Estimating causal effects from randomized experiments is central to clinical research. Reducing the statistical uncertainty in these analyses is an important objective for statisticians. Registries, prior trials, and health records constitute a growing compendium of historical data on patients under standard-of-care that may be exploitable to this end. However, most methods for historical borrowing achieve reductions in variance by sacrificing strict type-I error rate control. Here, we propose a use of historical data that exploits linear covariate adjustment to improve the efficiency of trial analyses without incurring bias. Specifically, we train a prognostic model on the historical data, then estimate the treatment effect using a linear regression while adjusting for the trial subjects' predicted outcomes (their prognostic scores). We prove that, under certain conditions, this prognostic covariate adjustment procedure attains the minimum variance possible among a large class of estimators. When those conditions are not met, prognostic covariate adjustment is still more efficient than raw covariate adjustment and the gain in efficiency is proportional to a measure of the predictive accuracy of the prognostic model above and beyond the linear relationship with the raw covariates. We demonstrate the approach using simulations and a reanalysis of an Alzheimer's Disease clinical trial and observe meaningful reductions in mean-squared error and the estimated variance. Lastly, we provide a simplified formula for asymptotic variance that enables power calculations that account for these gains. Sample size reductions between 10% and 30% are attainable when using prognostic models that explain a clinically realistic percentage of the outcome variance.
Covariate adjustment and methods of incorporating historical data in randomized clinical trials (RCTs) each provide opportunities to increase trial power. We unite these approaches for the analysis of RCTs with binary outcomes based on the Cochran-Mantel-Haenszel (CMH) test for marginal risk ratio (RR). In PROCOVA-CMH, subjects are stratified on a single prognostic covariate reflective of their predicted outcome on the control treatment (e.g. placebo). This prognostic score is generated based on baseline covariates through a model trained on historical data. We propose two closed-form prospect…
In randomized trials, appropriately adjusting for baseline variables and short-term outcomes can lead to increased precision and reduced sample size. We examine the impact of such adjustment in group sequential designs, i.e., designs with preplanned interim analyses where enrollment may be stopped early for efficacy or futility. We address the following questions: how much precision gain can be obtained by appropriately adjusting for baseline variables and a short-term outcome? How is this precision gain impacted by factors such as the proportion of pipeline participants (those who enrolled bu…
Conditional power calculations are frequently used to guide the decision whether or not to stop a trial for futility or to modify planned sample size. These ignore the information in short-term endpoints and baseline covariates, and thereby do not make fully efficient use of the information in the data. We therefore propose an interim decision procedure based on the conditional power approach which exploits the information contained in baseline covariates and short-term outcomes. We will realise this by considering the estimation of the treatment effect at the interim analysis as a missing dat…
The amount of data collected from patients involved in clinical trials is continuously growing. All patient characteristics are potential covariates that could be used to improve clinical trial analysis and power. However, the restricted number of patients in phases I and II studies limits the possible number of covariates included in the analyses. In this paper, we investigate the cost/benefit ratio of including covariates in the analysis of clinical trials. Within this context, we address the long-running question "What is the optimum number of covariates to include in a clinical trial?" To …
Covariate adjustment has the potential to increase power in the analysis of randomised trials, but mis-specification of the adjustment model could cause error. We explore what error is possible when the adjustment model omits a covariate by randomised treatment interaction, in a setting where the covariate is perfectly balanced between randomised treatments. We use mathematical arguments and analyses of single hypothetical data sets. We show that analysis by a generalised linear model with the canonical link function leads to no error under the null -- that is, if treatment effect is truly zer…
The purpose of this work is to improve the efficiency in estimating the average causal effect (ACE) on the survival scale where right-censoring exists and high-dimensional covariate information is available. We propose new estimators using regularized survival regression and survival random forests (SRF) to make the adjustment for the high dimensional covariates to improve efficiency. We study the behavior of the adjusted estimator under mild assumptions and show theoretical guarantees that the proposed estimators are more efficient than the unadjusted ones asymptotically when using SRF for ad…
Cluster-randomized trials (CRTs) involve randomizing entire groups of participants -- called clusters -- to treatment arms but are often comprised of a limited or fixed number of available clusters. While covariate adjustment can account for chance imbalances between treatment arms and increase statistical efficiency in individually-randomized trials, analytical methods for individual-level covariate adjustment in small CRTs have received little attention to date. In this paper, we systematically investigate, through extensive simulations, the operating characteristics of propensity score weig…
Background: It has long been advised to account for baseline covariates in the analysis of confirmatory randomised trials, with the main statistical justifications being that this increases power and, when a randomisation scheme balanced covariates, permits a valid estimate of experimental error. There are various methods available to account for covariates but it is not clear how to choose among them. Methods: Taking the perspective of writing a statistical analysis plan, we consider how to choose between the three most promising broad approaches: direct adjustment, standardisation and invers…
MEC-Cox: Machine-Learning-Assisted Generalized Entropy Calibration for ATT Marginal Hazard-Ratio Estimation
Department of Statistics, Texas A&M University（统计学系，德克萨斯A&M大学）；Department of Mathematics, Korea Military Academy（数学系，韩国军事学院）；Department of Statistics, Iowa State University（统计学系，爱荷华州立大学）
Chance imbalance in baseline characteristics is common in randomized clinical trials. Regression adjustment such as the analysis of covariance (ANCOVA) is often used to account for imbalance and increase precision of the treatment effect estimate. An objective alternative is through inverse probability weighting (IPW) of the propensity scores. Although IPW and ANCOVA are asymptotically equivalent, the former may demonstrate inferior performance in finite samples. In this article, we point out that IPW is a special case of the general class of balancing weights, and advocate to use overlap weig…
Improving the efficiency of infectious disease prevention trials using negative control outcome event times
University of Washington（华盛顿大学）；Fred Hutchinson Cancer Center（弗雷德·哈钦森癌症中心）；Penn State University（宾夕法尼亚州立大学）；Gillings School of Global Public Health, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校吉林斯全球公共卫生学院）
Background: Subgroup analyses are frequently conducted in randomized clinical trials to assess evidence of heterogeneous treatment effect across patient subpopulations. Although randomization balances covariates within subgroups in expectation, chance imbalance may be amplified in small subgroups and harm the precision. Covariate adjustment in overall analysis of RCT is often conducted, via either ANCOVA or propensity score weighting, but for subgroup analysis has been rarely discussed. In this article, we develop propensity score weighting methodology for covariate adjustment to improve the p…
Historical data about disease outcomes can be integrated into the analysis of clinical trials in many ways. We build on existing literature that uses prognostic scores from a predictive model to increase the efficiency of treatment effect estimates via covariate adjustment. Here we go further, utilizing a Bayesian framework that combines prognostic covariate adjustment with an empirical prior distribution learned from the predictive performances of the prognostic model on past trials. The Bayesian approach interpolates between prognostic covariate adjustment with strict type I error control wh…
Observing the unobserved confounding through its effects: toward randomized trial-like estimates from real-world survival data
Operations Research Center, Massachusetts Institute of Technology（麻省理工学院运营研究中心）；Sloan School of Management, Massachusetts Institute of Technology（麻省理工学院斯隆管理学院）；Department of Surgery, Memorial Sloan Kettering Cancer Center（纪念斯隆凯特琳癌症中心外科部）；Charité-Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt-Universität zu Berlin（柏林夏里特医学院，柏林自由大学和洪堡大学联合成员）
Valid estimation of treatment effects from observational data requires proper control of confounding. If the number of covariates is large relative to the number of observations, then controlling for all available covariates is infeasible. In cases where a sparsity condition holds, variable selection or penalization can reduce the dimension of the covariate space in a manner that allows for valid estimation of treatment effects. In this article, we propose matching on both the estimated propensity score and the estimated prognostic scores when the number of covariates is large relative to the …
When a novel treatment has successfully passed phase I, different options to design subsequent phase II trials are available. One approach is a single-arm trial, comparing the response rate in the intervention group against a fixed proportion. Another alternative is to conduct a randomized phase II trial, comparing the new treatment with placebo or the current standard. A significant problem arises in both approaches when the investigated patient population is very heterogeneous regarding prognostic factors. For the situation that a substantial dataset of historical controls exists, we propose…
Much evidence in comparative effectiveness research is based on observational studies. Researchers who conduct observational studies typically assume that there are no unobservable differences between the treated and control groups. Treatment effects are estimated after adjusting for observed differences between treated and controls. However, treatment effect estimates may be biased due to model misspecification. That is, if the method of treatment effect estimation imposes unduly strong functional form assumptions, treatment effect estimates may be significantly biased. In this study, we comp…
Some patients benefit from a treatment while others may do so less or do not benefit at all. We have previously developed a two-stage network meta-regression prediction model that synthesized randomized trials and evaluates how treatment effects vary across patient characteristics. In this article, we extended this model to combine different sources of types in different formats: aggregate data (AD) and individual participant data (IPD) from randomized and non-randomized evidence. In the first stage, a prognostic model is developed to predict the baseline risk of the outcome using a large coho…
In cluster randomized trials, patients are typically recruited after clusters are randomized, and the recruiters and patients may not be blinded to the assignment. This often leads to differential recruitment and consequently systematic differences in baseline characteristics of the recruited patients between intervention and control arms, inducing post-randomization selection bias. We rigorously define causal estimands in the presence of selection bias. We elucidate the conditions under which standard covariate adjustment methods can validly estimate these estimands. We further discuss the ad…
We aim to generalize the results of a randomized controlled trial (RCT) to a target population with the help of some observational data. This is a problem of causal effect identification with multiple data sources. Challenges arise when the RCT is conducted in a context that differs from the target population. Earlier research has focused on cases where the estimates from the RCT can be adjusted by observational data in order to remove the selection bias and other domain specific differences. We consider examples where the experimental findings cannot be generalized by an adjustment and show t…
The estimation of heterogeneous treatment effects (HTEs) has attracted considerable interest in many disciplines, most prominently in medicine and economics. Contemporary research has so far primarily focused on continuous and binary responses where HTEs are traditionally estimated by a linear model, which allows the estimation of constant or heterogeneous effects even under certain model misspecifications. More complex models for survival, count, or ordinal outcomes require stricter assumptions to reliably estimate the treatment effect. Most importantly, the noncollapsibility issue necessitat…
To improve precision of estimation and power of testing hypothesis for an unconditional treatment effect in randomized clinical trials with binary outcomes, researchers and regulatory agencies recommend using g-computation as a reliable method of covariate adjustment. However, the practical application of g-computation is hindered by the lack of an explicit robust variance formula that can be used for different unconditional treatment effects of interest. To fill this gap, we provide explicit and robust variance estimators for g-computation estimators and demonstrate through simulations that t…
Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand this phenomenon, we develop a unified comparison of the asymptotic variance of a class of linear regression-adjusted estimators. Our analysis is based on the classical theory for linear regression with heteroscedastic errors and thus does not assume that the postulated linear model is correct. For a completely randomized binary treatment, we provide sufficient …
Treatment effect heterogeneity occurs when individual characteristics influence the effect of a treatment. We propose a novel approach that combines prognostic score matching and conditional inference trees to characterize effect heterogeneity of a randomized binary treatment. One key feature that distinguishes our method from alternative approaches is that it controls the Type I error rate, i.e., the probability of identifying effect heterogeneity if none exists and retains the underlying subgroups. This feature makes our technique particularly appealing in the context of clinical trials, whe…
Calibrated Transfer Learning for Survival Prediction and Treatment Inference
University of Louisville（路易斯维尔大学）；University of Louisville School of Medicine（路易斯维尔大学医学院）；Louisville Clinical and Translational Research Center, University of Louisville（路易斯维尔大学路易维尔临床转化研究中心）；Takeda Pharmaceuticals（武田制药）；Bristol Myers Squibb（百时美施贵宝）
Estimating Causal Treatment Effects in Placebo-Controlled Randomized Clinical Trials When High Placebo Response is Anticipated
Smith Center for Outcomes Research in Cardiology, Beth Israel Deaconess Medical Center（贝斯以色列女医生医疗中心心脏结局研究史密斯中心）；Department of Statistics, SungKyunKwan University（成均馆大学统计系）；Biostatistics Department, Boston University（波士顿大学生物统计学系）
Background: Randomized controlled trials are often used to inform policy and practice for broad populations. The average treatment effect (ATE) for a target population, however, may be different from the ATE observed in a trial if there are effect modifiers whose distribution in the target population is different that from that in the trial. Methods exist to use trial data to estimate the target population ATE, provided the distributions of treatment effect modifiers are observed in both the trial and target population -- an assumption that may not hold in practice. Methods: The proposed sensi…
