Statistical Efficiency Research Articles

Random Surface Covariance Estimation by Shifted Partial Tracing

The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the covariance, even though the assumption may fail in practice. We consider a setting where the covariance structure may fail to be separable locally—either due to noise contamination or due to the presence of a nonseparable short-range dependent signal component. That is, the covariance is an additive perturbation of a separable component by a nonseparable but banded component. We introduce nonparametric estimators hinging on the novel concept of shifted partial tracing, enabling computationally efficient estimation of the model under dense observation. Due to the denoising properties of shifted partial tracing, our methods are shown to yield consistent estimators even under noisy discrete observation, without the need for smoothing. Further to deriving the convergence rates and limit theorems, we also show that the implementation of our estimators, including prediction, comes at no computational overhead relative to a separable model. Finally, we demonstrate empirical performance and computational feasibility of our methods in an extensive simulation study and on a real dataset. Supplementary materials for this article are available online.

Improved Gibbs samplers for cosmic microwave background power spectrum estimation

We study different variants of the Gibbs sampler algorithm from the perspective of their applicability to the estimation of power spectra of the cosmic microwave background (CMB) anisotropies. These include approaches studied earlier in the CMB literature as well as new ones which are proposed in this work. We demonstrate all these variants on full- and cut-sky simulations and compare their performance, assessing both their computational and statistical efficiency. For this we employ a consistent comparison metric, an effective sample size per second, commonly used in this context in the statistical literature. We show that one of the proposed approaches, referred to as Centered overrelax, which capitalizes on additional, auxiliary variables to minimize the computational time needed per sample, uses overrelaxation to decorrelate subsequent samples, and performs better than the standard Gibbs sampler by a factor between one and two orders of magnitude in the nearly full-sky, satellitelike cases. It therefore potentially provides an interesting alternative to the currently favored approaches.

Consideration of biological and inorganic additives in upgraded anaerobic digestion BioModel

This paper deals with the numerical simulation of biogas production in the anaerobic digestion process of organic waste. Special attention is focused on the modeling of the activities of biological and inorganic additives, which are used to enhance the process and reduce H2S content in the biogas. For this purpose, an existing BioModel is upgraded with the modified Michaelis-Menten kinetics in order to model the enzymatic hydrolysis and with adequate modeling of physicochemical processes. The upgraded BioModel was calibrated with experimental data obtained from a full-scale biogas plant, used in combination with an active set optimization procedure; the relative agreement indices were 0.9376, 0.9419, 0.7957, and 0.7663 for biogas, CH4, H2, and H2S flow rates, respectively. Statistical efficiency criteria differ up to 5% in model calibration and validation. The obtained results confirm the importance of additives modeling and the usefulness of the proposed model for industrial biogas plants’ performance improvement.

Forecast of meteorological droughts with neural networks in Sonora watershed, Mexico

Droughts are hydrometeorological hazards that are characterized by an abnormal and persistent humidity deficit. In the last years, this hazard has been present more frequently and with more severity levels, producing negative impacts on the ecosystem, agriculture, livestock, and society. Therefore, its monitoring and forecast, must be part of integral planning, preparation, and mitigation of its adverse effects at local, regional, and national levels. In Mexico, most of the drought studies are focused on characterization and analysis. Thus, in this research, we evaluated the application of artificial neural networks (ANN) to forecast the meteorological droughts in the medium and high parts of the Sonora River watershed. SPI and SPEI index were used, on scales of 3, 6, 12, and, 24 months, for the 1974 to 2013 period of years. Forecast results showed that ANN has a satisfactory level of prediction, with an average determination coefficient (R2) in the validation phase, of 0.76. It was observed that the statistical efficiency of SPEI was better than that of SPI, and that this efficiency increased with the longer temporal scale; maybe because in a short term, climate variability is greater.

Bandit Change-Point Detection for Real-Time Monitoring High-Dimensional Data Under Sampling Control

In many real-world problems of real-time monitoring high-dimensional streaming data, one wants to detect an undesired event or change quickly once it occurs, but under the sampling control constraint in the sense that one might be able to only observe or use selected components data for decision-making per time step in the resource-constrained environments. In this article, we propose to incorporate multi-armed bandit approaches into sequential change-point detection to develop an efficient bandit change-point detection algorithm based on the limiting Bayesian approach to incorporate a prior knowledge of potential changes. Our proposed algorithm, termed Thompson-Sampling-Shiryaev-Roberts-Pollak (TSSRP), consists of two policies per time step: the adaptive sampling policy applies the Thompson Sampling algorithm to balance between exploration for acquiring long-term knowledge and exploitation for immediate reward gain, and the statistical decision policy fuses the local Shiryaev–Roberts–Pollak statistics to determine whether to raise a global alarm by sum shrinkage techniques. Extensive numerical simulations and case studies demonstrate the statistical and computational efficiency of our proposed TSSRP algorithm.

Estimation of multiple ordered ROC curves using placement values.

In many diagnostic accuracy studies, a priori orders may be available on multiple receiver operating characteristic curves. For example, being closer to delivery, fetal ultrasound measures in the third trimester should be no less accurate than those in the second trimester in predicting small-for-gestational-age births. Such an a priori order should be incorporated in estimating receiver operating characteristic curves and associated summary accuracy statistics, as it can potentially improve statistical efficiency of these estimates. Early work in the literature has mainly taken an indirect approach to this task and has induced the desired a priori order through modeling test score distributions. We instead propose a new strategy that incorporates the order directly through the modeling of receiver operating characteristic curves. We achieve this by exploiting the link between placement value (the relative position of a diseased test score in the healthy score distribution), the cumulative distribution function of placement value, and receiver operating characteristic curve, and by building stochastically ordered random variables through mixture distributions. We take a Bayesian semiparametric approach in using Dirichlet process mixture models so that the placement values can be flexibly modeled. We conduct extensive simulation studies to examine the performance of the proposed methodology and apply the new framework to data from obstetrics and women's health studies.

An algorithm for distributed Bayesian inference

Monte Carlo algorithms, such as Markov chain Monte Carlo (MCMC) and Hamiltonian Monte Carlo (HMC), are routinely used for Bayesian inference; however, these algorithms are prohibitively slow in massive data settings because they require multiple passes through the full data in every iteration. Addressing this problem, we develop a scalable extension of these algorithms using the divide‐and‐conquer (D&C) technique that divides the data into a sufficiently large number of subsets, draws parameters in parallel on the subsets using a powered likelihood and produces Monte Carlo draws of the parameter by combining parameter draws obtained from each subset. The combined parameter draws play the role of draws from the original sampling algorithm. Our main contributions are twofold. First, we demonstrate through diverse simulated and real data analyses focusing on generalized linear models (GLMs) that our distributed algorithm delivers comparable results as the current state‐of‐the‐art D&C algorithms in terms of statistical accuracy and computational efficiency. Second, providing theoretical support for our empirical observations, we identify regularity assumptions under which the proposed algorithm leads to asymptotically optimal inference. We also provide illustrative examples focusing on normal linear and logistic regressions where parts of our D&C algorithm are analytically tractable.

On recurrent-event win ratio.

The win ratio approach proposed by Pocock et al. (2012) has become a popular tool for analyzing composite endpoints of death and non-fatal events like hospitalization. Its standard version, however, draws on the non-fatal event only through the first occurrence. For statistical efficiency and clinical interpretability, we construct and compare different win ratio variants that make fuller use of recurrent events. We pay special attention to a variant called last-event-assisted win ratio, which compares two patients on the cumulative frequency of the non-fatal event, with ties broken by the time of its latest episode. It is shown that last-event-assisted win ratio uses more data than the standard win ratio does but reduces to the latter when the non-fatal event occurs at most once. We further prove that last-event-assisted win ratio rejects the null hypothesis with large probability if the treatment stochastically delays all events. Simulations under realistic settings show that the last-event-assisted win ratio test consistently enjoys higher power than the standard win ratio and other competitors. Analysis of a real cardiovascular trial provides further evidence for the practical advantages of the last-event-assisted win ratio. Finally, we discuss future work to develop meaningful effect size estimands based on the extended rules of comparison. The R-code for the proposed methods is included in the package WR openly available on the Comprehensive R Archive Network.

Improving the Precision of the Glasgow Outcome Scale-Extended Using Item Response Theory: A TRACK-TBI Study.

The Glasgow Outcome Scale-Extended (GOSE) is a functional outcome measure intended to place individuals with traumatic brain injury (TBI) into one of eight broad levels of injury-related disability. This simplicity is not always optimal, particularly when more granular assessment of individuals' injury recovery is desired. The GOSE, however, is customarily assessed using a multi-question interview that contains richer information than is reflected in the GOSE score. Using data from the multi-center Transforming Research and Clinical Knowledge in TBI (TRACK-TBI) study (N = 1544), we used item response theory (IRT) to evaluate whether rescoring the GOSE using IRT, which posits that a continuous latent variable (disability) underlies responses, can yield a more precise index of injury-related functional limitations. We fit IRT models to GOSE interview responses collected at three months post-injury. Each participant's level of functional limitation was estimated from the model (GOSE-IRT) and comparisons were made between IRT-based and standard (GOSE-Ordinal) scores. The IRT scoring resulted in 141 possible scores (vs. 7 GOSE-Ordinal scores in this sample of individuals with GOSE scores ranging between 2 and 8). Moreover, GOSE-IRT scores were significantly more strongly associated with measures of TBI-related symptoms, psychological symptoms, and quality of life. Our findings demonstrate that rescoring the GOSE interview using IRT yields more granular, meaningful measurement of injury-related functional limitations, while adding no additional respondent or examiner burden. This technique may have utility for many applications, such as clinical trials aiming to detect small treatment effects, and small-scale studies that need to maximize statistical efficiency.

Inference and model determination for temperature-driven non-linear ecological models

This paper is concerned with a contemporary Bayesian approach to the effect of temperature on developmental rates. We develop statistical methods using recent computational tools to model four commonly used ecological non-linear mathematical curves that describe arthropods’ developmental rates. Such models address the effect of temperature fluctuations on the developmental rate of arthropods. In addition to the widely used Gaussian distributional assumption, we also explore Inverse Gamma-based alternatives, which naturally accommodate adaptive variance fluctuation with temperature. Moreover, to overcome the associated parameter indeterminacy in the case of no development, we suggest the zero-inflated Inverse Gamma model. The ecological models are compared graphically via posterior predictive plots and quantitatively via marginal likelihood estimates and Information criteria. Inference is performed using the Stan software and we investigate the statistical and computational efficiency of its Hamiltonian Monte Carlo and Variational Inference methods. We also explore model uncertainty and employ Bayesian Model Averaging framework for robust estimation of the key ecological parameters.

Laplacian‐P‐splines for Bayesian inference in the mixture cure model

The mixture cure model for analyzing survival data is characterized by the assumption that the population under study is divided into a group of subjects who will experience the event of interest over some finite time horizon and another group of cured subjects who will never experience the event irrespective of the duration of follow‐up. When using the Bayesian paradigm for inference in survival models with a cure fraction, it is common practice to rely on Markov chain Monte Carlo (MCMC) methods to sample from posterior distributions. Although computationally feasible, the iterative nature of MCMC often implies long sampling times to explore the target space with chains that may suffer from slow convergence and poor mixing. Furthermore, extra efforts have to be invested in diagnostic checks to monitor the reliability of the generated posterior samples. A sampling‐free strategy for fast and flexible Bayesian inference in the mixture cure model is suggested in this article by combining Laplace approximations and penalized B‐splines. A logistic regression model is assumed for the cure proportion and a Cox proportional hazards model with a P‐spline approximated baseline hazard is used to specify the conditional survival function of susceptible subjects. Laplace approximations to the posterior conditional latent vector are based on analytical formulas for the gradient and Hessian of the log‐likelihood, resulting in a substantial speed‐up in approximating posterior distributions. The spline specification yields smooth estimates of survival curves and functions of latent variables together with their associated credible interval are estimated in seconds. A fully stochastic algorithm based on a Metropolis‐Langevin‐within‐Gibbs sampler is also suggested as an alternative to the proposed Laplacian‐P‐splines mixture cure (LPSMC) methodology. The statistical performance and computational efficiency of LPSMC is assessed in a simulation study. Results show that LPSMC is an appealing alternative to MCMC for approximate Bayesian inference in standard mixture cure models. Finally, the novel LPSMC approach is illustrated on three applications involving real survival data.

Real-Time Regression Analysis of Streaming Clustered Data With Possible Abnormal Data Batches

This article develops an incremental learning algorithm based on quadratic inference function (QIF) to analyze streaming datasets with correlated outcomes such as longitudinal data and clustered data. We propose a renewable QIF (RenewQIF) method within a paradigm of renewable estimation and incremental inference, in which parameter estimates are recursively renewed with current data and summary statistics of historical data, but with no use of any historical subject-level raw data. We compare our renewable estimation method with both offline QIF and offline generalized estimating equations (GEE) approach that process the entire cumulative subject-level data all together, and show theoretically and numerically that our renewable procedure enjoys statistical and computational efficiency. We also propose an approach to diagnose the homogeneity assumption of regression coefficients via a sequential goodness-of-fit test as a screening procedure on occurrences of abnormal data batches. We implement the proposed methodology by expanding existing Spark’s Lambda architecture for the operation of statistical inference and data quality diagnosis. We illustrate the proposed methodology by extensive simulation studies and an analysis of streaming car crash datasets from the National Automotive Sampling System-Crashworthiness Data System (NASS CDS). Supplementary materials for this article are available online.

Sportsman’s Mental State Evaluation and Early Warning Method Based on Intelligent CNN

Aiming at the intelligent needs of psychological state assessment of university students, the text information-based psychological problem identification approach is investigated in the paper. This approach uses the text of student forums within universities as the database and introduces the convolutional neural network (CNN) model in deep learning, which contains a convolutional layer, a pooling layer, and a fully connected layer. After the convolution is completed, the convolution result is delinearized by the activation function, and then, pooling is performed to improve the fitting ability of the network for nonlinearities. For data processing, behavioral features, attribute features, content features, and social relationship features are extracted from text information as the input of the CNN. The psychological lexicon of expertise (LIWC) is used to enhance the efficiency of text word frequency statistics when performing text content extraction. To evaluate the performance of the proposed method, simulations are performed in the open dataset of CLPsyh2017 ReachOut Forum, and the FastText method is used as a comparison. The results show that the CNN model achieves an accuracy of 0.71 in the full-sample domain, which is significantly higher than that of the FastText model at 0.64. In the early warning evaluation of mental states, the CNN performance is better than that of FastText.

Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width

Traditional quantile estimators that are based on one or two order statistics are a common way to estimate distribution quantiles based on the given samples. These estimators are robust, but their statistical efficiency is not always good enough. A more efficient alternative is the Harrell-Davis quantile estimator which uses a weighted sum of all order statistics. Whereas this approach provides more accurate estimations for the light-tailed distributions, it’s not robust. To be able to customize the tradeoff between statistical efficiency and robustness, we could consider a trimmed modification of the Harrell-Davis quantile estimator. In this approach, we discard order statistics with low weights according to the highest density interval of the beta distribution.

Toward Better Practice of Covariate Adjustment in Analyzing Randomized Clinical Trials

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: (a) guaranteed efficiency gain: a model-assisted method should often gain but never hurt efficiency; (b) wide applicability: a valid procedure should be applicable, and preferably universally applicable, to all commonly used randomization schemes; (c) robust standard error: variance estimation should be robust to model misspecification and heteroscedasticity. To achieve these, we recommend a model-assisted estimator under an analysis of heterogeneous covariance working model that includes all covariates used in randomization. Our conclusions are based on an asymptotic theory that provides a clear picture of how covariate-adaptive randomization and regression adjustment alter statistical efficiency. Our theory is more general than the existing ones in terms of studying arbitrary functions of response means (including linear contrasts, ratios, and odds ratios), multiple arms, guaranteed efficiency gain, optimality, and universal applicability. Supplementary materials for this article are available online.

Reconstruction-based Monte Carlo method for accurate and efficient breakage simulation

Monte Carlo (MC) methods have been proven effective in population balance modeling; yet, in dealing with particle breakage problems, their performances in terms of statistical noise and computational efficiency still demand further improvement. In this work, we propose a time-driven MC method based on weighted particles that are reconstructed periodically by matching the shape of the number density function, which is defined on an adaptive subdomain mesh. By accounting for the weighted particles of all subdomains in a global sense rather than only a selected few in the traditional ways, this solver yields promising agreement with the analytical solutions of both binary- and multi-breakage cases. Compared with existing methods, the proposed method is able to resolve the particle size distribution as well as moments with much lower statistical noise, and is more suitable for long-time simulations. Moreover, its accuracy is less dependent on the weighted particle number or time increment.

Nonparametric inference of complier quantile treatment effects in randomized trials with imperfect compliance

To analyze randomized trials with imperfect compliance, a standard approach is to estimate the local average treatment effect in the sub-population of compliers using randomization status as an instrumental variable. Though quantile analysis has been popular in general, the local (or complier) quantile treatment effect (cQTE) as a causal estimand has received insufficient attention. In this paper, we map out the details for the estimation, inference, and sensitivity analysis of the cQTE in a completely nonparametric setting. We propose to estimate the cQTE using nonparametric plug-in estimators of the cumulative distribution functions for the potential outcomes of the compliers. The cQTE estimator is shown to be asymptotically normal, with asymptotic variance estimated through kernel-smoothed density estimators. The procedure is easily extended to adjust for discrete covariates for gains in statistical efficiency. Moreover, by exploiting the stochastic monotonicity of the quantile functional, we develop sensitivity bounds for the cQTE when key assumptions such as exclusion restriction and instrument monotonicity are violated. Extensive simulations show that the proposed methods provide valid inference of the target local estimand and outperform standard intent-to-treat tests, especially under low compliance rates and/or heterogeneous treatment effects. A recent study on a government-funded health insurance program in India is analyzed as an illustration.

Fast Multivariate Probit Estimation via a Two-Stage Composite Likelihood

The multivariate probit is popular for modeling correlated binary data, with an attractive balance of flexibility and simplicity. However, considerable challenges remain in computation and in devising a clear statistical framework. Interest in the multivariate probit has increased in recent years. Current applications include genomics and precision medicine, where simultaneous modeling of multiple traits may be of interest, and computational efficiency is an important consideration. We propose a fast method for multivariate probit estimation via a two-stage composite likelihood. We explore computational and statistical efficiency, and note that the approach sets the stage for extensions beyond the purely binary setting.

PRACT: a pragmatic randomized adaptive clinical trial protocol to investigate a culturally adapted brief negotiational intervention for alcohol use in the emergency department in Tanzania

BackgroundAlcohol use in resource-limited settings results in significant morbidity and mortality. These settings lack the necessary specialty-trained personnel and infrastructure. Therefore, implementing evidence-based interventions from high-income settings, like a brief negotiational intervention (BNI) for alcohol, will require rapid production of evidence of effectiveness to guide implementation priorities. Thus, this study describes a clinical trial protocol to rapidly optimize and evaluate the impact of a culturally adapted BNI to reduce alcohol-related harms and alcohol consumption among injury patients.MethodsOur pragmatic, adaptive, randomized controlled trial (PRACT) is designed to determine the most effective intervention approach to reduce hazardous alcohol use among adult (≥18 years old) in acute (< 24 h) injury patients. Our culturally adapted, nurse-delivered, intervention (PPKAY) has been augmented with evidence-based, culturally appropriate standards and will be evaluated as follows. Stage 1 of the trial will determine if PPKAY, either with a standard short-message-service (SMS) booster or with a personalized SMS booster is more effective than usual care (UC). While optimizing statistical efficiency, Stage 2 drops the UC arm to compare the PPKAY with a standard SMS booster to PPKAY with a personalized SMS booster. Finally, in Stage 3, the more effective arm in Stage 2 is compared to PPKAY without an SMS booster. The study population is acute injury patients who present to Kilimanjaro Christian Medical Centre, Tanzania, who (1) test alcohol positive by breathalyzer upon arrival; (2) have an Alcohol Use Disorder Identification Test of 8 or above; and/or (3) have reported drinking alcohol prior to their injury. Outcome measures will be evaluated for all arms at 3, 6, 9, 12, and 24 months. The primary outcome for the study is the reduction of the number of binge drinking days in the 4 weeks prior to follow-up. Secondary outcomes include alcohol-related consequences, measured by the Drinker Inventory of Consequences.DiscussionThe findings from this study will be critically important to identify alcohol harm reduction strategies where alcohol research and interventions are scarce. Our innovative and adaptive trial design can transform behavior change research and identify the most effective nurse-driven intervention to be targeted for integration into standard care.Trial registrationClinicalTrials.govNCT04535011. Registered on September 1, 2020.

Surrogate Hessian accelerated structural optimization for stochastic electronic structure theories.

We present an efficient energy-based method for structural optimization with stochastic electronic structure theories, such as diffusion quantum Monte Carlo (DMC). This method is based on robust line-search energy minimization in reduced parameter space, exploiting approximate but accurate Hessian information from a surrogate theory, such as density functional theory. The surrogate theory is also used to characterize the potential energy surface, allowing for simple but reliable ways to maximize statistical efficiency while retaining controllable accuracy. We demonstrate the method by finding the minimum DMC energy structures of the selected flake-like aromatic molecules, such as benzene, coronene, and ovalene, represented by 2, 6, and 19 structural parameters, respectively. In each case, the energy minimum is found within two parallel line-search iterations. The method is near-optimal for a line-search technique and suitable for a broad range of applications. It is easily generalized to any electronic structure method where forces and stresses are still under active development and implementation, such as diffusion Monte Carlo, auxiliary-field Monte Carlo, and stochastic configuration interaction, as well as deterministic approaches such as the random-phase approximation. Accurate and efficient means of geometry optimization could shed light on a broad class of materials and molecules, showing high sensitivity of induced properties to structural variables.