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Prognostic biomarkers for survival outcomes are widely used in clinical research and practice. Such biomarkers are often evaluated using a C-index as well as quantities based on time-dependent receiver operating characteristic curves. Existing methods for their evaluation generally assume that censoring is uninformative in the sense that the censoring time is independent of the failure time with or without conditioning on the biomarker under evaluation. With focus on the C-index and the area under a particular receiver operating characteristic curve, we describe and compare three estimation methods that account for informative censoring based on observed baseline covariates. Two of them are straightforward extensions of existing plug-in and inverse probability weighting methods for uninformative censoring. By appealing to semiparametric theory, we also develop a doubly robust, locally efficient method that is more robust than the plug-in and inverse probability weighting methods and typically more efficient than the inverse probability weighting method. The methods are evaluated and compared in a simulation study, and applied to real data from studies of breast cancer and heart failure.

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Longitudinal studies are often subject to missing data. The recent guidance from regulatory agencies, such as the ICH E9(R1) addendum addresses the importance of defining a treatment effect estimand with the consideration of intercurrent events. Jump-to-reference (J2R) is one classical control-based scenario for the treatment effect evaluation, where the participants in the treatment group after intercurrent events are assumed to have the same disease progress as those with identical covariates in the control group. We establish new estimators to assess the average treatment effect based on a proposed potential outcomes framework under J2R. Various identification formulas are constructed, motivating estimators that rely on different parts of the observed data distribution. Moreover, we obtain a novel estimator inspired by the efficient influence function, with multiple robustness in the sense that it achieves n1/2-consistency if any pairs of multiple nuisance functions are correctly specified, or if the nuisance functions converge at a rate not slower than n-1/4 when using flexible modeling approaches. The finite-sample performance of the proposed estimators is validated in simulation studies and an antidepressant clinical trial.

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We aim to make inferences about a smooth, finite-dimensional parameter by fusing data from multiple sources together. Previous works have studied the estimation of a variety of parameters in similar data fusion settings, including in the estimation of the average treatment effect and average reward under a policy, with the majority of them merging one historical data source with covariates, actions, and rewards and one data source of the same covariates. In this work, we consider the general case where one or more data sources align with each part of the distribution of the target population, for example, the conditional distribution of the reward given actions and covariates. We describe potential gains in efficiency that can arise from fusing these data sources together in a single analysis, which we characterize by a reduction in the semiparametric efficiency bound. We also provide a general means to construct estimators that achieve these bounds. In numerical simulations, we illustrate marked improvements in efficiency from using our proposed estimators rather than their natural alternatives. Finally, we illustrate the magnitude of efficiency gains that can be realized in vaccine immunogenicity studies by fusing data from two HIV vaccine trials.

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We consider the problem of optimizing treatment allocation for statistical efficiency in randomized clinical trials. Optimal allocation has been studied previously for simple treatment effect estimators such as the sample mean difference, which are not fully efficient in the presence of baseline covariates. More efficient estimators can be obtained by incorporating covariate information, and modern machine learning methods make it increasingly feasible to approach full efficiency. Accordingly, we derive the optimal allocation ratio by maximizing the design efficiency of a randomized trial, assuming that an efficient estimator will be used for analysis. We then expand the scope of optimization by considering covariate-dependent randomization (CDR), which has some flavor of an observational study but provides the same level of scientific rigor as a standard randomized trial. We describe treatment effect estimators that are consistent, asymptotically normal, and (nearly) efficient under CDR, and derive the optimal propensity score by maximizing the design efficiency of a CDR trial (under the assumption that an efficient estimator will be used for analysis). Our optimality results translate into optimal designs that improve upon standard practice. Real-world examples and simulation results demonstrate that the proposed designs can produce substantial efficiency improvements in realistic settings.

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When drawing causal inference from observational data, there is almost always concern about unmeasured confounding. One way to tackle this is to conduct a sensitivity analysis. One widely-used sensitivity analysis framework hypothesizes the existence of a scalar unmeasured confounder U and asks how the causal conclusion would change were U measured and included in the primary analysis. Work along this line often makes various parametric assumptions on U, for the sake of mathematical and computational convenience. In this article, we further this line of research by developing a valid sensitivity analysis that leaves the distribution of U unrestricted. Compared to many existing methods in the literature, our method allows for a larger and more flexible family of models, mitigates observable implications (Franks et al., 2019), and works seamlessly with any primary analysis that models the outcome regression parametrically. We construct both pointwise confidence intervals and confidence bands that are uniformly valid over a given sensitivity parameter space, thus formally accounting for unknown sensitivity parameters. We apply our proposed method on an influential yet controversial study of the causal relationship between war experiences and political activeness using observational data from Uganda.

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Unlike parametric regression, machine learning (ML) methods do not generally require precise knowledge of the true data generating mechanisms. As such, numerous authors have advocated for ML methods to estimate causal effects. Unfortunately, ML algorithmscan perform worse than parametric regression. We demonstrate the performance of ML-based single- and double-robust estimators. We use 100 Monte Carlo samples with sample sizes of 200, 1200, and 5000 to investigate bias and confidence interval coverage under several scenarios. In a simple confounding scenario, confounders were related to the treatment and the outcome via parametric models. In a complex confounding scenario, the simple confounders were transformed to induce complicated nonlinear relationships. In the simple scenario, when ML algorithms were used, double-robust estimators were superior to single-robust estimators. In the complex scenario, single-robust estimators with ML algorithms were at least as biased as estimators using misspecified parametric models. Double-robust estimators were less biased, but coverage was well below nominal. The use of sample splitting, inclusion of confounder interactions, reliance on a richly specified ML algorithm, and use of doubly robust estimators was the only explored approach that yielded negligible bias and nominal coverage. Our results suggest that ML based singly robust methods should be avoided.

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We consider causal inference in observational studies with choice-based sampling, in which subject enrollment is stratified on treatment choice. Choice-based sampling has been considered mainly in the econometrics literature, but it can be useful for biomedical studies as well, especially when one of the treatments being compared is uncommon. We propose new methods for estimating the population average treatment effect under choice-based sampling, including doubly robust methods motivated by semiparametric theory. A doubly robust, locally efficient estimator may be obtained by replacing nuisance functions in the efficient influence function with estimates based on parametric models. The use of machine learning methods to estimate nuisance functions leads to estimators that are consistent and asymptotically efficient under broader conditions. The methods are compared in simulation experiments and illustrated in the context of a large observational study in obstetrics. We also make suggestions on how to choose the target proportion of treated subjects and the sample size in designing a choice-based observational study.

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Clinical trials are widely considered the gold standard for treatment evaluation, and they can be highly expensive in terms of time and money. The efficiency of clinical trials can be improved by incorporating information from baseline covariates that are related to clinical outcomes. This can be done by modifying an unadjusted treatment effect estimator with an augmentation term that involves a function of covariates. The optimal augmentation is well characterized in theory but must be estimated in practice. In this article, we investigate the use of machine learning methods to estimate the optimal augmentation. We consider and compare an indirect approach based on an estimated regression function and a direct approach that aims directly to minimize the asymptotic variance of the treatment effect estimator. Theoretical considerations and simulation results indicate that the direct approach is generally preferable over the indirect approach. The direct approach can be implemented using any existing prediction algorithm that can minimize a weighted sum of squared prediction errors. Many such prediction algorithms are available, and the super learning principle can be used to combine multiple algorithms into a super learner under the direct approach. The resulting direct super learner has a desirable oracle property, is easy to implement, and performs well in realistic settings. The proposed methodology is illustrated with real data from a stroke trial.

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Two-stage randomization designs are broadly accepted and becoming increasingly popular in clinical trials for cancer and other chronic diseases to assess and compare the effects of different treatment policies. In this paper, we propose an inferential method to estimate the treatment effects in two-stage randomization designs, which can improve the efficiency and reduce bias in the presence of chance imbalance of a robust covariate-adjustment without additional assumptions required by Lokhnygina and Helterbrand (Biometrics, 63:422-428)'s inverse probability weighting (IPW) method. The proposed method is evaluated and compared with the IPW method using simulations and an application to data from an oncology clinical trial. Given the predictive power of baseline covariates collected in this real data, our proposed method obtains 17-38% gains in efficiency compared with the IPW method in terms of overall survival outcome. Copyright © 2017 John Wiley & Sons, Ltd.

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