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Register a new userEstimating the Efficiency Gain of Covariate-Adjusted Analyses in Future Clinical Trials Using External Data
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Xiudi Li
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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We present a general framework for using existing data to estimate the efficiency gain from using a covariate-adjusted estimator of a marginal treatment effect in a future randomized trial. We describe conditions under which it is possible to define a mapping from the distribution that generated the existing external data to the relative efficiency of a covariate-adjusted estimator compared to an unadjusted estimator. Under conditions, these relative efficiencies approximate the ratio of sample size needed to achieve a desired power. We consider two situations where the outcome is either fully or partially observed and several treatment effect estimands that are of particular interest in most trials. For each such estimand, we develop a semiparametrically efficient estimator of the relative efficiency that allows for the application of flexible statistical learning tools to estimate the nuisance functions and an analytic form of a corresponding Wald-type confidence interval. We also propose a double bootstrap scheme for constructing confidence intervals. We demonstrate the performance of the proposed methods through simulation studies and apply these methods to data to estimate the relative efficiency of using covariate adjustment in Covid-19 therapeutic trials.
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In randomized clinical trials, adjustments for baseline covariates at both design and analysis stages are highly encouraged by regulatory agencies. A recent trend is to use a model-assisted approach for covariate adjustment to gain credibility and efficiency while producing asymptotically valid inference even when the model is incorrect. In this article we present three considerations for better practice when model-assisted inference is applied to adjust for covariates under simple or covariate-adaptive randomized trials: (1) guaranteed efficiency gain: a model-assisted method should often gain but never hurt efficiency; (2) wide applicability: a valid procedure should be applicable, and preferably universally applicable, to all commonly used randomization schemes; (3) robust standard error: variance estimation should be robust to model misspecification and heteroscedasticity. To achieve these, we recommend a model-assisted estimator under an analysis of heterogeneous covariance working model including all covariates utilized in randomization. Our conclusions are based on an asymptotic theory that provides a clear picture of how covariate-adaptive randomization and regression adjustment alter statistical efficiency. Our theory is more general than the existing ones in terms of studying arbitrary functions of response means (including linear contrasts, ratios, and odds ratios), multiple arms, guaranteed efficiency gain, optimality, and universal applicability.
Two-stage least squares (TSLS) estimators and variants thereof are widely used to infer the effect of an exposure on an outcome using instrumental variables (IVs). They belong to a wider class of two-stage IV estimators, which are based on fitting a conditional mean model for the exposure, and then using the fitted exposure values along with the covariates as predictors in a linear model for the outcome. We show that standard TSLS estimators enjoy greater robustness to model misspecification than more general two-stage estimators. However, by potentially using a wrong exposure model, e.g. when the exposure is binary, they tend to be inefficient. In view of this, we study double-robust G-estimators instead. These use working models for the exposure, IV and outcome but only require correct specification of either the IV model or the outcome model to guarantee consistent estimation of the exposure effect. As the finite sample performance of the locally efficient G-estimator can be poor, we further develop G-estimation procedures with improved efficiency and robustness properties under misspecification of some or all working models. Simulation studies and a data analysis demonstrate drastic improvements, with remarkably good performance even when one or more working models are misspecified.
Most clinical trials involve the comparison of a new treatment to a control arm (e.g., the standard of care) and the estimation of a treatment effect. External data, including historical clinical trial data and real-world observational data, are commonly available for the control arm. Borrowing information from external data holds the promise of improving the estimation of relevant parameters and increasing the power of detecting a treatment effect if it exists. In this paper, we propose to use Bayesian additive regression trees (BART) for incorporating external data into the analysis of clinical trials, with a specific goal of estimating the conditional or population average treatment effect. BART naturally adjusts for patient-level covariates and captures potentially heterogeneous treatment effects across different data sources, achieving flexible borrowing. Simulation studies demonstrate that BART compares favorably to a hierarchical linear model and a normal-normal hierarchical model. We illustrate the proposed method with an acupuncture trial.
Covariate adjustment is an important tool in the analysis of randomized clinical trials and observational studies. It can be used to increase efficiency and thus power, and to reduce possible bias. While most statistical tests in randomized clinical trials are nonparametric in nature, approaches for covariate adjustment typically rely on specific regression models, such as the linear model for a continuous outcome, the logistic regression model for a dichotomous outcome and the Cox model for survival time. Several recent efforts have focused on model-free covariate adjustment. This paper makes use of the empirical likelihood method and proposes a nonparametric approach to covariate adjustment. A major advantage of the new approach is that it automatically utilizes covariate information in an optimal way without fitting nonparametric regression. The usual asymptotic properties, including the Wilks-type result of convergence to a chi-square distribution for the empirical likelihood ratio based test, and asymptotic normality for the corresponding maximum empirical likelihood estimator, are established. It is also shown that the resulting test is asymptotically most powerful and that the estimator for the treatment effect achieves the semiparametric efficiency bound. The new method is applied to the Global Use of Strategies to Open Occluded Coronary Arteries (GUSTO)-I trial. Extensive simulations are conducted, validating the theoretical findings.
Detection of interactions between treatment effects and patient descriptors in clinical trials is critical for optimizing the drug development process. The increasing volume of data accumulated in clinical trials provides a unique opportunity to discover new biomarkers and further the goal of personalized medicine, but it also requires innovative robust biomarker detection methods capable of detecting non-linear, and sometimes weak, signals. We propose a set of novel univariate statistical tests, based on the theory of random walks, which are able to capture non-linear and non-monotonic covariate-treatment interactions. We also propose a novel combined test, which leverages the power of all of our proposed univariate tests into a single general-case tool. We present results for both synthetic trials as well as real-world clinical trials, where we compare our method with state-of-the-art techniques and demonstrate the utility and robustness of our approach.
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