Demystifying a class of multiply robust estimators

Wei, Li; Gu, Yuwen; Liu, Lan

doi:10.1093/biomet/asaa026

Cited by 13 publications

(8 citation statements)

References 33 publications

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“…Chan 51 proposed a regression‐based MR estimator for missing response problem, which includes multiple missingness models in a least square framework. Li et al 52 adapted a model mixing procedure, which mixes multiple candidate models into a final missingness model. These alternative methods for combining multiple candidate models may also be used in our situation.…”

Section: Discussionmentioning

confidence: 99%

Multiply robust subgroup analysis based on a single‐index threshold linear marginal model for longitudinal data with dropouts

Wei

Zhu

Qin

et al. 2022

Statistics in Medicine

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Identifying subpopulations that may be sensitive to the specific treatment is an important step toward precision medicine. On the other hand, longitudinal data with dropouts is common in medical research, and subgroup analysis for this data type is still limited. In this paper, we consider a single‐index threshold linear marginal model, which can be used simultaneously to identify subgroups with differential treatment effects based on linear combination of the selected biomarkers, estimate the treatment effects in different subgroups based on regression coefficients, and test the significance of the difference in treatment effects based on treatment‐subgroup interaction. The regression parameters are estimated by solving a penalized smoothed generalized estimating equation and the selection bias caused by missingness is corrected by a multiply robust weighting matrix, which allows multiple missingness models to be taken account into estimation. The proposed estimator remains consistent when any model for missingness is correctly specified. Under regularity conditions, the asymptotic normality of the estimator is established. Simulation studies confirm the desirable finite‐sample performance of the proposed method. As an application, we analyze the data from a clinical trial on pancreatic cancer.

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Section: Discussionmentioning

confidence: 99%

Multiply robust subgroup analysis based on a single‐index threshold linear marginal model for longitudinal data with dropouts

Wei

Zhu

Qin

et al. 2022

Statistics in Medicine

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“…Therefore, the nonparametric models, such as the kernel function, ANN, and random forest are not suitable as candidate models for the MiPS estimator because the coefficients of covariates cannot be obtained. When the candidate models are constructed by nonparametric models, some other multiply robust approaches may be adopted to integrate the information from multiple candidate models, such as the regression-based estimator under least square’s framework [ 40 ], the estimator based on empirical likelihood weighting [ 20 ], and the estimator based on model mixture procedures [ 41 ]. At this point, double/debiased machine learning approach may be extended to multiple/debiased machine learning for obtaining valid inference about ATE [ 42 ].…”

Section: Discussionmentioning

confidence: 99%

Estimation of average treatment effect based on a multi-index propensity score

Wei

Huang

et al. 2022

BMC Med Res Methodol

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Background Estimating the average effect of a treatment, exposure, or intervention on health outcomes is a primary aim of many medical studies. However, unbalanced covariates between groups can lead to confounding bias when using observational data to estimate the average treatment effect (ATE). In this study, we proposed an estimator to correct confounding bias and provide multiple protection for estimation consistency. Methods With reference to the kernel function-based double-index propensity score (Ker.DiPS) estimator, we proposed the artificial neural network-based multi-index propensity score (ANN.MiPS) estimator. The ANN.MiPS estimator employed the artificial neural network to estimate the MiPS that combines the information from multiple candidate models for propensity score and outcome regression. A Monte Carlo simulation study was designed to evaluate the performance of the proposed ANN.MiPS estimator. Furthermore, we applied our estimator to real data to discuss its practicability. Results The simulation study showed the bias of the ANN.MiPS estimators is very small and the standard error is similar if any one of the candidate models is correctly specified under all evaluated sample sizes, treatment rates, and covariate types. Compared to the kernel function-based estimator, the ANN.MiPS estimator usually yields smaller standard error when the correct model is incorporated in the estimator. The empirical study indicated the point estimation for ATE and its bootstrap standard error of the ANN.MiPS estimator is stable under different model specifications. Conclusions The proposed estimator extended the combination of information from two models to multiple models and achieved multiply robust estimation for ATE. Extra efficiency was gained by our estimator compared to the kernel-based estimator. The proposed estimator provided a novel approach for estimating the causal effects in observational studies.

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“…The methods based on empirical likelihood and model‐calibration have inspired further developments on improving the efficiency and robustness against model misspecification. One particular development is the so‐called multiply robust estimators; see Han & Wang (2013), Chan & Yam (2014), Han (2014a, 2014b, 2016a, 2016b), Chen & Haziza (2017, 2018, 2019), Duan & Yin (2017) & Li et al (2020), among others. The model‐calibration approach allows multiple working models

scriptP = false{π^{j} false(bold-italicX; {bold-italicα}^{j} false), j = 1, \dots, J false}

for the propensity score

π false(bold-italicX false)

and multiple working models

scriptA = false{a^{k} false(bold-italicX; {bold-italicγ}^{k} false), k = 1, \dots, K false}

for the outcome regression

E false(Y false| bold-italicX false)

to be accommodated simultaneously in a way similar to the constraints in (20) and (18).…”

Section: Calibration Methods For Missing Data Analysismentioning

confidence: 99%

Calibration Techniques Encompassing Survey Sampling, Missing Data Analysis and Causal Inference

Zhang

Han

2022

Int Statistical Rev

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SummaryWe provide a critical review on calibration methods developed in three different areas: survey sampling, missing data analysis and causal inference. We highlight the connections and variations of calibration techniques used in missing data analysis and causal inference to conventional calibration weighting and estimation in survey sampling and provide a common framework through model‐calibration and empirical likelihood to unify different calibration methods proposed in recent literature. The goal is to demonstrate the success and effectiveness of calibration methods in achieving some highly desired properties for missing data analysis and causal inference.

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Demystifying a class of multiply robust estimators

Cited by 13 publications

References 33 publications

Multiply robust subgroup analysis based on a single‐index threshold linear marginal model for longitudinal data with dropouts

Multiply robust subgroup analysis based on a single‐index threshold linear marginal model for longitudinal data with dropouts

Estimation of average treatment effect based on a multi-index propensity score

Calibration Techniques Encompassing Survey Sampling, Missing Data Analysis and Causal Inference

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