds is discussed. In the Supporting Information, we discuss how to adjust our estimator when the biomarker is missing at random, as occurs in clinical trials with biased sampling designs, using inverse probability weighting. Efficiency and bias reduction of the proposed estimator are assessed in simulations. The methods are employed to estimate neutralizing antibody thresholds for virologically confirmed dengue risk in the CYD14 and CYD15 dengue vaccine trials.
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Affiliation(s)
- Lars van der Laan
- Department of Statistics, University of Washington, Seattle, Washington, 98109, U.S.A
- Vaccine and Infectious Disease and Public Health Sciences Divisions, Fred Hutchinson Cancer Research Center, Seattle, Washington, 98109, U.S.A
| | - Wenbo Zhang
- Department of Biostatistics University of Washington, Seattle, Washington, 98109, U.S.A
| | - Peter B. Gilbert
- Department of Biostatistics University of Washington, Seattle, Washington, 98109, U.S.A
- Vaccine and Infectious Disease and Public Health Sciences Divisions, Fred Hutchinson Cancer Research Center, Seattle, Washington, 98109, U.S.A
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8
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Chen D, Petersen ML, Rytgaard HC, Grøn R, Lange T, Rasmussen S, Pratley RE, Marso SP, Kvist K, Buse J, van der Laan MJ. Beyond the Cox Hazard Ratio: A Targeted Learning Approach to Survival Analysis in a Cardiovascular Outcome Trial Application. Stat Biopharm Res 2023. [DOI: 10.1080/19466315.2023.2173644] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/05/2023]
Affiliation(s)
- David Chen
- Division of Biostatistics, UC Berkeley School of Public Health, Berkeley, CA
| | - Maya L. Petersen
- Division of Biostatistics, UC Berkeley School of Public Health, Berkeley, CA
| | | | | | - Theis Lange
- Section of Biostatistics, University of Copenhagen, Copenhagen, Denmark
| | | | | | - Steven P. Marso
- Midwest Heart and Vascular Institute, HCA Midwest Health, Overland Park, KS
| | | | - John Buse
- Division of Endocrinology and Metabolism, UNC School of Medicine, Chapel Hill, NC
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9
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Phillips RV, van der Laan MJ. Discussion on "Adaptive enrichment designs with a continuous biomarker" by Nigel Stallard. Biometrics 2023; 79:20-22. [PMID: 35332936 DOI: 10.1111/biom.13640] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Accepted: 12/22/2021] [Indexed: 11/30/2022]
Affiliation(s)
- Rachael V Phillips
- Division of Biostatistics, University of California at Berkeley, Berkeley, California, USA
| | - Mark J van der Laan
- Division of Biostatistics, University of California at Berkeley, Berkeley, California, USA
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10
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Denz R, Klaaßen-Mielke R, Timmesfeld N. A comparison of different methods to adjust survival curves for confounders. Stat Med 2023; 42:1461-1479. [PMID: 36748630 DOI: 10.1002/sim.9681] [Citation(s) in RCA: 24] [Impact Index Per Article: 24.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Revised: 11/17/2022] [Accepted: 01/30/2023] [Indexed: 02/08/2023]
Abstract
Treatment specific survival curves are an important tool to illustrate the treatment effect in studies with time-to-event outcomes. In non-randomized studies, unadjusted estimates can lead to biased depictions due to confounding. Multiple methods to adjust survival curves for confounders exist. However, it is currently unclear which method is the most appropriate in which situation. Our goal is to compare forms of inverse probability of treatment weighting, the G-Formula, propensity score matching, empirical likelihood estimation and augmented estimators as well as their pseudo-values based counterparts in different scenarios with a focus on their bias and goodness-of-fit. We provide a short review of all methods and illustrate their usage by contrasting the survival of smokers and non-smokers, using data from the German Epidemiological Trial on Ankle-Brachial-Index. Subsequently, we compare the methods using a Monte-Carlo simulation. We consider scenarios in which correctly or incorrectly specified models for describing the treatment assignment and the time-to-event outcome are used with varying sample sizes. The bias and goodness-of-fit is determined by taking the entire survival curve into account. When used properly, all methods showed no systematic bias in medium to large samples. Cox regression based methods, however, showed systematic bias in small samples. The goodness-of-fit varied greatly between different methods and scenarios. Methods utilizing an outcome model were more efficient than other techniques, while augmented estimators using an additional treatment assignment model were unbiased when either model was correct with a goodness-of-fit comparable to other methods. These "doubly-robust" methods have important advantages in every considered scenario.
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Affiliation(s)
- Robin Denz
- Department of Medical Informatics, Biometry and Epidemiology, Ruhr-University of Bochum, Bochum, North-Rhine Westphalia, Germany
| | - Renate Klaaßen-Mielke
- Department of Medical Informatics, Biometry and Epidemiology, Ruhr-University of Bochum, Bochum, North-Rhine Westphalia, Germany
| | - Nina Timmesfeld
- Department of Medical Informatics, Biometry and Epidemiology, Ruhr-University of Bochum, Bochum, North-Rhine Westphalia, Germany
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11
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Vansteelandt S, Dukes O, Van Lancker K, Martinussen T. Assumption-lean Cox regression. J Am Stat Assoc 2022. [DOI: 10.1080/01621459.2022.2126362] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
Affiliation(s)
- Stijn Vansteelandt
- Department of Applied Mathematics, Computer Science and Statistics, Ghent University
- Department of Medical Statistics, London School of Hygiene and Tropical Medicine
| | - Oliver Dukes
- Department of Applied Mathematics, Computer Science and Statistics, Ghent University
| | - Kelly Van Lancker
- Department of Applied Mathematics, Computer Science and Statistics, Ghent University
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12
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Wen L, Hernán MA, Robins JM. MULTIPLY ROBUST ESTIMATORS OF CAUSAL EFFECTS FOR SURVIVAL OUTCOMES. Scand Stat Theory Appl 2022; 49:1304-1328. [PMID: 36033967 PMCID: PMC9401091 DOI: 10.1111/sjos.12561] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2020] [Accepted: 08/30/2021] [Indexed: 11/27/2022]
Abstract
Multiply robust estimators of the longitudinal g-formula have recently been proposed to protect against model misspecification better than the standard augmented inverse probability weighted estimator (Rotnitzky et al., 2017; Luedtke et al., 2018). These multiply robust estimators ensure consistency if one of the models for the treatment process or outcome process is correctly specified at each time point. We study the multiply robust estimators of Rotnitzky et al. (2017) in the context of a survival outcome. Specifically, we compare various estimators of the g-formula for survival outcomes in order to 1) understand how the estimators may be related to one another, 2) understand each estimator's robustness to model misspecification, and 3) construct estimators that can be more efficient than others in certain model misspecification scenarios. We propose a modification of the multiply robust estimators to gain efficiency under misspecification of the outcome model by using calibrated propensity scores over non-calibrated propensity scores at each time point. Theoretical results are confirmed via simulation studies, and a practical comparison of these estimators is conducted through an application to the US Veterans Aging Cohort Study.
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Affiliation(s)
- Lan Wen
- DEPARTMENT OF EPIDEMIOLOGY, HARVARD T. H. CHAN SCHOOL OF PUBLIC HEALTH
- CAUSALAB, HARVARD T.H. CHAN SCHOOL OF PUBLIC HEALTH
| | - Miguel A Hernán
- DEPARTMENT OF EPIDEMIOLOGY, HARVARD T. H. CHAN SCHOOL OF PUBLIC HEALTH
- CAUSALAB, HARVARD T.H. CHAN SCHOOL OF PUBLIC HEALTH
- DEPARTMENT OF BIOSTATISTICS, HARVARD T. H. CHAN SCHOOL OF PUBLIC HEALTH
| | - James M Robins
- DEPARTMENT OF EPIDEMIOLOGY, HARVARD T. H. CHAN SCHOOL OF PUBLIC HEALTH
- CAUSALAB, HARVARD T.H. CHAN SCHOOL OF PUBLIC HEALTH
- DEPARTMENT OF BIOSTATISTICS, HARVARD T. H. CHAN SCHOOL OF PUBLIC HEALTH
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13
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Lin J, Trinquart L. Doubly-robust estimator of the difference in restricted mean times lost with competing risks data. Stat Methods Med Res 2022; 31:1881-1903. [PMID: 35607287 DOI: 10.1177/09622802221102625] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In the context of competing risks data, the subdistribution hazard ratio has limited clinical interpretability to measure treatment effects. An alternative is the difference in restricted mean times lost (RMTL), which gives the mean time lost to a specific cause of failure between treatment groups. In non-randomized studies, the average causal effect is conventionally used for decision-making about treatment and public health policies. We show how the difference in RMTL can be estimated by contrasting the integrated cumulative incidence functions from a Fine-Gray model. We also show how the difference in RMTL can be estimated by using inverse probability of treatment weighting and contrasts between weighted non-parametric estimators of the area below the cumulative incidence. We use pseudo-observation approaches to estimate both component models and we integrate them into a doubly-robust estimator. We demonstrate that this estimator is consistent when either component is correctly specified. We conduct simulation studies to assess its finite-sample performance and demonstrate its inherited consistency property from its component models. We also examine the performance of this estimator under varying degrees of covariate overlap and under a model misspecification of nonlinearity. We apply the proposed method to assess biomarker-treatment interaction in subpopulations of the POPLAR and OAK randomized controlled trials of second-line therapy for advanced non-small-cell lung cancer.
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Affiliation(s)
- Jingyi Lin
- Department of Biostatistics, Boston University School of Public Health, Boston, MA, USA
| | - Ludovic Trinquart
- Department of Biostatistics, Boston University School of Public Health, Boston, MA, USA.,550030Institute for Clinical Research and Health Policy Studies, Tufts Medical Center, Boston, MA, USA.,551843Tufts Clinical and Translational Science Institute, Tufts University, Boston, MA, USA
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14
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Lee Y, Kennedy EH, Mitra N. Doubly robust nonparametric instrumental variable estimators for survival outcomes. Biostatistics 2021; 24:518-537. [PMID: 34676400 DOI: 10.1093/biostatistics/kxab036] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2021] [Revised: 09/15/2021] [Accepted: 09/20/2021] [Indexed: 11/12/2022] Open
Abstract
Instrumental variable (IV) methods allow us the opportunity to address unmeasured confounding in causal inference. However, most IV methods are only applicable to discrete or continuous outcomes with very few IV methods for censored survival outcomes. In this article, we propose nonparametric estimators for the local average treatment effect on survival probabilities under both covariate-dependent and outcome-dependent censoring. We provide an efficient influence function-based estimator and a simple estimation procedure when the IV is either binary or continuous. The proposed estimators possess double-robustness properties and can easily incorporate nonparametric estimation using machine learning tools. In simulation studies, we demonstrate the flexibility and double robustness of our proposed estimators under various plausible scenarios. We apply our method to the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial for estimating the causal effect of screening on survival probabilities and investigate the causal contrasts between the two interventions under different censoring assumptions.
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Affiliation(s)
- Youjin Lee
- Department of Biostatistics, Brown University, 121 S Main St, Providence, RI 02912, USA
| | - Edward H Kennedy
- Department of Statistics and Data Science, Carnegie Mellon University, 132 J Baker Hall, Pittsburgh, PA 15213, USA
| | - Nandita Mitra
- Department of Biostatistics and Epidemiology, University Pennsylvania, 423 Guardian Drive, Philadelphia, PA 19104, USA
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15
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Hu L, Ji J, Li F. Estimating heterogeneous survival treatment effect in observational data using machine learning. Stat Med 2021; 40:4691-4713. [PMID: 34114252 PMCID: PMC9827499 DOI: 10.1002/sim.9090] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2020] [Revised: 05/16/2021] [Accepted: 05/19/2021] [Indexed: 01/12/2023]
Abstract
Methods for estimating heterogeneous treatment effect in observational data have largely focused on continuous or binary outcomes, and have been relatively less vetted with survival outcomes. Using flexible machine learning methods in the counterfactual framework is a promising approach to address challenges due to complex individual characteristics, to which treatments need to be tailored. To evaluate the operating characteristics of recent survival machine learning methods for the estimation of treatment effect heterogeneity and inform better practice, we carry out a comprehensive simulation study presenting a wide range of settings describing confounded heterogeneous survival treatment effects and varying degrees of covariate overlap. Our results suggest that the nonparametric Bayesian Additive Regression Trees within the framework of accelerated failure time model (AFT-BART-NP) consistently yields the best performance, in terms of bias, precision, and expected regret. Moreover, the credible interval estimators from AFT-BART-NP provide close to nominal frequentist coverage for the individual survival treatment effect when the covariate overlap is at least moderate. Including a nonparametrically estimated propensity score as an additional fixed covariate in the AFT-BART-NP model formulation can further improve its efficiency and frequentist coverage. Finally, we demonstrate the application of flexible causal machine learning estimators through a comprehensive case study examining the heterogeneous survival effects of two radiotherapy approaches for localized high-risk prostate cancer.
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Affiliation(s)
- Liangyuan Hu
- Department of Population Health Science and Policy, Icahn School of Medicine at Mount Sinai, New York, NY
- Department of Biostatistics and Epidemiology, Rutgers School of Public Health, Piscataway, NJ
| | - Jiayi Ji
- Department of Population Health Science and Policy, Icahn School of Medicine at Mount Sinai, New York, NY
| | - Fan Li
- Department of Biostatistics, Yale University School of Public Health, New Haven, Connecticut
- Center for Methods in Implementation and Prevention Science, Yale University School of Public Health, New Haven, Connecticut
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16
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Zhu J, Gallego B. Targeted estimation of heterogeneous treatment effect in observational survival analysis. J Biomed Inform 2020; 107:103474. [DOI: 10.1016/j.jbi.2020.103474] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2020] [Revised: 05/29/2020] [Accepted: 06/02/2020] [Indexed: 10/24/2022]
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