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Register a new userA Generalizability Score for Aggregate Causal Effect
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Guanhua Chen
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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Scientists frequently generalize population level causal quantities such as average treatment effect from a source population to a target population. When the causal effects are heterogeneous, differences in subject characteristics between the source and target populations may make such a generalization difficult and unreliable. Reweighting or regression can be used to adjust for such differences when generalizing. However, these methods typically suffer from large variance if there is limited covariate distribution overlap between the two populations. We propose a generalizability score to address this issue. The score can be used as a yardstick to select target subpopulations for generalization. A simplified version of the score avoids using any outcome information and thus can prevent deliberate biases associated with inadvertent access to such information. Both simulation studies and real data analysis demonstrate convincing results for such selection.
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In this paper, we propose a propensity score adapted variable selection procedure to select covariates for inclusion in propensity score models, in order to eliminate confounding bias and improve statistical efficiency in observational studies. Our variable selection approach is specially designed for causal inference, it only requires the propensity scores to be $sqrt{n}$-consistently estimated through a parametric model and need not correct specification of potential outcome models. By using estimated propensity scores as inverse probability treatment weights in performing an adaptive lasso on the outcome, it successfully excludes instrumental variables, and includes confounders and outcome predictors. We show its oracle properties under the linear association conditions. We also perform some numerical simulations to illustrate our propensity score adapted covariate selection procedure and evaluate its performance under model misspecification. Comparison to other covariate selection methods is made using artificial data as well, through which we find that it is more powerful in excluding instrumental variables and spurious covariates.
Understanding how treatment effects vary on individual characteristics is critical in the contexts of personalized medicine, personalized advertising and policy design. When the characteristics are of practical interest are only a subset of full covariate, non-parametric estimation is often desirable; but few methods are available due to the computational difficult. Existing non-parametric methods such as the inverse probability weighting methods have limitations that hinder their use in many practical settings where the values of propensity scores are close to 0 or 1. We propose the propensity score regression (PSR) that allows the non-parametric estimation of the heterogeneous treatment effects in a wide context. PSR includes two non-parametric regressions in turn, where it first regresses on the propensity scores together with the characteristics of interest, to obtain an intermediate estimate; and then, regress the intermediate estimates on the characteristics of interest only. By including propensity scores as regressors in the non-parametric manner, PSR is capable of substantially easing the computational difficulty while remain (locally) insensitive to any value of propensity scores. We present several appealing properties of PSR, including the consistency and asymptotical normality, and in particular the existence of an explicit variance estimator, from which the analytical behaviour of PSR and its precision can be assessed. Simulation studies indicate that PSR outperform existing methods in varying settings with extreme values of propensity scores. We apply our method to the national 2009 flu survey (NHFS) data to investigate the effects of seasonal influenza vaccination and having paid sick leave across different age groups.
Causal effect estimation from observational data is an important but challenging problem. Causal effect estimation with unobserved variables in data is even more difficult. The challenges lie in (1) whether the causal effect can be estimated from observational data (identifiability); (2) accuracy of estimation (unbiasedness), and (3) fast data-driven algorithm for the estimation (efficiency). Each of the above problems by its own, is challenging. There does not exist many data-driven methods for causal effect estimation so far, and they solve one or two of the above problems, but not all. In this paper, we present an algorithm that is fast, unbiased and is able to confirm if a causal effect is identifiable or not under a very practical and commonly seen problem setting. To achieve high efficiency, we approach the causal effect estimation problem as a local search for the minimal adjustment variable sets in data. We have shown that identifiability and unbiased estimation can be both resolved using data in our problem setting, and we have developed theorems to support the local search for searching for adjustment variable sets to achieve unbiased causal effect estimation. We make use of frequent pattern mining strategy to further speed up the search process. Experiments performed on an extensive collection of synthetic and real-world datasets demonstrate that the proposed algorithm outperforms the state-of-the-art causal effect estimation methods in both accuracy and time-efficiency.
While a randomized controlled trial (RCT) readily measures the average treatment effect (ATE), this measure may need to be generalized to the target population to account for a sampling bias in the RCTs population. Identifying this target population treatment effect needs covariates in both sets to capture all treatment effect modifiers that are shifted between the two sets. Standard estimators then use either weighting (IPSW), outcome modeling (G-formula), or combine the two in doubly robust approaches (AIPSW). However such covariates are often not available in both sets. Therefore, after completing existing proofs on the complete case consistency of those three estimators, we compute the expected bias induced by a missing covariate, assuming a Gaussian distribution and a semi-parametric linear model. This enables sensitivity analysis for each missing covariate pattern, giving the sign of the expected bias. We also show that there is no gain in imputing a partially-unobserved covariate. Finally we study the replacement of a missing covariate by a proxy. We illustrate all these results on simulations, as well as semi-synthetic benchmarks using data from the Tennessee Student/Teacher Achievement Ratio (STAR), and with a real-world example from critical care medicine.
Missing data and confounding are two problems researchers face in observational studies for comparative effectiveness. Williamson et al. (2012) recently proposed a unified approach to handle both issues concurrently using a multiply-robust (MR) methodology under the assumption that confounders are missing at random. Their approach considers a union of models in which any submodel has a parametric component while the remaining models are unrestricted. We show that while their estimating function is MR in theory, the possibility for multiply robust inference is complicated by the fact that parametric models for different components of the union model are not variation independent and therefore the MR property is unlikely to hold in practice. To address this, we propose an alternative transparent parametrization of the likelihood function, which makes explicit the model dependencies between various nuisance functions needed to evaluate the MR efficient score. The proposed method is genuinely doubly-robust (DR) in that it is consistent and asymptotic normal if one of two sets of modeling assumptions holds. We evaluate the performance and doubly robust property of the DR method via a simulation study.
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