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Wang Y, Deng Y, Zhou XH. Causal inference for time-to-event data with a cured subpopulation. Biometrics 2024; 80:ujae028. [PMID: 38708764 DOI: 10.1093/biomtc/ujae028] [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: 05/27/2023] [Revised: 12/21/2023] [Accepted: 04/05/2024] [Indexed: 05/07/2024]
Abstract
When studying the treatment effect on time-to-event outcomes, it is common that some individuals never experience failure events, which suggests that they have been cured. However, the cure status may not be observed due to censoring which makes it challenging to define treatment effects. Current methods mainly focus on estimating model parameters in various cure models, ultimately leading to a lack of causal interpretations. To address this issue, we propose 2 causal estimands, the timewise risk difference and mean survival time difference, in the always-uncured based on principal stratification as a complement to the treatment effect on cure rates. These estimands allow us to study the treatment effects on failure times in the always-uncured subpopulation. We show the identifiability using a substitutional variable for the potential cure status under ignorable treatment assignment mechanism, these 2 estimands are identifiable. We also provide estimation methods using mixture cure models. We applied our approach to an observational study that compared the leukemia-free survival rates of different transplantation types to cure acute lymphoblastic leukemia. Our proposed approach yielded insightful results that can be used to inform future treatment decisions.
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Affiliation(s)
- Yi Wang
- The School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China
- Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
| | - Yuhao Deng
- Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
| | - Xiao-Hua Zhou
- Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
- Department of Biostatistics, School of Public Health, Peking University, Beijing 100871, China
- Peking University Chongqing Big Data Research Institute, Chongqing 401333, China
- Pazhou Lab, Guangzhou 510335, China
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2
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Luo S, Li W, He Y. Causal inference with outcomes truncated by death in multiarm studies. Biometrics 2023; 79:502-513. [PMID: 34435657 DOI: 10.1111/biom.13554] [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: 09/10/2020] [Revised: 08/10/2021] [Accepted: 08/20/2021] [Indexed: 11/29/2022]
Abstract
It is challenging to evaluate causal effects when the outcomes of interest suffer from truncation-by-death in many clinical studies; that is, outcomes cannot be observed if patients die before the time of measurement. To address this problem, it is common to consider average treatment effects by principal stratification, for which, the identifiability results and estimation methods with a binary treatment have been established in previous literature. However, in multiarm studies with more than two treatment options, estimation of causal effects becomes more complicated and requires additional techniques. In this article, we consider identification, estimation, and bounds of causal effects with multivalued ordinal treatments and the outcomes subject to truncation-by-death. We define causal parameters of interest in this setting and show that they are identifiable either using some auxiliary variable or based on linear model assumption. We then propose a semiparametric method for estimating the causal parameters and derive their asymptotic results. When the identification conditions are invalid, we derive sharp bounds of the causal effects by use of covariates adjustment. Simulation studies show good performance of the proposed estimator. We use the estimator to analyze the effects of a four-level chronic toxin on fetal developmental outcomes such as birth weight in rats and mice, with data from a developmental toxicity trial conducted by the National Toxicology Program. Data analyses demonstrate that a high dose of the toxin significantly reduces the weights of pups.
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Affiliation(s)
- Shanshan Luo
- School of Mathematical Sciences, Peking University, Beijing, China
| | - Wei Li
- Center for Applied Statistics and School of Statistics, Renmin University of China, Beijing, China
| | - Yangbo He
- School of Mathematical Sciences, Peking University, Beijing, China
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3
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Josefsson M, Daniels MJ. Bayesian semi-parametric G-computation for causal inference in a cohort study with MNAR dropout and death. J R Stat Soc Ser C Appl Stat 2021; 70:398-414. [PMID: 33692597 PMCID: PMC7939177 DOI: 10.1111/rssc.12464] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
Causal inference with observational longitudinal data and time-varying exposures is often complicated by time-dependent confounding and attrition. The G-computation formula is one approach for estimating a causal effect in this setting. The parametric modeling approach typically used in practice relies on strong modeling assumptions for valid inference, and moreover depends on an assumption of missing at random, which is not appropriate when the missingness is missing not at random (MNAR) or due to death. In this work we develop a flexible Bayesian semi-parametric G-computation approach for assessing the causal effect on the subpopulation that would survive irrespective of exposure, in a setting with MNAR dropout. The approach is to specify models for the observed data using Bayesian additive regression trees, and then use assumptions with embedded sensitivity parameters to identify and estimate the causal effect. The proposed approach is motivated by a longitudinal cohort study on cognition, health, and aging, and we apply our approach to study the effect of becoming a widow on memory. We also compare our approach to several standard methods.
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Affiliation(s)
- Maria Josefsson
- Centre for Demographic and Ageing Research, Umeå University, Sweden
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4
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Wang L, Zhou XH, Richardson TS. Identification and estimation of causal effects with outcomes truncated by death. Biometrika 2017; 104:597-612. [PMID: 29430035 PMCID: PMC5793679 DOI: 10.1093/biomet/asx034] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2016] [Indexed: 11/14/2022] Open
Abstract
It is common in medical studies that the outcome of interest is truncated by death, meaning that a subject has died before the outcome could be measured. In this case, restricted analysis among survivors may be subject to selection bias. Hence, it is of interest to estimate the survivor average causal effect, defined as the average causal effect among the subgroup consisting of subjects who would survive under either exposure. In this paper, we consider the identification and estimation problems of the survivor average causal effect. We propose to use a substitution variable in place of the latent membership in the always-survivor group. The identification conditions required for a substitution variable are conceptually similar to conditions for a conditional instrumental variable, and may apply to both randomized and observational studies. We show that the survivor average causal effect is identifiable with use of such a substitution variable, and propose novel model parameterizations for estimation of the survivor average causal effect under our identification assumptions. Our approaches are illustrated via simulation studies and a data analysis.
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Affiliation(s)
- Linbo Wang
- Department of Biostatistics, Harvard School of Public Health, 677 Huntington Avenue, Boston, Massachusetts 02115,
| | - Xiao-Hua Zhou
- Department of Biostatistics, University of Washington, Seattle, Washington 98195,
| | - Thomas S Richardson
- Department of Statistics, University of Washington, Seattle, Washington 98195,
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5
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Wang L, Richardson TS, Zhou XH. Causal analysis of ordinal treatments and binary outcomes under truncation by death. J R Stat Soc Series B Stat Methodol 2017; 79:719-735. [PMID: 28458613 DOI: 10.1111/rssb.12188] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
It is common that in multi-arm randomized trials, the outcome of interest is "truncated by death," meaning that it is only observed or well-defined conditioning on an intermediate outcome. In this case, in addition to pairwise contrasts, the joint inference for all treatment arms is also of interest. Under a monotonicity assumption we present methods for both pairwise and joint causal analyses of ordinal treatments and binary outcomes in presence of truncation by death. We illustrate via examples the appropriateness of our assumptions in different scientific contexts.
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Affiliation(s)
| | | | - Xiao-Hua Zhou
- University of Washington, Seattle, USA.,Veterans Affairs Puget Sound Health Care System, Seattle, USA
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6
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Josefsson M, de Luna X, Daniels MJ, Nyberg L. Causal inference with longitudinal outcomes and non-ignorable drop-out: Estimating the effect of living alone on cognitive decline. J R Stat Soc Ser C Appl Stat 2015; 65:131-144. [PMID: 26839439 DOI: 10.1111/rssc.12110] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
In this paper we develop a model to estimate the causal effect of living arrangement (living alone versus living with someone) on cognitive decline based on a 15-year prospective cohort study, where episodic memory function is measured every five years. One key feature of the model is the combination of propensity score matching to balance confounding variables between the two living arrangement groups -in order to reduce bias due to unbalanced covariates at baseline, with a pattern mixture model for longitudinal data -in order to deal with non-ignorable drop-out. A fully Bayesian approach allows us to convey the uncertainty in the estimation of the propensity score and subsequent matching in the inference of the causal effect of interest. The analysis conducted here adds to previous studies in the literature concerning the protective effect of living with someone, by proposing a modeling approach treating living arrangement as an exposure.
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Affiliation(s)
- Maria Josefsson
- Department of Statistics, Umeå School of Business and Economics, Umeå University, Umeå, Sweden
| | - Xavier de Luna
- Department of Statistics, Umeå School of Business and Economics, Umeå University, Umeå, Sweden
| | - Michael J Daniels
- Department of Integrative Biology, Department of Statistics & Data Sciences, University of Texas at Austin
| | - Lars Nyberg
- Department of Integrative Medical Biology & Radiation Sciences, Umeå University Umeå, Sweden
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7
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Shardell M, Hicks GE, Ferrucci L. Doubly robust estimation and causal inference in longitudinal studies with dropout and truncation by death. Biostatistics 2015; 16:155-68. [PMID: 24997309 PMCID: PMC4263224 DOI: 10.1093/biostatistics/kxu032] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2013] [Revised: 05/23/2014] [Accepted: 05/31/2014] [Indexed: 11/13/2022] Open
Abstract
Motivated by aging research, we propose an estimator of the effect of a time-varying exposure on an outcome in longitudinal studies with dropout and truncation by death. We use an inverse-probability weighted (IPW) estimator to derive a doubly robust augmented inverse-probability weighted (AIPW) estimator. IPW estimation involves weights for the exposure mechanism, dropout, and mortality; AIPW estimation additionally involves estimating data-generating models via regression. We demonstrate that the estimators identify a causal contrast that is a function of principal strata effects under a set of assumptions. Simulations show that AIPW estimation is unbiased when weights or outcome regressions are correct, and that AIPW estimation is more efficient than IPW estimation when all models are correct. We apply the method to a study of vitamin D and gait speed among older adults.
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Affiliation(s)
- Michelle Shardell
- Department of Epidemiology and Public Health, University of Maryland 660 West Redwood Street, Baltimore, MD 21201, USA
| | - Gregory E Hicks
- Department of Physical Therapy, University of Delaware 303 McKinly Lab, Newark, DE 19716, USA
| | - Luigi Ferrucci
- National Institute on Aging, 3001 S Hanover Street, Baltimore, MD 21225, USA
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Lee M, Lee K, Lee J. Marginalized transition shared random effects models for longitudinal binary data with nonignorable dropout. Biom J 2014; 56:230-42. [PMID: 24430985 DOI: 10.1002/bimj.201200085] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2012] [Revised: 09/10/2013] [Accepted: 10/04/2013] [Indexed: 11/11/2022]
Abstract
In longitudinal studies investigators frequently have to assess and address potential biases introduced by missing data. New methods are proposed for modeling longitudinal categorical data with nonignorable dropout using marginalized transition models and shared random effects models. Random effects are introduced for both serial dependence of outcomes and nonignorable missingness. Fisher-scoring and Quasi-Newton algorithms are developed for parameter estimation. Methods are illustrated with a real dataset.
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Affiliation(s)
- Myungok Lee
- Sekolah Pelita Harapan International Jl. Dago Permai No. 1, Komplek Dago Villas Lippo Cikarang, Bekasi, 17550, Indonesia
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Lee K, Daniels MJ. Causal inference for bivariate longitudinal quality of life data in presence of death by using global odds ratios. Stat Med 2013; 32:4275-84. [PMID: 23720372 DOI: 10.1002/sim.5857] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2012] [Revised: 04/18/2013] [Accepted: 04/26/2013] [Indexed: 11/05/2022]
Abstract
In longitudinal clinical trials, if a subject drops out due to death, certain responses, such as those measuring quality of life (QoL), will not be defined after the time of death. Thus, standard missing data analyses, e.g., under ignorable dropout, are problematic because these approaches implicitly 'impute' values of the response after death. In this paper we define a new survivor average causal effect for a bivariate response in a longitudinal quality of life study that had a high dropout rate with the dropout often due to death (or tumor progression). We show how principal stratification, with a few sensitivity parameters, can be used to draw causal inferences about the joint distribution of these two ordinal quality of life measures.
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Affiliation(s)
- Keunbaik Lee
- Department of Statistics, Sungkyunkwan University, Seoul, 110-745, Korea
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10
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Ding P, Geng Z, Yan W, Zhou XH. Identifiability and Estimation of Causal Effects by Principal Stratification With Outcomes Truncated by Death. J Am Stat Assoc 2011. [DOI: 10.1198/jasa.2011.tm10265] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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