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Variance estimation for the average treatment effects on the treated and on the controls

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arXiv 2022年

Common causal estimands include the average treatment effect (ATE), the average treatment effect of the treated (ATT), and the average treatment effect on the controls (ATC). Using augmented inverse probability weighting methods, parametric models are judiciously leveraged to yield doubly robust estimators, i.e., estimators that are consistent when at least one the parametric models is correctly specified. Three sources of uncertainty are associated when we evaluate these estimators and their variances, i.e., when we estimate the treatment and outcome regression models as well as the desired treatment effect. In this paper, we propose methods to calculate the variance of the normalized, doubly robust ATT and ATC estimators and investigate their finite sample properties. We consider both the asymptotic sandwich variance estimation, the standard bootstrap as well as two wild bootstrap methods. For the asymptotic approximations, we incorporate the aforementioned uncertainties via estimating equations. Moreover, unlike the standard bootstrap procedures, the proposed wild bootstrap methods use perturbations of the influence functions of the estimators through independently distributed random variables. We conduct an extensive simulation study where we vary the heterogeneity of the treatment effect as well as the proportion of participants assigned to the active treatment group. We illustrate the methods using an observational study of critical ill patients on the use of right heart catherization. Copyright © 2022, The Authors. All rights reserved.

关键词： Regression analysis

Average treatment effect on the treated, under lack of positivity

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arXiv 2023年

作者： Liu, Yi Li, Huiyue Zhou, Yunji Matsouaka, Roland A. Department of Statistics North Carolina State University RaleighNC United States Baim Institute for Clinical Research BostonMA United States Department of Biostatistics University of Washington SeattleWA United States Department of Biostatistics and Bioinformatics Duke University DurhamNC United States Program for Comparative Effectiveness Methodology Duke Clinical Research Institute DurhamNC United States

The use of propensity score (PS) methods has become ubiquitous in causal inference. At the heart of these methods is the positivity assumption. Violation of the positivity assumption leads to the presence of extreme PS weights when estimating average causal effects of interest, such as the average treatment effect (ATE) or the average treatment effect on the treated (ATT), which renders invalid related statistical inference. To circumvent this issue, trimming or truncating the extreme estimated PSs have been widely used. However, these methods require that we specify a priori a threshold and sometimes an additional smoothing parameter. While there are a number of methods dealing with the lack of positivity when estimating ATE, surprisingly there is no much effort in the same issue for ATT. In this paper, we first review widely used methods, such as trimming and truncation in ATT. We emphasize the underlying intuition behind these methods to better understand their applications and highlight their main limitations. Then, we argue that the current methods simply target estimands that are scaled ATT (and thus move the goalpost to a different target of interest), where we specify the scale and the target populations. We further propose a PS weight-based alternative for the average causal effect on the treated, called overlap weighted average treatment effect on the treated (OWATT). The appeal of our proposed method lies in its ability to obtain similar or even better results than trimming and truncation while relaxing the constraint to choose a priori a threshold (or even specify a smoothing parameter). The performance of the proposed method is illustrated via a series of Monte Carlo simulations and a data analysis on racial disparities in health care expenditures. Copyright © 2023, The Authors. All rights reserved.

关键词： Trimming

Propensity score weighting under limited overlap and model misspecification

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arXiv 2020年

作者： Zhou, Yunji Matsouaka, Roland A. Thomas, Laine Department of Biostatistics and Bioinformatics Duke Global Health Institute Duke University DurhamNC United States Department of Biostatistics and Bioinformatics & Program for Comparative Effectiveness Methodology Duke Clinical Research Institute Duke University DurhamNC United States

Propensity score (PS) weighting methods are often used in non-randomized studies to adjust for confounding and assess treatment effects. The most popular among them, the inverse probability weighting (IPW), assigns weights that are proportional to the inverse of the conditional probability of a specific treatment assignment, given observed covariates. A key requirement for IPW estimation is the positivity assumption, i.e., the PS must be bounded away from 0 and 1. In practice, violations of the positivity assumption often manifest by the presence of limited overlap in the PS distributions between treatment groups. When these practical violations occur, a small number of highly influential IPW weights may lead to unstable IPW estimators, with biased estimates and large variances. To mitigate these issues, a number of alternative methods have been proposed, including IPW trimming, overlap weights (OW), matching weights (MW), and entropy weights (EW). Because OW, MW, and EW target the population for whom there is equipoise (and with adequate overlap) and their estimands depend on the true PS, a common criticism is that these estimators may be more sensitive to misspecifications of the PS model. In this paper, we conduct extensive simulation studies to compare the performances of IPW and IPW trimming against those of OW, MW, and EW under limited overlap and misspecified propensity score models. Across the wide range of scenarios we considered, OW, MW, and EW consistently outperform IPW in terms of bias, root mean squared error, and coverage probability. Copyright © 2020, The Authors. All rights reserved.

关键词： Trimming

A framework for causal inference in the presence of extreme inverse probability weights: the role of overlap weights

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arXiv 2020年

作者： Matsouaka, Roland A. Zhou, Yunji Department of Biostatistics and Bioinformatics Duke University DurhamNC United States Program for Comparative Effectiveness Methodology Duke Clinical Research Institute DurhamNC United States Duke Global Health Institute Duke University DurhamNC United States

What do we do when violations of the positivity assumption are expected? Several possible solutions exist in the literature. We consider propensity score (PS) methods that are commonly used in observational studies to assess causal treatment effects when the positivity assumption is violated. We focus on and examine four specific alternative solutions to the inverse probability weighting (IPW) trimming and truncation: matching weight (MW), Shannon’s entropy weight (EW), overlap weight (OW) and beta weight (BW) estimators. In this paper, we demonstrate that these estimators target the same population of interest, the population of patients for whom we have sufficient PS overlap, i.e., where lies clinical equipoise. Then, we establish the nexus among the different corresponding weights (and estimators);this allows us to highlight the share properties and theoretical implications of these estimators. Finally, we introduce their augmented estimators that take advantage of estimating both the propensity score and regression models to enhance the treatment effect estimators in terms of bias and efficiency. We also elucidate the role of OW estimator as the flagship of all these methods that target the overlap population. Our analytic results demonstrate that OW, MW, and EW are preferable when there is a moderate or extreme violations of the positivity assumption. We then evaluate, compare, and confirm their finite-sample performance of the aforementioned estimators via Monte Carlo simulations. Finally, we illustrate these methods using two real-world data examples marked by expected violations of the positivity assumption. Copyright © 2020, The Authors. All rights reserved.

关键词： Monte Carlo methods

Robust statistical inference for the matched net benefit and the matched win ratio using prioritized composite endpoints

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arXiv 2020年

作者： Matsouaka, Roland A. Coles, Adrian Lilly Research Laboratories Eli Lilly and Company IndianapolisIN United States Program for Comparative Effectiveness Methodology Duke Clinical Research Institute Duke University DurhamNC United States Department of Biostatistics and Bioinformatics Duke University DurhamNC United States

As alternatives to the time-to-first-event analysis of composite endpoints, the net benefit (NB) and the win ratio (WR)—which assess treatment effects using prioritized component outcomes based on clinical importance— have been proposed. However, statistical inference of NB and WR relies on a large-sample assumptions, which can lead to an invalid test statistic and inadequate, unsatisfactory confidence intervals, especially when the sample size is small or the proportion of wins is near 0 or 1. In this paper, we develop a systematic approach to address these limitations in a paired-sample design. We first introduce a new test statistic under the null hypothesis of no treatment difference. Then, we present the formula to calculate the sample size. Finally, we develop the confidence interval estimations of these two estimators. To estimate the confidence intervals, we use the method of variance estimates recovery (MOVER), that combines two separate individual-proportion confidence intervals into a hybrid interval for the estimand of interest. We assess the performance of the proposed test statistic and MOVER confidence interval estimations through simulation studies. We demonstrate that the MOVER confidence intervals are as good as the large-sample confidence intervals when the sample is large and when the proportions of wins is bounded away from 0 and 1. Moreover, the MOVER intervals outperform their competitors when the sample is small or the proportions are at or near the boundaries 0 and 1. We illustrate the method (and its competitors) using three examples from randomized clinical studies. © 2020, CC0.

关键词： Statistical tests

Regression with a right-censored predictor, using inverse probability weighting methods

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arXiv 2020年

作者： Matsouaka, Roland A. Atem, Folefac D. Department of Biostatistics and Bioinformatics & Program for Comparative Effectiveness Methodology Duke Clinical Research Institute Duke University DurhamNC United States Department of Biostatistics and Data Science University of Texas Health Science Center at Houston HoustonTX United States

In a longitudinal study, measures of key variables might be incomplete or partially recorded due to drop-out, loss to follow-up, or early termination of the study occurring before the advent of the event of interest. In this paper, we focus primarily on the implementation of a regression model with a randomly censored predictor. We examine, particularly, the use of inverse probability weighting methods in a generalized linear model (GLM), when the predictor of interest is right-censored, to adjust for censoring. To improve the performance of the complete-case analysis and prevent selection bias, we consider three different weighting schemes: inverse censoring probability weights, Kaplan-Meier weights, and Cox proportional hazards weights. We use Monte Carlo simulation studies to evaluate and compare the empirical properties of different weighting estimation methods. Finally, we apply these methods to the Framingham Heart Study data as an illustrative example to estimate the relationship between age of onset of a clinically diagnosed cardiovascular event and low-density lipoprotein (LDL) among cigarette smokers. Copyright © 2020, The Authors. All rights reserved.

关键词： Monte Carlo methods