Reader Reaction: Instrumental Variable Additive Hazards Models with Exposure-Dependent Censoring

Chan, Kwun Chuen Gary

doi:10.1111/biom.12471

Cited by 12 publications

(20 citation statements)

References 2 publications

(8 reference statements)

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“…For example, using additive hazards model rather than Cox proportional hazards model for survival outcomes when model specification is reasonably justified. 8,11,15 In case of rare binary events, we may consider log-linear model instead of logistic model.…”

Section: Discussionmentioning

confidence: 99%

“…c(X, ) does not include exposure variable D and c(X, ) ⟂ ⟂ D|X, . Two previous studies 11,15 established the consistency of 2SRI estimator in additive hazards model under the assumption that is a random error independent of D, X, and . In this current work, we do not make this strong assumption but we demonstrated earlier that when c(X, ) is omitted, the coefficient of the exposure variable D will not change under a linear model.…”

Section: Additive Hazards Modelmentioning

confidence: 98%

“…When constructing a 2SRI nonlinear model, previous studies 8,11,15 simply assume the decomposition of unmeasured factors T 3 U into 2 parts, residuals from the treatment model and a remainder term , as follows:…”

Section: Construction Of 2-stage IV Modelsmentioning

confidence: 99%

“…Similarly, the 2SPS estimator can be shown to be consistent under the same conditions. In the presence of censoring, the 2SRI estimator is consistent under the assumption that censoring time is conditionally independent of event time given X, R, and D. 15 The 2SPS estimator is consistent under the assumption that censoring time is conditionally independent of event time given R and X. 12…”

Section: Additive Hazards Modelmentioning

confidence: 99%

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A general approach to evaluating the bias of 2‐stage instrumental variable estimators

Wan

Small

Mitra

2018

Statistics in Medicine

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Unmeasured confounding is a common concern when researchers attempt to estimate a treatment effect using observational data or randomized studies with nonperfect compliance. To address this concern, instrumental variable methods, such as 2-stage predictor substitution (2SPS) and 2-stage residual inclusion (2SRI), have been widely adopted. In many clinical studies of binary and survival outcomes, 2SRI has been accepted as the method of choice over 2SPS, but a compelling theoretical rationale has not been postulated. We evaluate the bias and consistency in estimating the conditional treatment effect for both 2SPS and 2SRI when the outcome is binary, count, or time to event. We demonstrate analytically that the bias in 2SPS and 2SRI estimators can be reframed to mirror the problem of omitted variables in nonlinear models and that there is a direct relationship with the collapsibility of effect measures. In contrast to conclusions made by previous studies (Terza et al, 2008), we demonstrate that the consistency of 2SRI estimators only holds under the following conditions: (1) when the null hypothesis is true; (2) when the outcome model is collapsible; or (3) when estimating the nonnull causal effect from Cox or logistic regression models, the strong and unrealistic assumption that the effect of the unmeasured covariates on the treatment is proportional to their effect on the outcome needs to hold. We propose a novel dissimilarity metric to provide an intuitive explanation of the bias of 2SRI estimators in noncollapsible models and demonstrate that with increasing dissimilarity between the effects of the unmeasured covariates on the treatment versus outcome, the bias of 2SRI increases in magnitude.

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Section: Discussionmentioning

confidence: 99%

Section: Additive Hazards Modelmentioning

confidence: 98%

Section: Construction Of 2-stage IV Modelsmentioning

confidence: 99%

Section: Additive Hazards Modelmentioning

confidence: 99%

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A general approach to evaluating the bias of 2‐stage instrumental variable estimators

Wan

Small

Mitra

2018

Statistics in Medicine

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“…Bosco et al (2010) generalized the 2SLS method to account for censoring by fitting a logistic regression that includes the treatment as dependent variable and the provider-preference based IV as independent variable in the first-stage and included the predicted values obtained by the first-stage in the Cox proportional hazard regression in the second-stage (MacKenzie et al, 2014). In the context of additive hazard models, Li et al (2015a) developed a closed-form, two-stage treatment effect estimator that relies on assuming linear structural equation models for the hazard function (Tchetgen et al, 2015;Chan, 2016). An alternative two-stage residual inclusion (2SRI) that includes the residual of the first-stage model in the second stage is proposed by Terza et al (2008) that can be used in nonlinear regression models, e.g., Weibull models.…”

Section: Introductionmentioning

confidence: 99%

Instrumental variable analysis with censored data in the presence of many weak instruments: Application to the effect of being sentenced to prison on time to employment

Ertefaie¹,

Nguyen²,

Harding³

et al. 2018

Ann. Appl. Stat.

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This article discusses an instrumental variable approach for analyzing censored data that includes many instruments that are weakly associated with the endogenous variable. We study the effect of imprisonment on time to employment using an administrative data on all individuals sentenced for felony in Michigan in the years 2003-2006. Despite the large body of research on the effect of prison on employment, this is still a controversial topic, especially since some of the studies could have been affected by unmeasured confounding. We take advantage of a natural experiment based on the random assignment of judges to felony cases and construct a vector of instruments based on judges' ID that can avoid the confounding bias. However, some of the constructed instruments are weakly associated with the sentence type, i.e., the endogenous variable, which can potentially lead to misleading results. Using a dimension reduction technique, we propose a novel semi-parametric estimation procedure in a survival context that is robust to the presence of many weak instruments. Specifically, we construct a test statistic based on the structural failure time model and provide inference by inverting the testing procedure. Under some assumptions, the optimal choice of the test statistic has also been derived.

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Instrumental variable with competing risk model

Zheng

Dai

Hari

et al. 2017

Statistics in Medicine

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In this paper, we discuss causal inference on the efficacy of a treatment or medication on a time-to-event outcome with competing risks. Although the treatment group can be randomized, there can be confoundings between the compliance and the outcome. Unmeasured confoundings may exist even after adjustment for measured covariates. Instrumental variable methods are commonly used to yield consistent estimations of causal parameters in the presence of unmeasured confoundings. On the basis of a semiparametric additive hazard model for the subdistribution hazard, we propose an instrumental variable estimator to yield consistent estimation of efficacy in the presence of unmeasured confoundings for competing risk settings. We derived the asymptotic properties for the proposed estimator. The estimator is shown to be well performed under finite sample size according to simulation results. We applied our method to a real transplant data example and showed that the unmeasured confoundings lead to significant bias in the estimation of the effect (about 50% attenuated).

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Reader Reaction: Instrumental Variable Additive Hazards Models with Exposure-Dependent Censoring

Cited by 12 publications

References 2 publications

A general approach to evaluating the bias of 2‐stage instrumental variable estimators

A general approach to evaluating the bias of 2‐stage instrumental variable estimators

Instrumental variable analysis with censored data in the presence of many weak instruments: Application to the effect of being sentenced to prison on time to employment

Instrumental variable with competing risk model

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