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Author: Ying Zhang
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Languages : en
Pages : 0
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Estimation of average and quantile treatment effects is crucial in causal inference for evaluation of treatments or interventions in biomedical, economic, and social studies. Under the assumption of treatment and potential outcomes are independent conditional on all covariates, valid treatment effect estimators can be obtained using nonparametric inverse propensity weighting and/or regression, which are popular because no model on propensity or regression is imposed. To obtain valid and efficient treatment effect estimators, typically the set of all covariates can be replaced by lower dimensional sets containing linear combinations of covariates. We propose to construct a lower dimensional set separately for each treatment and show that the resulting asymptotic variance of treatment effect estimator reaches a lower bound that is smaller than those based on other sets. Since the lower dimensional sets have to be constructed, for example, using nonparametric sufficient dimension reduction, we derive theoretical results on when the efficiency of treatment effect estimation is affected by sufficient dimension reduction. We find that, except for some special cases, the efficiency of treatment effect estimation is affected even though the sufficient dimension reduction is consistent in the rate of the square root of the sample size. As causal setting is similar with that of missing data, we apply the same technics to handle missing covariate value problems in estimating equations. Our theory is complemented by some simulation results. We use the data from the University of Wisconsin Health Accountable Care Organization as an example for average/quantile treatment effects estimations, and the automobile data from University of California-Irvine as an example for estimating regression parameters in estimating equations with missing covariate value.
Author: Ying Zhang
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Languages : en
Pages : 0
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Estimation of average and quantile treatment effects is crucial in causal inference for evaluation of treatments or interventions in biomedical, economic, and social studies. Under the assumption of treatment and potential outcomes are independent conditional on all covariates, valid treatment effect estimators can be obtained using nonparametric inverse propensity weighting and/or regression, which are popular because no model on propensity or regression is imposed. To obtain valid and efficient treatment effect estimators, typically the set of all covariates can be replaced by lower dimensional sets containing linear combinations of covariates. We propose to construct a lower dimensional set separately for each treatment and show that the resulting asymptotic variance of treatment effect estimator reaches a lower bound that is smaller than those based on other sets. Since the lower dimensional sets have to be constructed, for example, using nonparametric sufficient dimension reduction, we derive theoretical results on when the efficiency of treatment effect estimation is affected by sufficient dimension reduction. We find that, except for some special cases, the efficiency of treatment effect estimation is affected even though the sufficient dimension reduction is consistent in the rate of the square root of the sample size. As causal setting is similar with that of missing data, we apply the same technics to handle missing covariate value problems in estimating equations. Our theory is complemented by some simulation results. We use the data from the University of Wisconsin Health Accountable Care Organization as an example for average/quantile treatment effects estimations, and the automobile data from University of California-Irvine as an example for estimating regression parameters in estimating equations with missing covariate value.
Author: Christoph Rothe
Publisher:
ISBN:
Category :
Languages : en
Pages : 27
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In a treatment effect model with unconfoundedness, treatment assignments are not only independent of potential outcomes given the covariates, but also given the propensity score alone. Despite this powerful dimension reduction property, adjusting for the propensity score is known to lead to an estimator of the average treatment effect with lower asymptotic efficiency than one based on adjusting for all covariates. Moreover, knowledge of the propensity score does not change the efficiency bound for estimating average treatment effects, and many empirical strategies are more efficient when an estimate of the propensity score is used instead of its true value. Here, we resolve this "propensity score paradox" by demonstrating the value of knowledge of the propensity score.We show that by exploiting such knowledge properly, it is possible to construct an efficient treatment effect estimator that is not affected by the "curse of dimensionality", which yields desirable second order asymptotic properties and finite sample performance. The method combines knowledge of the propensity score with a nonparametric adjustment for covariates, building on ideas from the literature on double robust estimation. It is straightforward to implement, and performs well in simulations. We also show that confidence intervals based on our estimator and a simple variance estimate have remarkably robust coverage properties with respect to the implementation details of the nonparametric adjustment step.
Author: Liqiang Shi
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Category :
Languages : en
Pages : 119
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Book Description
This dissertation consists of three chapters that study treatment effect estimation and treatment choice learning under the potential outcome framework (Neyman, 1923; Rubin, 1974). The first two chapters study how to efficiently combine an experimental sample with an auxiliary observational sample when estimating treatment effects. In chapter 1, I derive a new semiparametric efficiency bound under the two-sample setup for estimating ATE and other functions of the average potential outcomes. The efficiency bound for estimating ATE with an experimental sample alone is derived in Hahn (1998) and has since become an important reference point for studies that aim at improving the ATE estimation. This chapter answers how an auxiliary sample containing only observable characteristics (covariates, or features) can lower this efficiency bound. The newly obtained bound has an intuitive expression and shows that the (maximum possible) amount of variance reduction depends positively on two factors: 1) the size of the auxiliary sample, and 2) how well the covariates predict the individual treatment effect. The latter naturally motivates having high dimensional covariates and the adoption of modern machine learning methods to avoid over-fitting. In chapter 2, under the same setup, I propose a two-stage machine learning (ML) imputation estimator that achieves the efficiency bound derived in chapter 1, so that no other regular estimators for ATE can have lower asymptotic variance in the same setting. This estimator involves two steps. In the first step, conditional average potential outcome functions are estimated nonparametrically via ML, which are then used to impute the unobserved potential outcomes for every unit in both samples. In the second step, the imputed potential outcomes are aggregated together in a robust way to produce the final estimate. Adopting the cross-fitting technique proposed in Chernozhukov et al. (2018), our two-step estimator can use a wide range of supervised ML tools in its first step, while maintaining valid inference to construct confidence intervals and perform hypothesis tests. In fact, any method that estimates the relevant conditional mean functions consistently in square norm, with no rate requirement, will lead to efficiency through the proposed two-step procedure. I also show that cross-fitting is not necessary when the first step is implemented via LASSO or post-LASSO. Furthermore, our estimator is robust in the sense that it remains consistent and root n normal (no longer efficient) even if the first step estimators are inconsistent. Chapter 3 (coauthored with Kirill Ponomarev) studies model selection in treatment choice learning. When treatment effects are heterogeneous, a decision maker, given either experiment or quasi-experiment data, can attempt to find a policy function that maps observable characteristics to treatment choices, aiming at maximizing utilitarian welfare. When doing so, one often has to pick a constrained class of functions as candidates for the policy function. The choice of this function class poses a model selection problem. Following Mbakop and Tabord-Meehan (2021) we propose a policy learning algorithm that incorporates data-driven model selection. Our method also leverages doubly robust estimation (Athey and Wager, 2021) so that it could retain the optimal root n rate in expected regret in general setups including quasi-experiments where propensity scores are unknown. We also refined some related results in the literature and derived a new finite sample lower bound on expected regret to show that the root n rate is indeed optimal.
Author: Agency for Health Care Research and Quality (U.S.)
Publisher: Government Printing Office
ISBN: 1587634236
Category : Medical
Languages : en
Pages : 236
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Book Description
This User’s Guide is a resource for investigators and stakeholders who develop and review observational comparative effectiveness research protocols. It explains how to (1) identify key considerations and best practices for research design; (2) build a protocol based on these standards and best practices; and (3) judge the adequacy and completeness of a protocol. Eleven chapters cover all aspects of research design, including: developing study objectives, defining and refining study questions, addressing the heterogeneity of treatment effect, characterizing exposure, selecting a comparator, defining and measuring outcomes, and identifying optimal data sources. Checklists of guidance and key considerations for protocols are provided at the end of each chapter. The User’s Guide was created by researchers affiliated with AHRQ’s Effective Health Care Program, particularly those who participated in AHRQ’s DEcIDE (Developing Evidence to Inform Decisions About Effectiveness) program. Chapters were subject to multiple internal and external independent reviews. More more information, please consult the Agency website: www.effectivehealthcare.ahrq.gov)
Author: Li Li
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Languages : en
Pages : 0
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Covariates selection is essential when faced with many variables in modern causal inference in a data-rich environment. Particularly, the efficiency of the average causal effect (ACE) can be improved by including covariates only related to the outcome and reduced by including covariates related to the treatment but not the outcome in the propensity score (PS) model. In this paper, we estimate the causal effect in the presence of censored outcome and high-dimensional covariates. To improve the efficiency of the estimation of ACE, we propose the censored outcome adaptive Lasso (COAL) to select covariates, where the weighted least square method is applied to account for censoring. Based on the covariate selection, we propose a double inverse propensity weighted estimator for ACE. Furthermore, we establish the oracle properties of the variable selection and derive the asymptotic properties of the proposed estimator.
Author: Trinetri Ghosh
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Languages : en
Pages :
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Average causal effect is often used to compare the treatments or interventions in both randomized and observational studies. It has a wide variety of applications in medical, natural, and social sciences, for example, psychology, political science, economics, and so on. Due to the increased availability of high-dimensional pre-treatment information sets, dimension reduction is a major methodological issue in observational studies to estimate the average causal effect of a non-randomized treatment. Often assumptions are made to ensure model identifiability and to establish theoretical guarantees for nuisance conditional models. But these assumptions can be less flexible. In the first work (Chapter 2), to estimate the average causal effect in an observational study, we use a semiparametric locally efficient dimension-reduction approach to assess the treatment assignment mechanisms and average responses in both the treated and the non-treated groups. We then integrate our results using imputation, inverse probability weighting, and doubly robust augmentation estimators. Doubly robust estimators are locally efficient, and imputation estimators are super-efficient when the response models are correct. To take advantage of both procedures, we introduce a shrinkage estimator that combines the two. The proposed estimators retain the double robustness property while improving on the variance when the response model is correct. We demonstrate the performance of these estimators using simulated experiments and a real data set on the effect of maternal smoking on baby birth weight. In the second work (Chapter 3), we implemented semiparametric efficient method in an emerging topic, precision medicine, an approach to tailoring disease prevention and treatment that takes into account individual variability in genes, environment, and lifestyle for each person. The goal of precision medicine is to deploy appropriate and optimal treatment based on the context of a patient's individual characteristics to maximize the clinical benefit. In this work, we propose a new modeling and estimation approach to select the optimal treatment regime from two different options through constructing a robust estimating equation. The method is protected against misspecification of the propensity score function or the outcome regression model for the non-treated group or the potential non-monotonic treatment difference model. Nonparametric smoothing and dimension reduction are incorporated to estimate the treatment difference model. We then identify the optimal treatment by maximizing the value function and established theoretical properties of the treatment assignment strategy. We illustrate the performance and effectiveness of our proposed estimators through extensive simulation studies and a real-world application to Huntington's disease patients. In the third work (Chapter 4), we aim to obtain optimal individualized treatment rules in the covariate-adjusted randomization clinical trial with many covariates. We model the treatment effect with an unspecified function of a single index of the covariates and leave the baseline response completely arbitrary. We devise a class of estimators to consistently estimate the treatment effect function and its associated index while bypassing the estimation of the baseline response, which is subject to the curse of dimensionality. We further develop inference tools to identify predictive covariates and isolate effective treatment regions. The usefulness of the methods is demonstrated in both simulations and a clinical data example.
Author: Keisuke Hirano
Publisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 68
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We are interested in estimating the average effect of a binary treatment on a scalar outcome. If assignment to the treatment is independent of the potential outcomes given pretreatment variables, biases associated with simple treatment-control average comparisons can be removed by adjusting for differences in the pre-treatment variables. Rosenbaum and Rubin (1983, 1984) show that adjusting solely for differences between treated and control units in a scalar function of the pre-treatment, the propensity score, also removes the entire bias associated with differences in pre-treatment variables. Thus it is possible to obtain unbiased estimates of the treatment effect without conditioning on a possibly high-dimensional vector of pre-treatment variables. Although adjusting for the propensity score removes all the bias, this can come at the expense of efficiency. We show that weighting with the inverse of a nonparametric estimate of the propensity score, rather than the true propensity score, leads to efficient estimates of the various average treatment effects. This result holds whether the pre-treatment variables have discrete or continuous distributions. We provide intuition for this result in a number of ways. First we show that with discrete covariates, exact adjustment for the estimated propensity score is identical to adjustment for the pre-treatment variables. Second, we show that weighting by the inverse of the estimated propensity score can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score. Finally, we make a connection to results to other results on efficient estimation through weighting in the context of variable probability sampling.
Author: Wolfgang Karl Härdle
Publisher: Springer Science & Business Media
ISBN: 364217146X
Category : Mathematics
Languages : en
Pages : 317
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Book Description
The statistical and mathematical principles of smoothing with a focus on applicable techniques are presented in this book. It naturally splits into two parts: The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers. The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity.
Author: Ge Zhao
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Languages : en
Pages :
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In the robust nonparametric kernel regression context, we prescribe a data driven method to select the trimming parameter and the bandwidth robustly. The estimator is obtained through solving estimating equations, and it controls the effect from outlying observations through a combination of weighting and trimming. We show asymptotic consistency, establish the estimation bias, variance properties and derive the asymptotic distribution of the resulting estimator. The finite sample performance of the estimator is illustrated through both simulation studies and analysis on a problem related to wind power generation, which motivated this study at the first place.We propose a general index model for survival data, which generalizes many commonly used semiparametric survival models and belongs to the framework of dimension reduction. Using a combination of geometric approach in semiparametrics and martingale treatment in survival data analysis, we devise estimation procedures that are feasible and do not require covariate-independent censoring as assumed in many dimension reduction methods for censored survival data. We establish the root-$n$ consistency and asymptotic normality of the proposed estimators and derive the most efficient estimator in this class forthe general index model. Numerical experiments are carried out to demonstrate the empirical performance of the proposed estimators and an application to an AIDS data further illustrates the usefulness of the work.Kidney transplantation is the most effective renal replacement therapy for renal failure patients. With the severe shortage of kidney supplies and for the clinical effectiveness of transplantation, it would be crucial to design objective measures, such as the Estimated Post-Transplant Survival (EPTS) score, to quantify the benefit that a renal failure patient would gain from a potential transplantation by comparing the expected residual lives of the same patient with and without transplant. However, in the current EPTS system, the mostdominant predictors are severe comorbidity conditions (such as diabetes) and age, which might preclude old and sick patients for receiving transplants. To help design a morefair score system, we propose a flexible and general covariate-dependent mean residual life model to estimate EPTS. Our method is both efficient and robust as the covariate effect is estimated via a semiparametrically efficient estimator, while the mean residual life function is estimated nonparametrically. We further provide a formula to predict the residual life increment potential for any given patients. Our method would facilitate allocating kidneys to patients who would have the largest residual life increment among all the eligibles. Our analysis of the kidney transplant data from the U.S. Scientific Registry of Transplant Recipients indicated that the most important predictor is the waiting time for transplantation: a shorter waiting time may lead to larger potential gains. We also identified an index which could serve as an additional important predictor if the waiting time is approximately between 1.5 years and three years. As our framework is general, we envision that our analytical strategies can be adopted to other organ transplantation settings.
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Languages : en
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Inference on treatment effect in a pretest-posttest study is a routine objective in medicine, public health, and other fields, and a number of approaches have been advocated. Typically, subjects are randomized to two treatments, the response is measured at baseline and a prespecified follow & ndash;up time, and interest focuses on the effect of treatment on follow--up mean response. Covariate information at baseline and in the intervening period until follow--up may also be collected. Missing posttest response for some subjects is routine, and disregarding these missing cases can lead to biased and inefficient inference. Despite the widespread popularity of this design, a consensus on an appropriate method of analysis when no data are missing, let alone on an accepted practice for taking account of missing follow--up response, does not exist. We take a semiparametric perspective, making no assumptions about the distributions of baseline and posttest responses. Exploiting the work of Robins et al. (1994), we characterize the class of all consistent estimators for treatment effect, identify the efficient member of this class, and propose practical procedures for implementation. The result is a unified framework for handling pretest--posttest inferences when follow--up response may be missing at random that allows the analyst to incorporate baseline and intervening information so as to improve efficiency of inference. Simulation studies and application to data from an HIV clinical trial illustrate the utility of the approach.
