A flexible sensitivity analysis approach for unmeasured confounding with multiple treatments and a binary outcome with application to SEER-Medicare lung cancer data

Zou, Jungang; Gu, Chenyang; Ji, Jiayi; Lopez, Michael J.; Kale, Minal

doi:10.1214/21-aoas1530

Cited by 11 publications

(22 citation statements)

References 41 publications

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“…For notational brevity, we suppress the

ik

subscript denoting individual. Following Brumback et al 35 and Hu et al, 12 we first define the confounding function for any pair of treatments

\left({a}_j,{a}_{j^{\prime }}\right)

c\left({a}_j,{a}_{j^{\prime }},\boldsymbol{x},v\right)=E\left[\log T\left({a}_j\right)\;|\;A={a}_j,\boldsymbol{X}=\boldsymbol{x},V=v\right]-E\left[\log T\left({a}_j\right)\;|\;A={a}_{j^{\prime }},\boldsymbol{X}=\boldsymbol{x},V=v\right].

This confounding function directly represents the difference in the mean potential log survival times under treatment

{a}_j

between those treated with

{a}_j

and those treated with

{a}_{j^{\prime }}

, who have the same level of

\boldsymbol{x}

.…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…For notational brevity, we suppress the ik subscript denoting individual. Following Brumback et al 35 and Hu et al, 12 we first define the confounding function for any pair of treatments (a j , a j ′ ) as…”

Section: Confounding Function Adjusted Treatment Effect Estimatesmentioning

confidence: 99%

“…In fact, the STROBE guidelines recommend observational studies be accompanied by sensitivity analysis investigating the ramifications of potential unmeasured confounding 11 . Many sensitivity analysis methods have been developed, including Rosenbaum's

\Gamma

, 28 external adjustment, 29 confounding functions, 12,30 and the E value, 31 to name a few. These methods differ in how unmeasured confounding is formulated and parameterized.…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…Our sensitivity analysis approach is along the line of work by Hu et al, 12 and is based within the framework of confounding function 30,35 . The confounding function based methods have the advantage of avoiding introducing a hypothetical unmeasured confounder and making an assumption about its underlying structure, on which there is a lack of consensus, and are preferred when the primary interest is in understanding the total effect of all unmeasured confounders 12,35 …”

Section: Sensitivity Analysismentioning

confidence: 99%

“…Because the survival times

T

may be right censored and we deal with right censoring using data augmentation, the outcome modification can be implemented on the complete‐data survival times. We propose a Monte Carlo sensitivity analysis approach along the line of work by Hu et al, 12 which was developed for binary outcomes. We extend their work to accommodate multilevel censored survival outcomes.…”

Section: Sensitivity Analysismentioning

confidence: 99%

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A flexible approach for causal inference with multiple treatments and clustered survival outcomes

Ennis

Hogan

2022

Statistics in Medicine

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When drawing causal inferences about the effects of multiple treatments on clustered survival outcomes using observational data, we need to address implications of the multilevel data structure, multiple treatments, censoring, and unmeasured confounding for causal analyses. Few off-the-shelf causal inference tools are available to simultaneously tackle these issues. We develop a flexible random-intercept accelerated failure time model, in which we use Bayesian additive regression trees to capture arbitrarily complex relationships between censored survival times and pre-treatment covariates and use the random intercepts to capture cluster-specific main effects. We develop an efficient Markov chain Monte Carlo algorithm to draw posterior inferences about the population survival effects of multiple treatments and examine the variability in cluster-level effects. We further propose an interpretable sensitivity analysis approach to evaluate the sensitivity of drawn causal inferences about treatment effect to the potential magnitude of departure from the causal assumption of no unmeasured confounding. Expansive simulations empirically validate and demonstrate good practical operating characteristics of our proposed methods. Applying the proposed methods to a dataset on older high-risk localized prostate cancer patients drawn from the National Cancer Database, we evaluate the comparative effects of three treatment approaches on patient survival, and assess the ramifications of potential unmeasured confounding.

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“…For notational brevity, we suppress the

ik

subscript denoting individual. Following Brumback et al 35 and Hu et al, 12 we first define the confounding function for any pair of treatments

\left({a}_j,{a}_{j^{\prime }}\right)

c\left({a}_j,{a}_{j^{\prime }},\boldsymbol{x},v\right)=E\left[\log T\left({a}_j\right)\;|\;A={a}_j,\boldsymbol{X}=\boldsymbol{x},V=v\right]-E\left[\log T\left({a}_j\right)\;|\;A={a}_{j^{\prime }},\boldsymbol{X}=\boldsymbol{x},V=v\right].

This confounding function directly represents the difference in the mean potential log survival times under treatment

{a}_j

between those treated with

{a}_j

and those treated with

{a}_{j^{\prime }}

, who have the same level of

\boldsymbol{x}

.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Section: Confounding Function Adjusted Treatment Effect Estimatesmentioning

confidence: 99%

\Gamma

, 28 external adjustment, 29 confounding functions, 12,30 and the E value, 31 to name a few. These methods differ in how unmeasured confounding is formulated and parameterized.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Section: Sensitivity Analysismentioning

confidence: 99%

“…Because the survival times

T

Section: Sensitivity Analysismentioning

confidence: 99%

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A flexible approach for causal inference with multiple treatments and clustered survival outcomes

Ennis

Hogan

2022

Statistics in Medicine

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A new method for clustered survival data: Estimation of treatment effect heterogeneity and variable selection

2023

Biometrical J

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We recently developed a new method random‐intercept accelerated failure time model with Bayesian additive regression trees (riAFT‐BART) to draw causal inferences about population treatment effect on patient survival from clustered and censored survival data while accounting for the multilevel data structure. The practical utility of this method goes beyond the estimation of population average treatment effect. In this work, we exposit how riAFT‐BART can be used to solve two important statistical questions with clustered survival data: estimating the treatment effect heterogeneity and variable selection. Leveraging the likelihood‐based machine learning, we describe a way in which we can draw posterior samples of the individual survival treatment effect from riAFT‐BART model runs, and use the drawn posterior samples to perform an exploratory treatment effect heterogeneity analysis to identify subpopulations who may experience differential treatment effects than population average effects. There is sparse literature on methods for variable selection among clustered and censored survival data, particularly ones using flexible modeling techniques. We propose a permutation‐based approach using the predictor's variable inclusion proportion supplied by the riAFT‐BART model for variable selection. To address the missing data issue frequently encountered in health databases, we propose a strategy to combine bootstrap imputation and riAFT‐BART for variable selection among incomplete clustered survival data. We conduct an expansive simulation study to examine the practical operating characteristics of our proposed methods, and provide empirical evidence that our proposed methods perform better than several existing methods across a wide range of data scenarios. Finally, we demonstrate the methods via a case study of predictors for in‐hospital mortality among severe COVID‐19 patients and estimating the heterogeneous treatment effects of three COVID‐specific medications. The methods developed in this work are readily available in the package .

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Estimating heterogeneous survival treatment effect in observational data using machine learning

2021

Statistics in Medicine

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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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A flexible sensitivity analysis approach for unmeasured confounding with multiple treatments and a binary outcome with application to SEER-Medicare lung cancer data

Cited by 11 publications

References 41 publications

A flexible approach for causal inference with multiple treatments and clustered survival outcomes

A flexible approach for causal inference with multiple treatments and clustered survival outcomes

A new method for clustered survival data: Estimation of treatment effect heterogeneity and variable selection

Estimating heterogeneous survival treatment effect in observational data using machine learning

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