Robust Alternatives to ANCOVA for Estimating the Treatment Effect via a Randomized Comparative Study

Jiang, Fei; Tian, Lu; Fu, Haoda; Hasegawa, Takahiro; Wei, Lee‐Jen

doi:10.1080/01621459.2018.1527226

Cited by 22 publications

(30 citation statements)

References 35 publications

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“…The above results build on key ideas from Tsiatis et al (); Rubin and van der Laan (); Moore and van der Laan (); Moore et al (); Rubin and van der Laan (); Jiang et al (); Tian et al (). As in their work, our results are asymptotic, that is, they hold in the limit as sample size grows to infinity while the set of covariates is fixed.…”

Section: Introductionsupporting

confidence: 78%

“…Specifically, we prove in the Supporting Information that each term in Equation equals 4 times the corresponding term in Equation , i.e.,

V a r^{*} ({\overset{true^}{normalΔ}}^{normalu normaln normala normald normalj}) = 4 V a r (Y - {\underset{β}{true}}_{A} A), V a r^{*} ({\underset{β}{true}}_{bold-italicW}^{t} I) = 4 V a r ({\underset{β}{true}}_{bold-italicW}^{t} W)

, and

V a r^{*} ({\overset{true^}{normalΔ}}^{normala normaln normalc normalo normalv normala}) = 4 V a r (Y - {\underset{β}{true}}_{A} A - {\underset{β}{true}}_{bold-italicW}^{t} W)

. This is summarized in Figure , where the first row is the variance decomposition in OLS, the second row is the variance decomposition of

{\overset{true^}{normalΔ}}^{normalu normaln normala normald normalj}

from Jiang et al (), and our contribution is to connect them by proving equality of quantities in the same column. When model () is misspecified, all equalities in Figure still hold.…”

Section: Ry−normalδa~bold-italicw2 and The Relationship Among Unadjusmentioning

confidence: 96%

“…Jiang et al () proved the following relationship among the unadjusted estimator

{\overset{true^}{normalΔ}}^{normalu normaln normala normald normalj}

, ANCOVA estimator

{\overset{true^}{normalΔ}}^{normala normaln normalc normalo normalv normala}

, and chance imbalance

bold-italicI

{\overset{Δ}{true}}^{u n a d j} \approx {\underset{β}{true}}_{bold-italicW}^{t} I + {\overset{Δ}{true}}^{a n c o v a} .

(Formally, the difference between the left and right sides of the above display, after multiplying by

n^{1 ∕ 2}

, converges to

0

in probability.) They also showed the following variance decomposition:

V a r^{*} ({\overset{true^}{normalΔ}}^{normalu normaln normala normald normalj}) = V a r^{*} ({\underset{β}{true}}_{bold-italicW}^{t} I) + V a r^{*} ({\overset{true^}{normalΔ}}^{normala normaln normalc normalo normalv normala}),

where

V a r^{*}

denotes asymptotic (i.e., large sample) variance.…”

Section: Ry−normalδa~bold-italicw2 and The Relationship Among Unadjusmentioning

confidence: 99%

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Analysis of Covariance in Randomized Trials: More Precision and Valid Confidence Intervals, Without Model Assumptions

2019

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Covariate adjustment" in the randomized trial context refers to an estimator of the average treatment effect that adjusts for chance imbalances between study arms in baseline variables (called "covariates"). The baseline variables could include, for example, age, sex, disease severity, and biomarkers. According to two surveys of clinical trial reports, there is confusion about the statistical properties of covariate adjustment. We focus on the analysis of covariance (ANCOVA) estimator, which involves fitting a linear model for the outcome given the treatment arm and baseline variables, and trials that use simple randomization with equal probability of assignment to treatment and control.We prove the following new (to the best of our knowledge) robustness property of ANCOVA to arbitrary model misspecification: Not only is the ANCOVA point estimate consistent (as proved by Yang and Tsiatis, 2001) but so is its standard error. This implies that confidence intervals and hypothesis tests conducted as if the linear model were correct are still asymptotically valid even when the linear model is arbitrarily misspecified, for example, when the baseline variables are nonlinearly related to the outcome or there is treatment effect heterogeneity. We also give a simple, robust formula for the variance reduction (equivalently, sample size reduction) from using ANCOVA. By reanalyzing completed randomized trials for mild cognitive impairment, schizophrenia, and depression, we demonstrate how ANCOVA can achieve variance reductions of 4 to 32%. K E Y W O R D Simbalance, relative efficiency, robustness

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Section: Introductionsupporting

confidence: 78%

“…Specifically, we prove in the Supporting Information that each term in Equation equals 4 times the corresponding term in Equation , i.e.,

V a r^{*} ({\overset{true^}{normalΔ}}^{normalu normaln normala normald normalj}) = 4 V a r (Y - {\underset{β}{true}}_{A} A), V a r^{*} ({\underset{β}{true}}_{bold-italicW}^{t} I) = 4 V a r ({\underset{β}{true}}_{bold-italicW}^{t} W)

, and

V a r^{*} ({\overset{true^}{normalΔ}}^{normala normaln normalc normalo normalv normala}) = 4 V a r (Y - {\underset{β}{true}}_{A} A - {\underset{β}{true}}_{bold-italicW}^{t} W)

. This is summarized in Figure , where the first row is the variance decomposition in OLS, the second row is the variance decomposition of

{\overset{true^}{normalΔ}}^{normalu normaln normala normald normalj}

from Jiang et al (), and our contribution is to connect them by proving equality of quantities in the same column. When model () is misspecified, all equalities in Figure still hold.…”

Section: Ry−normalδa~bold-italicw2 and The Relationship Among Unadjusmentioning

confidence: 96%

“…Jiang et al () proved the following relationship among the unadjusted estimator

{\overset{true^}{normalΔ}}^{normalu normaln normala normald normalj}

, ANCOVA estimator

{\overset{true^}{normalΔ}}^{normala normaln normalc normalo normalv normala}

, and chance imbalance

bold-italicI

{\overset{Δ}{true}}^{u n a d j} \approx {\underset{β}{true}}_{bold-italicW}^{t} I + {\overset{Δ}{true}}^{a n c o v a} .

(Formally, the difference between the left and right sides of the above display, after multiplying by

n^{1 ∕ 2}

, converges to

0

in probability.) They also showed the following variance decomposition:

V a r^{*} ({\overset{true^}{normalΔ}}^{normalu normaln normala normald normalj}) = V a r^{*} ({\underset{β}{true}}_{bold-italicW}^{t} I) + V a r^{*} ({\overset{true^}{normalΔ}}^{normala normaln normalc normalo normalv normala}),

where

V a r^{*}

denotes asymptotic (i.e., large sample) variance.…”

Section: Ry−normalδa~bold-italicw2 and The Relationship Among Unadjusmentioning

confidence: 99%

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Analysis of Covariance in Randomized Trials: More Precision and Valid Confidence Intervals, Without Model Assumptions

2019

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“…It is interesting to extend the discussion to covariate adjustment in more complicated settings, such as high dimensional covariates (Bloniarz et al, 2016;Wager et al, 2016;Lei and Ding, 2018), logistic regression for binary outcomes Freedman, 2008d;Moore and van der Laan, 2009;Moore et al, 2011) and adjustment using machine learning methods (Bloniarz et al, 2016;Wager et al, 2016;Wu and Gagnon-Bartsch, 2018). It is also important to consider covariate adjustment for general non-linear estimands Jiang et al, 2019;Tian et al, 2019) and general designs (Middleton, 2018), such as blocking (Miratrix et al, 2013;Bugni et al, 2018), matched pairs (Fogarty, 2018), and factorial designs (Lu, 2016).…”

Section: Discussionmentioning

confidence: 99%

Rerandomization and Regression Adjustment

Ding

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Randomization is a basis for the statistical inference of treatment effects without strong assumptions on the outcome‐generating process. Appropriately using covariates further yields more precise estimators in randomized experiments. R. A. Fisher suggested blocking on discrete covariates in the design stage or conducting analysis of covariance in the analysis stage. We can embed blocking in a wider class of experimental design called rerandomization, and extend the classical analysis of covariance to more general regression adjustment. Rerandomization trumps complete randomization in the design stage, and regression adjustment trumps the simple difference‐in‐means estimator in the analysis stage. It is then intuitive to use both rerandomization and regression adjustment. Under the randomization inference framework, we establish a unified theory allowing the designer and analyser to have access to different sets of covariates. We find that asymptotically, for any given estimator with or without regression adjustment, rerandomization never hurts either the sampling precision or the estimated precision, and, for any given design with or without rerandomization, our regression‐adjusted estimator never hurts the estimated precision. Therefore, combining rerandomization and regression adjustment yields better coverage properties and thus improves statistical inference. To quantify these statements theoretically, we discuss optimal regression‐adjusted estimators in terms of the sampling precision and the estimated precision, and then measure the additional gains of the designer and the analyser. We finally suggest the use of rerandomization in the design and regression adjustment in the analysis followed by the Huber–White robust standard error.

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“…Nonparametric approaches can also be applied to CA for odds ratios. One of such approach is based on the joint distribution of the outcome and covariates, hence, is model free . It also has a close connection to the doubly robust estimator.…”

Section: Nonlinear Outcome Modelsmentioning

confidence: 99%

Covariate adjustment for randomized controlled trials revisited

Wang

2019

Pharmaceutical Statistics

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Covariate adjustment for the estimation of treatment effect for randomized controlled trials (RCT) is a simple approach with a long history, hence, its pros and cons have been well-investigated and published in the literature. It is worthwhile to revisit this topic since recently there has been significant investigation and development on model assumptions, robustness to model mis-specification, in particular, regarding the Neyman-Rubin model and the average treatment effect estimand. This paper discusses key results of the investigation and development and their practical implication on pharmaceutical statistics. Accordingly, we recommend that appropriate covariate adjustment should be more widely used for RCTs for both hypothesis testing and estimation. KEYWORDS average treatment effect, covariate adjustment, model misspecification, Neyman-Rubin model Pharmaceutical Statistics. 2019;1-7.wileyonlinelibrary.com/journal/pst

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Robust Alternatives to ANCOVA for Estimating the Treatment Effect via a Randomized Comparative Study

Cited by 22 publications

References 35 publications

Analysis of Covariance in Randomized Trials: More Precision and Valid Confidence Intervals, Without Model Assumptions

Analysis of Covariance in Randomized Trials: More Precision and Valid Confidence Intervals, Without Model Assumptions

Rerandomization and Regression Adjustment

Covariate adjustment for randomized controlled trials revisited

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