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.
In clinical trials, there is potential to improve precision and reduce the required sample size by appropriately adjusting for baseline variables in the statistical analysis. This is called covariate adjustment. Despite recommendations by regulatory agencies in favor of covariate adjustment, it remains underutilized leading to inefficient trials. We address two obstacles that make it challenging to use covariate adjustment. A first obstacle is the incompatibility of many covariate adjusted estimators with commonly used boundaries in group sequential designs (GSDs). A second obstacle is the unc…
There has been a split in the statistics community about the need for taking covariates into account in the design phase of a clinical trial. There are many advocates of using stratification and covariate-adaptive randomization to promote balance on certain known covariates. However, balance does not always promote efficiency or ensure more patients are assigned to the better treatment. We describe these procedures, including model-based procedures, for incorporating covariates into the design of clinical trials, and give examples where balance, efficiency and ethical considerations may be in …
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…
Two commonly used methods for improving precision and power in clinical trials are stratified randomization and covariate adjustment. However, many trials do not fully capitalize on the combined precision gains from these two methods, which can lead to wasted resources in terms of sample size and trial duration. We derive consistency and asymptotic normality of model-robust estimators that combine these two methods, and show that these estimators can lead to substantial gains in precision and power. Our theorems cover a class of estimators that handle continuous, binary, and time-to-event outc…
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 gai…
It is often important to incorporating covariate information in the design of clinical trials. In literature, there are many designs of using stratification and covariate-adaptive randomization to balance on certain known covariate. Recently Zhang, Hu, Cheung and Chan (2007) have proposed a family of covariate-adjusted response-adaptive (CARA) designs and studied their asymptotic properties. However, these CARA designs often have high variabilities. In this paper, we propose a new family of covariate-adjusted response-adaptive (CARA) designs. We show that the new designs have smaller variabili…
Covariate-adjusted win statistics in randomized clinical trials with ordinal outcomes
Shenzhen Technology University（深圳理工大学）；Feinberg School of Medicine, Northwestern University（西北大学费恩伯格医学院）；University of Wisconsin - Madison（威斯康星大学麦迪逊分校）；Yale University School of Public Health（耶鲁大学公共卫生学院）；Yale Center for Analytical Sciences, Yale University School of Public Health（耶鲁大学公共卫生学院分析科学中心）；University of Washington（华盛顿大学）；Clinical Learning, Evidence, and Research (CLEAR) Center, University of Washington（华盛顿大学临床学习、证据与研究（CLEAR）中心）；Section of Cardiovascular Medicine, Department of Internal Medicine, Yale School of Medicine（耶鲁医学院内科学系心血管医学部）；Cardiovascular Medicine Analytics Center, Yale School of Medicine（耶鲁医学院心血管医学分析中心）；Center for Methods in Implementation and Prevention Science, Yale School of Public Health（耶鲁大学公共卫生学院实施与预防科学方法中心）
Nonparametric covariate adjustment is considered for log-rank type tests of treatment effect with right-censored time-to-event data from clinical trials applying covariate-adaptive randomization. Our proposed covariate-adjusted log-rank test has a simple explicit formula and a guaranteed efficiency gain over the unadjusted test. We also show that our proposed test achieves universal applicability in the sense that the same formula of test can be universally applied to simple randomization and all commonly used covariate-adaptive randomization schemes such as the stratified permuted block and P…
On a penalised likelihood approach for joint modelling of longitudinal covariates and partly interval-censored data -- an application to the Anti-PD1 brain collaboration trial
Response-adaptive designs have been extensively studied and used in clinical trials. However, there is a lack of a comprehensive study of response-adaptive designs that include covariates, despite their importance in clinical experiments. Because the allocation scheme and the estimation of parameters are affected by both the responses and the covariates, covariate-adjusted response-adaptive (CARA) designs are very complex to formulate. In this paper, we overcome the technical hurdles and lay out a framework for general CARA designs for the allocation of subjects to $K (\geq 2)$ treatments. The…
The analysis of randomized trials with time-to-event endpoints is nearly always plagued by the problem of censoring. As the censoring mechanism is usually unknown, analyses typically employ the assumption of non-informative censoring. While this assumption usually becomes more plausible as more baseline covariates are being adjusted for, such adjustment also raises concerns. Pre-specification of which covariates will be adjusted for (and how) is difficult, thus prompting the use of data-driven variable selection procedures, which may impede valid inferences to be drawn. The adjustment for cova…
In two harmonized efficacy studies to prevent HIV infection through multiple infusions of the monoclonal antibody VRC01, a key objective is to evaluate whether the serum concentration of VRC01, which changes cyclically over time along with the infusion schedule, is associated with the rate of HIV infection. Simulation studies are needed in the development of such survival models. In this paper, we consider simulating event time data with a continuous time-varying covariate whose values vary with time through multiple drug administration cycles, and whose effect on survival changes differently …
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 covari…
The present paper deals with the problem of allocating patients to two competing treatments in the presence of covariates or prognostic factors in order to achieve a good trade-off among ethical concerns, inferential precision and randomness in the treatment allocations. In particular we suggest a multipurpose design methodology that combines efficiency and ethical gain when the linear homoscedastic model with both treatment/covariate interactions and interactions among covariates is adopted. The ensuing compound optimal allocations of the treatments depend on the covariates and their distribu…
Combining patient-level data from clinical trials can connect rare phenomena with clinical endpoints, but statistical techniques applied to a single trial may become problematical when trials are pooled. Estimating the hazard of a binary variable unevenly distributed across trials showcases a common pooled database issue. We studied how an unevenly distributed binary variable can compromise the integrity of fixed and random effects Cox proportional hazards models. We compared fixed effect and random effects Cox proportional hazards models on a set of simulated datasets inspired by a 17-trial p…
Understanding the factors that explain differences in survival times is an important issue for establishing policies to improve national health systems. Motivated by breast cancer data arising from the Surveillance Epidemiology and End Results program, we propose a covariate-adjusted proportional hazards frailty model for the analysis of clustered right-censored data. Rather than incorporating exchangeable frailties in the linear predictor of commonly-used survival models, we allow the frailty distribution to flexibly change with both continuous and categorical cluster-level covariates and mod…
A recent method using Dynamic Linear Models to improve preferred treatment allocation budget in random allocation models was proposed by Lee, Boone, et al (2020). However this model failed to include the impact covariates such as smoking, gender, etc, had on model performance. The current paper addresses random allocation to treatments using the DLM in Bayesian Adaptive Allocation Models with a single covariate. We show a reduced treatment allocation budget along with a reduced time to locate preferred treatment. Furthermore, a sensitivity analysis is performed on mean and variance parameters …
The rapid finding of effective therapeutics requires the efficient use of available resources in clinical trials. The use of covariate adjustment can yield statistical estimates with improved precision, resulting in a reduction in the number of participants required to draw futility or efficacy conclusions. We focus on time-to-event and ordinal outcomes. A key question for covariate adjustment in randomized studies is how to fit a model relating the outcome and the baseline covariates to maximize precision. We present a novel theoretical result establishing conditions for asymptotic normality …
Bias reduction in g-computation for covariate adjustment in randomized clinical trials
Data Sciences and Analytics, Pfizer Inc.（辉瑞公司数据科学与分析部）；Institute of Natural Sciences, MOE–LSC, School of Mathematical Sciences, CMA–Shanghai, and SJTU–Yale Joint Center for Biostatistics and Data Science, Shanghai Jiao Tong University（上海交通大学数学科学学院自然科学与工程教育部重点实验室、上海中心数学与应用数学研究所及上海交大-耶鲁生物统计与数据科学联合中心）；Division of Biostatistics and Health Data Science, University of Minnesota Twin Cities（明尼苏达大学双城分校生物统计与健康数据科学系）
A robust score test in g-computation for covariate adjustment in randomized clinical trials leveraging different variance estimators via influence functions
Data Sciences and Analytics, Pfizer Inc（辉瑞公司数据科学与分析部）；Division of Biostatistics and Health Data Science, University of Minnesota（明尼苏达大学生物统计学与健康数据科学系）；Institute of Natural Sciences, MOE-LSC, School of Mathematical Sciences, CMA-Shanghai, and SJTU-Yale Joint Center for Biostatistics and Data Science, Shanghai Jiao Tong University（上海交通大学自然科学研究院、教育部拉曼森数学中心、数学科学学院、上海数学中心及上交-耶鲁生物统计与数据科学联合中心）
We propose a novel adaptive design for clinical trials with time-to-event outcomes and covariates (which may consist of or include biomarkers). Our method is based on the expected entropy of the posterior distribution of a proportional hazards model. The expected entropy is evaluated as a function of a patient's covariates, and the information gained due to a patient is defined as the decrease in the corresponding entropy. Candidate patients are only recruited onto the trial if they are likely to provide sufficient information. Patients with covariates that are deemed uninformative are filtere…
To maximize clinical benefit, clinicians routinely tailor treatment to the individual characteristics of each patient, where individualized treatment rules are needed and are of significant research interest to statisticians. 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 th…
Differences between biological networks corresponding to disease conditions can help delineate the underlying disease mechanisms. Existing methods for differential network analysis do not account for dependence of networks on covariates. As a result, these approaches may detect spurious differential connections induced by the effect of the covariates on both the disease condition and the network. To address this issue, we propose a general covariate-adjusted test for differential network analysis. Our method assesses differential network connectivity by testing the null hypothesis that the net…
We consider the problem of identifying sub-groups of participants in a clinical trial that have enhanced treatment effect. Recursive partitioning methods that recursively partition the covariate space based on some measure of between groups treatment effect difference are popular for such sub-group identification. The most commonly used recursive partitioning method, the classification and regression tree algorithm, first creates a large tree by recursively partitioning the covariate space using some splitting criteria and then selects the final tree from all subtrees of the large tree. In the…
Enhancing Longitudinal Clinical Trial Efficiency with Digital Twins and Prognostic Covariate-Adjusted Mixed Models for Repeated Measures (PROCOVA-MMRM)
We study the design of multi-armed parallel group clinical trials to estimate personalized treatment rules that identify the best treatment for a given patient with given covariates. Assuming that the outcomes in each treatment arm are given by a homoscedastic linear model, with possibly different variances between treatment arms, and that the trial subjects form a random sample from an unselected overall population, we optimize the (possibly randomized) treatment allocation allowing the allocation rates to depend on the covariates. We find that, for the case of two treatments, the approximate…
In this paper we propose a general class of covariate-adjusted response-adaptive (CARA) designs based on a new functional urn model. We prove strong consistency concerning the functional urn proportion and the proportion of subjects assigned to the treatment groups, in the whole study and for each covariate profile, allowing the distribution of the responses conditioned on covariates to be estimated nonparametrically. In addition, we establish joint central limit theorems for the above quantities and the sufficient statistics of features of interest, which allow to construct procedures to make…
Accurate diagnosis of disease is of fundamental importance in clinical practice and medical research. Before a medical diagnostic test is routinely used in practice, its ability to distinguish between diseased and nondiseased states must be rigorously assessed through statistical analysis. The receiver operating characteristic (ROC) curve is the most popular used tool for evaluating the discriminatory ability of continuous-outcome diagnostic tests. It has been acknowledged that several factors (e.g., subject-specific characteristics, such as age and/or gender) can affect the test's accuracy be…
In this paper, we present three estimators of the ROC curve when missing observations arise among the biomarkers. Two of the procedures assume that we have covariates that allow to estimate the propensity and the estimators are obtained using an inverse probability weighting method or a smoothed version of it. The other one assumes that the covariates are related to the biomarkers through a regression model which enables us to construct convolution--based estimators of the distribution and quantile functions. Consistency results are obtained under mild conditions. Through a numerical study we …
We present an objective Bayes method for covariance selection in Gaussian multivariate regression models whose error term has a covariance structure which is Markov with respect to a Directed Acyclic Graph (DAG). The scope is covariate-adjusted sparse graphical model selection, a topic of growing importance especially in the area of genetical genomics (eQTL analysis). Specifically, we provide a closed-form expression for the marginal likelihood of any DAG (with small parent sets) whose computation virtually requires no subjective elicitation by the user and involves only conjugate matrix norma…
