Effient Propensity Score Regression Estimators of Multi-valued Treatment Effects for the Treated PDF Download
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Author: Ying-Ying Lee
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Category :
Languages : en
Pages :
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Book Description
Author: Ying-Ying Lee
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Ying-Ying Lee
Publisher:
ISBN:
Category :
Languages : en
Pages : 35
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Book Description
Matching is a widely used program evaluation estimation method when treatment is assigned at random conditional on observable characteristics. When a multivalued treatment takes on more than two values, valid causal comparisons for a subpopulation who is treated a particular treatment level are based on two propensity scores - one for the treated level and one for the counterfactual level. The main contribution of this paper is propensity score regression estimators for a class of treatment effects for the treated that achieve the semiparametric efficiency bounds under the cases when the propensity scores are unknown and when they are known. We derive the large sample distribution that accounts for the estimation error of the propensity score as generated regressors. We contribute to the binary treatment literature by a new propensity score regression estimator for the average/quantile treatment effect for the treated: our efficient estimator matches on a normalized propensity score that is a combination of the true propensity score and its nonparametric estimate. There are two key findings: (I) The efficiency bound is reduced by knowledge of the propensity scores for the treated levels, but is not affected by knowledge of the propensity score for the counterfactual level. (II) Matching on the nonparametrically estimated propensity score recovers the information contained in matching on the pretreatment variables.
Author: Keisuke Hirano
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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: Markus Frölich
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ISBN:
Category :
Languages : en
Pages : 28
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Author: Zirui Gu
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Category : Multivariate analysis
Languages : en
Pages :
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Propensity score methods (PSM) that have been widely used to reduce selection bias in observational studies are restricted to a binary treatment. Imai and van Dyk extended PSM to estimate non-binary treatment effect using stratification with P-Function, and generalized inverse treatment probability weighting (GIPTW). However, propensity score (PS) matching methods on multiple treatments received little attention, and existing generalized PSMs merely focused on estimates of main treatment effects but omitted potential interaction effects that are of essential interest in many studies. In this dissertation, I extend Rubin's PS matching theory to general treatment regimens under the P-Function framework. From theory to practice, I propose an innovative distance measure that can summarize similarities among subjects in multiple treatment groups. Based on this distance measure I propose four generalized propensity score matching methodologies. The first two methods are extensions of nearest neighbor matching. I implemented Monte Carlo simulation studies to compare them with GIPTW and stratification on P-Function methods. The next two methods are extensions of the nearest neighbor caliper width matching and variable matching. I define the caliper width as the product of a weighted standard deviation of all possible pairwise distances between two treatment groups. I conduct a series of simulation studies to determine an optimal caliper width by searching the lowest mean square error of average causal interaction effect. I further compare the ones with optimal caliper width with other methods using simulations. Finally, I apply these methods to the National Medical Expenditure Survey data to examine the average causal main effect of duration and frequency of smoking as well as their interaction effect on annual medical expenditures. Using proposed methods, researchers can apply regression models with specified interaction terms to the matched data and simultaneously obtain both main and interaction effects estimate with improved statistical properties.
Author: Diqiong Xie
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ISBN:
Category : Estimation theory
Languages : en
Pages : 257
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Observational studies are an indispensable complement to randomized clinical trials (RCT) for comparison of treatment effectiveness. Often RCTs cannot be carried out due to the costs of the trial, ethical questions and rarity of the outcome. When noncompliance and missing data are prevalent, RCTs become more like observational studies. The main problem is to adjust for the selection bias in the observational study. One increasingly used method is propensity-score matching. Compared to traditional multi-covariate matching methods, matching on the propensity score alleviates the curse of dimensionality. It allows investigators to balance multiple covariate distributions between treatment groups by matching on a single score. This thesis focuses on the large sample properties of the matching estimators of the treatment effect. The first part of this thesis deals with problems of the analytic supports of the logit propensity score and various matching methods. The second part of this thesis focuses on the matching estimators of additive and multiplicative treatment effects. We derive the asymptotic order of the biases and asymptotic distributions of the matching estimators. We also derive the large sample variance estimators for the treatment effect estimators. The methods and theoretical results are applied and checked in a series of simulation studies. The third part of this thesis is devoted to a comparison between propensity-score matching and multiple linear regression using simulation.
Author: Ricarda Schmidl
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ISBN:
Category :
Languages : en
Pages : 174
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Author: Guido Imbens
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Category : Analysis of covariance
Languages : en
Pages : 36
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Estimation of average treatment effects in observational, or non-experimental in pre-treatment variables. If the number of pre-treatment variables is large, and their distribution varies substantially with treatment status, standard adjustment methods such as covariance adjustment are often inadequate. Rosenbaum and Rubin (1983) propose an alternative method for adjusting for pre-treatment variables based on the propensity score conditional probability of receiving the treatment given pre-treatment variables. They demonstrate that adjusting solely for the propensity score removes all the bias associated with differences in pre-treatment variables between treatment and control groups. The Rosenbaum-Rubin proposals deal exclusively with the case where treatment takes on only two values. In this paper an extension of this methodology is proposed that allows for estimation of average causal effects with multi-valued treatments while maintaining the advantages of the propensity score approach.
Author: Ying Zhang
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Category :
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:
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Category :
Languages : en
Pages :
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Estimation of treatment effects with causalinterpretation from obervational data is complicated by the fact thatexposure to treatment is confounded with subject characteristics. Thepropensity score, the probability of exposure to treatment conditionalon covariates, is the basis for two competing classes of approachesfor adjusting for confounding: methods based on stratification ofobservations by quantiles of estimated propensity scores, and methods based on weighting individual observations by weights depending onestimated propensity scores. We review these approaches andinvestigate their relative performance. Some clinical trials follow a design in which patientsare randomized to a primary therapy upon entry followed by anotherrandomization to maintenance therapy contingent upon diseaseremission. Ideally, analysis would allow different treatmentpolicies, i.e. combinations of primary and maintenance therapy ifspecified up-front, to be compared. Standard practice is to conductseparate analyses for the primary and follow-up treatments, which doesnot address this issue directly. We propose consistent estimators ofthe survival distribution and mean survival time for each treatmentpolicy in such two-stage studies and derive large sampleproperties. The methods are demonstrated on a leukemia clinical trialdata set and through simulation.
