Statistics

Use of historical data and real-world evidence holds great potential to improve the efficiency of clinical trials. One major challenge is how to effectively borrow information from historical data while maintaining a reasonable type I error. We propose the elastic prior approach to address this challenge and achieve dynamic information borrowing. Unlike existing approaches, this method proactively controls the behavior of dynamic information borrowing and type I errors by incorporating a well-known concept of clinically meaningful difference through an elastic function, defined as a monotonic function of a congruence measure between historical data and trial data. The elastic function is constructed to satisfy a set of information-borrowing constraints prespecified by researchers or regulatory agencies, such that the prior will borrow information when historical and trial data are congruent, but refrain from information borrowing when historical and trial data are incongruent. In doing so, the elastic prior improves power and reduces the risk of data dredging and bias. The elastic prior is information borrowing consistent, i.e. asymptotically controls type I and II errors at the nominal values when historical data and trial data are not congruent, a unique characteristics of the elastic prior approach. Our simulation study that evaluates the finite sample characteristic confirms that, compared to existing methods, the elastic prior has better type I error control and yields competitive or higher power.

Pharmaceutical companies regularly need to make decisions about drug development programs based on the limited knowledge from early stage clinical trials. In this situation, eliciting the judgements of experts is an attractive approach for synthesising evidence on the unknown quantities of interest. When calculating the probability of success for a drug development program, multiple quantities of interest - such as the effect of a drug on different endpoints - should not be treated as unrelated. We discuss two approaches for establishing a multivariate distribution for several related quantities within the SHeffield ELicitation Framework (SHELF). The first approach elicits experts' judgements about a quantity of interest conditional on knowledge about another one. For the second approach, we first elicit marginal distributions for each quantity of interest. Then, for each pair of quantities, we elicit the concordance probability that both lie on the same side of their respective elicited medians. This allows us to specify a copula to obtain the joint distribution of the quantities of interest. We show how these approaches were used in an elicitation workshop that was performed to assess the probability of success of the registrational program of an asthma drug. The judgements of the experts, which were obtained prior to completion of the pivotal studies, were well aligned with the final trial results.

The paper discusses empirical Bayes methodology for repeated quality comparisons of health care institutions using data from the Dutch VOKS study that annually monitors the relative performance and quality of nearly all Dutch gynecological centres with respect to different aspects of the childbirths taking place in these centres. This paper can be seen as an extension of the pioneering work of Thomas, Longford and Rolph and Goldstein and Spiegelhalter. First of all, this paper introduces a new simple crude estimate of the centre effect in a logistic regression setting. Next, a simple estimate of the expected percentile of a centre given all data and a measure of rankability of the centres based on the expected percentiles are presented. Finally, the temporal dimension is explored and methods are discussed to predict next years performance.

The System Usability Scale (SUS) is a short, survey-based approach used to determine the usability of a system from an end user perspective once a prototype is available for assessment. Individual scores are gathered using a 10-question survey with the survey results reported in terms of central tendency (sample mean) as an estimate of the system's usability (the SUS study score), and confidence intervals on the sample mean are used to communicate uncertainty levels associated with this point estimate. When the number of individuals surveyed is large, the SUS study scores and accompanying confidence intervals relying upon the central limit theorem for support are appropriate. However, when only a small number of users are surveyed, reliance on the central limit theorem falls short, resulting in confidence intervals that suffer from parameter bound violations and interval widths that confound mappings to adjective and other constructed scales. These shortcomings are especially pronounced when the underlying SUS score data is skewed, as it is in many instances. This paper introduces an empirically-based remedy for such small-sample circumstances, proposing a set of decision rules that leverage either an extended bias-corrected accelerated (BCa) bootstrap confidence interval or an empirical Bayesian credibility interval about the sample mean to restore and bolster subsequent confidence interval accuracy. Data from historical SUS assessments are used to highlight shortfalls in current practices and to demonstrate the improvements these alternate approaches offer while remaining statistically defensible. A freely available, online application is introduced and discussed that automates SUS analysis under these decision rules, thereby assisting usability practitioners in adopting the advocated approaches.

There has been growing attention on how to effectively and objectively use covariate information when the primary goal is to estimate the average treatment effect (ATE) in randomized clinical trials (RCTs). In this paper, we propose an effective weighting approach to extract covariate information based on the empirical likelihood (EL) method. The resulting two-sample empirical likelihood weighted (ELW) estimator includes two classes of weights, which are obtained from a constrained empirical likelihood estimation procedure, where the covariate information is effectively incorporated into the form of general estimating equations. Furthermore, this ELW approach separates the estimation of ATE from the analysis of the covariate-outcome relationship, which implies that our approach maintains objectivity. In theory, we show that the proposed ELW estimator is semiparametric efficient. We extend our estimator to tackle the scenarios where the outcomes are missing at random (MAR), and prove the double robustness and multiple robustness properties of our estimator. Furthermore, we derive the semiparametric efficiency bound of all regular and asymptotically linear semiparametric ATE estimators under MAR mechanism and prove that our proposed estimator attains this bound. We conduct simulations to make comparisons with other existing estimators, which confirm the efficiency and multiple robustness property of our proposed ELW estimator. An application to the AIDS Clinical Trials Group Protocol 175 (ACTG 175) data is conducted.

A balanced sampling design should always be the adopted strategies if auxiliary information is available. Besides, integrating a stratified structure of the population in the sampling process can considerably reduce the variance of the estimators. We propose here a new method to handle the selection of a balanced sample in a highly stratified population. The method improves substantially the commonly used sampling design and reduces the time-consuming problem that could arise if inclusion probabilities within strata do not sum to an integer.

Ensemble Conditional Variance Estimation (ECVE) is a novel sufficient dimension reduction (SDR) method in regressions with continuous response and predictors. ECVE applies to general non-additive error regression models. It operates under the assumption that the predictors can be replaced by a lower dimensional projection without loss of information. It is a semiparametric forward regression model based exhaustive sufficient dimension reduction estimation method that is shown to be consistent under mild assumptions. It is shown to outperform central subspace mean average variance estimation (csMAVE), its main competitor, under several simulation settings and in a benchmark data set analysis.

In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Eulerian penalization of error in the Euclidean space, the Wasserstein metric can capture translation and difference between the shapes of square-integrable probability distributions of the background state and observations -- enabling to formally penalize geophysical biases in state-space with non-Gaussian distributions. The new approach is applied to dissipative and chaotic evolutionary dynamics and its potential advantages and limitations are highlighted compared to the classic variational and filtering data assimilation approaches under systematic and random errors.

The recent growth in multi-fidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a high-fidelity model. In this paper we provide two contributions: (1) we utilize an ensemble estimator to account for uncertainties in the optimal weights of approximate control variate (ACV) approaches and derive lower bounds on the number of samples required to guarantee variance reduction; and (2) we extend an existing multi-fidelity importance sampling (MFIS) scheme to leverage control variates. As such we make significant progress towards both increasing the practicality of approximate control variates ??for instance, by accounting for the effect of pilot samples ??and using multi-fidelity approaches more effectively for estimating low-probability events. The numerical results indicate our hybrid MFIS-ACV estimator achieves up to 50% improvement in variance reduction over the existing state-of-the-art MFIS estimator, which had already shown outstanding convergence rate compared to the Monte Carlo method, on several problems of computational mechanics.

A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and longitudinal data. Envelope methods have been proposed to improve estimation efficiency in the class of unconstrained multivariate linear models, but have not yet been developed for constrained models that we develop in this article. We first compare the standard envelope estimator based on an unconstrained multivariate model with the standard estimator arising from a constrained multivariate model in terms of bias and efficiency. Then, to further improve efficiency, we propose a novel envelope estimator based on a constrained multivariate model. Novel envelope-based testing methods are also proposed. We provide support for our proposals by simulations and by studying the classical dental data and data from the China Health and Nutrition Survey and a study of probiotic capacity to reduced Salmonella infection.