In this paper we consider the estimation of population size from one-source capture--recapture data, that is, a list in which individuals can potentially be found repeatedly and where the question is how many individuals are missed by the list. As a typical example, we provide data from a drug user study in Bangkok from 2001 where the list consists of drug users who repeatedly contact treatment institutions. Drug users with 1, 2, 3$,...$ contacts occur, but drug users with zero contacts are not present, requiring the size of this group to be estimated. Statistically, these data can be considered as stemming from a zero-truncated count distribution. We revisit an estimator for the population size suggested by Zelterman that is known to be robust under potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a locally truncated Poisson likelihood which is equivalent to a binomial likelihood. This result allows the extension of the Zelterman estimator by means of logistic regression to include observed heterogeneity in the form of covariates. We also review an estimator proposed by Chao and explain why we are not able to obtain similar results for this estimator. The Zelterman estimator is applied in two case studies, the first a drug user study from Bangkok, the second an illegal immigrant study in the Netherlands. Our results suggest the new estimator should be used, in particular, if substantial unobserved heterogeneity is present.
When estimating a Global Average Treatment Effect (GATE) under network interference, units can have widely different relationships to the treatment depending on a combination of the structure of their network neighborhood, the structure of the interference mechanism, and how the treatment was distributed in their neighborhood. In this work, we introduce a sequential procedure to generate and select graph- and treatment-based covariates for GATE estimation under regression adjustment. We show that it is possible to simultaneously achieve low bias and considerably reduce variance with such a pro…
We consider inference for the mean and covariance functions of covariate adjusted functional data using Local Linear Kernel (LLK) estimators. By means of a double asymptotic, we differentiate between sparse and dense covariate adjusted functional data - depending on the relative order of m (the discretization points per function) and n (the number of functions). Our simulation results demonstrate that the existing asymptotic normality results can lead to severely misleading inferences in finite samples. We explain this phenomenon based on our theoretical results and propose finite-sample corre…
Continuous biomarkers are common for disease screening and diagnosis. To reach a dichotomous clinical decision, a threshold would be imposed to distinguish subjects with disease from non-diseased individuals. Among various performance metrics for a continuous biomarker, specificity at a controlled sensitivity level (or vice versa) is often desirable for clinical utility since it directly targets where the clinical test is intended to operate. Covariates, such as age, race, and sample collection, could impact the controlled sensitivity level in subpopulations and may also confound the associati…
The Welch-Satterthwaite t-test is one of the most prominent and often used statistical inference method in applications. The method is, however, not flexible with respect to adjustments for baseline values or other covariates, which may impact the response variable. Existing analysis of covariance methods are typically based on the assumption of equal variances across the groups. This assumption is hard to justify in real data applications and the methods tend to not control the type-1 error rate satisfactorily under variance heteroscedasticity. In the present paper, we tackle this problem and…
The accuracy of a diagnostic test is typically characterised using the receiver operating characteristic (ROC) curve. Summarising indexes such as the area under the ROC curve (AUC) are used to compare different tests as well as to measure the difference between two populations. Often additional information is available on some of the covariates which are known to influence the accuracy of such measures. We propose nonparametric methods for covariate adjustment of the AUC. Models with normal errors and non-normal errors are discussed and analysed separately. Nonparametric regression is used for…
Hierarchical inference in (generalized) regression problems is powerful for finding significant groups or even single covariates, especially in high-dimensional settings where identifiability of the entire regression parameter vector may be ill-posed. The general method proceeds in a fully data-driven and adaptive way from large to small groups or singletons of covariates, depending on the signal strength and the correlation structure of the design matrix. We propose a novel hierarchical multiple testing adjustment that can be used in combination with any significance test for a group of covar…
Randomized block factorial experiments are widely used in industrial engineering, clinical trials, and social science. Researchers often use a linear model and analysis of covariance to analyze experimental results; however, limited studies have addressed the validity and robustness of the resulting inferences because assumptions for a linear model might not be justified by randomization in randomized block factorial experiments. In this paper, we establish a new finite population joint central limit theorem for usual (unadjusted) factorial effect estimators in randomized block $2^K$ factorial…
Towards Best Practices for Covariate Adjustment in Regulatory Trials: From Fixed to Data-Adaptive Approaches
University of California Berkeley（加州大学伯克利分校）；Division of Biometrics IV, OB/OTS/CDER/FDA（美国食品药品监督管理局药物评价与研究中心生物统计学第四处）；Harvard T.H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）；Beth Israel Deaconess Hospital（贝斯以色列女执事医疗中心）；Novo Nordisk A/S（诺和诺德公司）；Pfizer Inc.（辉瑞公司）；Northeastern University（东北大学）；Gilead Sciences（吉利德科学公司）；National Center for the Advancement of Translational Science, National Institutes of Health（美国国立卫生研究院转化科学促进国家中心）；Section of Epidemiology, Biostatistics and Biodemography, University of Southern Denmark（南丹麦大学流行病学、生物统计学和生物人口学系）；Forum for Collaborative Research, School of Public Health, University of California Berkeley（加州大学伯克利分校公共卫生学院合作研究论坛）；OncoBrain Inc（OncoBrain 公司）；Moffitt Cancer Center（莫菲特癌症中心）；Department of Biostatistics, University of Michigan（密歇根大学生物统计学系）；Department of Mathematics, Computer Science and Statistics, Ghent University（根特大学数学、计算机科学和统计系）；Department of Mathematics and Data Science, Vrije Universiteit Brussel（布鲁塞尔自由大学数学与数据科学系）
Concerns have been expressed over the validity of statistical inference under covariate-adaptive randomization despite the extensive use in clinical trials. In the literature, the inferential properties under covariate-adaptive randomization have been mainly studied for continuous responses; in particular, it is well known that the usual two sample t-test for treatment effect is typically conservative, in the sense that the actual test size is smaller than the nominal level. This phenomenon of invalid tests has also been found for generalized linear models without adjusting for the covariates …
We study problems with multiple missing covariates and partially observed responses. We develop a new framework to handle complex missing covariate scenarios via inverse probability weighting, regression adjustment, and a multiply-robust procedure. We apply our framework to three classical problems: the Cox model from survival analysis, missing response, and binary treatment from causal inference. We also discuss how to handle missing covariates in these scenarios, and develop associated identifying theories and asymptotic theories. We apply our procedure to simulations and an Alzheimer's dise…
Pocock and Simon's marginal procedure (Pocock and Simon, 1975) is often implemented forbalancing treatment allocation over influential covariates in clinical trials. However, the theoretical properties of Pocock and Simion's procedure have remained largely elusive for decades. In this paper, we propose a general framework for covariate-adaptive designs and establish the corresponding theory under widely satisfied conditions. As a special case, we obtain the theoretical properties of Pocock and Simon's marginal procedure: the marginal imbalances and overall imbalance are bounded in probability,…
When investigators seek to estimate causal effects, they often assume that selection into treatment is based only on observed covariates. Under this identification strategy, analysts must adjust for observed confounders. While basic regression models have long been the dominant method of statistical adjustment, more robust methods based on matching or weighting have become more common. Of late, even more flexible methods based on machine learning methods have been developed for statistical adjustment. These machine learning methods are designed to be black box methods with little input from th…
In paired experiments, participants are grouped into pairs with similar characteristics, and one observation from each pair is randomly assigned to treatment. Because of both the pairing and the randomization, the treatment and control groups should be well balanced; however, there may still be small chance imbalances. It may be possible to improve the precision of the treatment effect estimate by adjusting for these imbalances. Building on related work for completely randomized experiments, we propose the P-LOOP (paired leave-one-out potential outcomes) estimator for paired experiments. We le…
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…
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…
Classical randomized experiments, equipped with randomization-based inference, provide assumption-free inference for treatment effects. They have been the gold standard for drawing causal inference and provide excellent internal validity. However, they have also been criticized for questionable external validity, in the sense that the conclusion may not generalize well to a larger population. The randomized survey experiment is a design tool that can help mitigate this concern, by randomly selecting the experimental units from the target population of interest. However, as pointed out by Morga…
Individual participant data (IPD) meta-analyses of randomised trials are considered a reliable way to assess participant-level treatment effect modifiers but may not make the best use of the available data. Traditionally, effect modifiers are explored one covariate at a time, which gives rise to the possibility that evidence of treatment-covariate interaction may be due to confounding from a different, related covariate. We aimed to evaluate current practice when estimating treatment-covariate interactions in IPD meta-analysis, specifically focusing on involvement of additional covariates in t…
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…
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）
Population-adjusted indirect comparisons estimate treatment effects when access to individual patient data is limited and there are cross-trial differences in effect modifiers. Popular methods include matching-adjusted indirect comparison (MAIC) and simulated treatment comparison (STC). There is limited formal evaluation of these methods and whether they can be used to accurately compare treatments. Thus, we undertake a comprehensive simulation study to compare standard unadjusted indirect comparisons, MAIC and STC across 162 scenarios. This simulation study assumes that the trials are investi…
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…
We often seek to estimate the causal effect of an exposure on a particular outcome in both randomized and observational settings. One such estimation method is the covariate-adjusted residuals estimator, which was designed for individually or cluster randomized trials. In this manuscript, we study the properties of this estimator and develop a new estimator that utilizes both covariate adjustment and inverse probability weighting We support our theoretical results with a simulation study and an application in an infectious disease setting. The covariate-adjusted residuals estimator is an effic…
