Frequentist Perspective Research Articles

Comparative effect of oral drugs in improving spasticity of different etiology: a network meta-analysis.

Spasticity, a prevalent manifestation of various neurological conditions, significantly impacts the quality of life of patients. Research on the effects of oral drugs on spasticity has produced controversial results. Thus, the aim of this network meta-analysis was to compare the efficacy of oral drugs for improving spasticity in patients with different etiologies. We searched four different databases from their inception to 30 November 2023. A network meta-analysis using a frequentist perspective was conducted to assess the effects of different oral drugs on spasticity, evaluated by the modified Ashworth scale. Our findings showed that, in a frequentist network meta-analysis, eperisone, diazepam, and baclofen had significantly greater spasticity, as measured by the modified Ashworth scale, than did the placebo (MD: -0.80; 95% CIs: -1.42, -0.18; MD: -0.68; 95% CIs: -1.28, -0.09; MD: -0.58; 95% CIs: -1.11, -0.06, respectively). In summary, our study confirmed that eperisone, diazepam, and baclofen could be effective approaches for reducing spasticity of different etiologies and could be useful approaches for improving patient quality of life. Key messages What is already known on this topic: The impact of oral drugs, such as baclofen, gabapentin, tizanidine, and dantrolene, in the treatment of spasticity has been documented. What this study adds: This study determines which of the oral drugs aimed at treating spasticity is the most effective across different etiologies. How this study might affect research, practice, or policy: This study suggests tailored treatment strategies for spasticity based on its etiology.

Forecasting the opening goal in second-half of a football match: Bayesian and frequentist perspectives

Forecasting the opening goal in second-half of a football match: Bayesian and frequentist perspectives

Problematic meta-analyses: Bayesian and frequentist perspectives on combining randomized controlled trials and non-randomized studies

PurposeIn the literature, the propriety of the meta-analytic treatment-effect produced by combining randomized controlled trials (RCT) and non-randomized studies (NRS) is questioned, given the inherent confounding in NRS that may bias the meta-analysis. The current study compared an implicitly principled pooled Bayesian meta-analytic treatment-effect with that of frequentist pooling of RCT and NRS to determine how well each approach handled the NRS bias.Materials & methodsBinary outcome Critical-Care meta-analyses, reflecting the importance of such outcomes in Critical-Care practice, combining RCT and NRS were identified electronically. Bayesian pooled treatment-effect and 95% credible-intervals (BCrI), posterior model probabilities indicating model plausibility and Bayes-factors (BF) were estimated using an informative heavy-tailed heterogeneity prior (half-Cauchy). Preference for pooling of RCT and NRS was indicated for Bayes-factors > 3 or < 0.333 for the converse. All pooled frequentist treatment-effects and 95% confidence intervals (FCI) were re-estimated using the popular DerSimonian-Laird (DSL) random effects model.ResultsFifty meta-analyses were identified (2009–2021), reporting pooled estimates in 44; 29 were pharmaceutical-therapeutic and 21 were non-pharmaceutical therapeutic. Re-computed pooled DSL FCI excluded the null (OR or RR = 1) in 86% (43/50). In 18 meta-analyses there was an agreement between FCI and BCrI in excluding the null. In 23 meta-analyses where FCI excluded the null, BCrI embraced the null. BF supported a pooled model in 27 meta-analyses and separate models in 4. The highest density of the posterior model probabilities for 0.333 < Bayes factor < 1 was 0.8.ConclusionsIn the current meta-analytic cohort, an integrated and multifaceted Bayesian approach gave support to including NRS in a pooled-estimate model. Conversely, caution should attend the reporting of naïve frequentist pooled, RCT and NRS, meta-analytic treatment effects.

Enhanced Laplace approximation

The Laplace approximation has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators derived from the Laplace approximation are often biased for binary or temporally and/or spatially correlated data. Additionally, the corresponding Hessian matrix tends to underestimates the standard errors of these approximate maximum likelihood estimators. While higher-order approximations have been suggested, they are not applicable to complex models, such as correlated random effects models, and fail to provide consistent variance estimators. In this paper, we propose an enhanced Laplace approximation that provides the true maximum likelihood estimator and its consistent variance estimator. We study its relationship with the variational Bayes method. We also define a new restricted maximum likelihood estimator for estimating dispersion parameters and study their asymptotic properties. Enhanced Laplace approximation generally demonstrates how to obtain the true restricted maximum likelihood estimators and their variance estimators. Our numerical studies indicate that the enhanced Laplace approximation provides a satisfactory maximum likelihood estimator and restricted maximum likelihood estimator, as well as their variance estimators in the frequentist perspective. The maximum likelihood estimator and restricted maximum likelihood estimator can be also interpreted as the posterior mode and marginal posterior mode under flat priors, respectively. Furthermore, we present some comparisons with Bayesian procedures under different priors.

What is a standard error? (And how should we compute it?)

I review the definition of a standard error from a frequentist perspective, including both exact analysis and asymptotic analysis. Using the linear model for illustration, I discuss the model-based, design-based, and sampling-based approaches to uncertainty in obtaining standard errors. The model-based approach is widely applicable and produces reasonable measures of estimator precision in many settings. In some situations, particularly in the context of clustering, the model-based approach can suffer from ambiguity, and can lead to standard errors that are systematically biased. A combination of the design-based and sampling-based approaches requires the researcher to think about the variation in key explanatory variables when computing standard errors, and it can even apply to cases where the entire population is observed.

A Flexible Probability Model for Proportion Data: Unit Gumbel Type-II Distribution, Development, Properties, Different Method of Estimations and Applications

In explaining and forecasting real life scenarios, statistical distributions are very helpful. It is very important to select the best fitting statistical distribution for modelling data. In analysis of real world phenomena like in reliability and economics, we may finddistributions for bounded data observed as percentages, proportions or fractions (see, for example, Marshall and Olkin (2007)). In this context, in view of pertinent transformation on the Gumbel Type-II model, we suggest and study the unit Gumbel Type-II (UG-TII)model and explore few of its statistical characteristics. We also consider various methods of estimating the unknown parameters of UG-TII model from the frequentist perspective. Monte Carlo simulations are worked out in order to compare efficiency of suggestedestimation methods for small as well as large samples. The efficiency of estimators is measured using simulated samples in terms of their bias and mean square error. In the end, two datasets have been examined in attempt to validate the realistic possibilities ofnew model. In comparison to the six severe competitors.

An analytically tractable solution for hierarchical Bayesian model updating with variational inference scheme

The hierarchical Bayesian modelling (HBM) framework has recently been proposed to properly account for the model parameter uncertainty in structural dynamics. This framework postulates a hierarchical prior for the model parameters that depend on the hyper parameters to be identified using the multiple datasets. However, the number of hyper parameters increases linearly with the number of model parameters as well as the number of datasets, making the framework computationally challenging and analytically intractable. To this end, this study employs a variational inference scheme within the framework, deriving explicit expressions for the posterior distributions of the hyper parameters and further the predictive distribution of the model parameters so as to avoid resorting to sampling-based strategy, thus efficiently enhancing the computational efficiency of the HBM framework. In particular, the posterior distribution of the hyper parameters is derived as a Normal-Inverse-Wishart (NIW) distribution, and the predictive distribution of the model parameters are expressed as a normal distribution conditional on the samples of its hyper parameters. Such derivations offer valuable insights into the interpretations of different sources of uncertainties existing in the procedure of model updating. Specifically, it reveals that the ensemble uncertainty of the model parameters consists of both the identification uncertainty obtained from each dataset as well as the test-to-test variability across the overall datasets. Additionally, it suggests that, when the test-to-test variability dominates the uncertainty of the model parameters, the HBM framework with negligible identification uncertainty can reduce to the same expression with a frequentist perspective. Linear models with modal properties data and nonlinear models with time histories data of building systems are utilized to verify and demonstrate the effectiveness of the proposed framework. Results indicate that the proposed formulations provide sufficiently accurate solutions with efficient computational performance, compared to the full sampling approach regarded as the reference of the HBM framework.

Enhanced Lot Acceptance Testing Based on Defect Counts and Posterior Odds Ratios

Optimal defects-per-unit test plans based on posterior odds ratios are developed for the disposition of product lots. The number of nonconformities per unit is modeled by the Conway–Maxwell–Poisson distribution rather than the typical Poisson model. In essence, a submitted batch is conforming if its posterior acceptability is sufficiently large. First, a useful approximation of the optimal test plan is derived in closed form using the asymptotic normality of the log ratio. A mixed-integer nonlinear programming problem is then solved via Monte Carlo simulation to find the smallest number of inspected items per lot and the maximum tolerable posterior odds ratio. The methodology is applied to the manufacturing of paper and glass. The suggested sampling plan for lot sentencing provides the specified protections to both manufacturers and customers and minimizes the needed sample size. In terms of inspection effort and accuracy, the proposed approach is virtually an advantageous extension of the classical frequentist perspective. In many practical cases, it yields more precise assessments of the current consumer and producer risks, as well as more realistic decision rules.

Confidence deficits and reducibility: Toward a coherent conceptualization of uncertainty level.

Outside of the field of risk analysis, an important theoretical conversation on the slippery concept of uncertainty has unfolded over the last 40 years within the adjacent field of environmental risk. This literature has become increasingly standardized behind the tripartite distinction between uncertainty location, the nature of uncertainty, and uncertainty level, popularized by the "W&H framework." This article introduces risk theorists and practitioners to the conceptual literature on uncertainty with the goal of catalyzing further development and clarification of the uncertainty concept within the field of risk analysis. It presents two critiques of the W&H framework's dimension of uncertainty level-the dimension that attempts to define the characteristics separating greater uncertainties from lesser uncertainties. First, I argue the framework's conceptualization of uncertainty level lacks a clear and consistent epistemological position and fails to acknowledge or reconcile the tensions between Bayesian and frequentist perspectives present within the framework. This article reinterprets the dimension of uncertainty level from a Bayesian perspective, which understands uncertainty as a mental phenomenon arising from "confidence deficits" as opposed to the ill-defined notion of "knowledge deficits" present in the framework. And second, I elaborate the undertheorized concept of uncertainty "reducibility." These critiques inform a clarified conceptualization of uncertainty level that can be integrated with risk analysis concepts and usefully applied by modelers and decisionmakers engaged in model-based decision support.

Structural reliability analysis: A Bayesian perspective

Numerical methods play a dominant role in structural reliability analysis, and the goal has long been to produce a failure probability estimate with a desired level of accuracy using a minimum number of performance function evaluations. In the present study, we attempt to offer a Bayesian perspective on the failure probability integral estimation, as opposed to the classical frequentist perspective. For this purpose, a principled Bayesian Failure Probability Inference (BFPI) framework is first developed, which allows to quantify, propagate and reduce numerical uncertainty behind the failure probability due to discretization error. Especially, the posterior variance of the failure probability is derived in a semi-analytical form, and the Gaussianity of the posterior failure probability distribution is investigated numerically. Then, a Parallel Adaptive-Bayesian Failure Probability Learning (PA-BFPL) method is proposed within the Bayesian framework. In the PA-BFPL method, a variance-amplified importance sampling technique is presented to evaluate the posterior mean and variance of the failure probability, and an adaptive parallel active learning strategy is proposed to identify multiple updating points at each iteration. Thus, a novel advantage of PA-BFPL is that both prior knowledge and parallel computing can be used to make inference about the failure probability. Four numerical examples are investigated, indicating the potential benefits by advocating a Bayesian approach to failure probability estimation.

Some estimation methods for mixture of extreme value distributions with simulation and application in medicine

In recent years, statisticians have grown increasingly engaged in research of mixture models, particularly in the previous decade, without adequate consideration of challenge of estimating the parameters of mixture models from a frequentist perspective. Except for maximum likelihood estimation, this study addresses this vacuum by discussing the two other classical methods of estimation for mixture model. We commence by briefly describing the three frequentist approaches, namely maximum likelihood, ordinary, and weighted least squares, and then comparing them through extensive numerical simulations. The model’s applicability is illustrated by its application to simulated and real-world data, which yields promising results in terms of enhanced estimation.

The Comparative Effects of Different Types of Oral Vitamin Supplements on Arterial Stiffness: A Network Meta-Analysis.

Arterial stiffness, a significant prognostic factor of cardiovascular disease, may be affected by dietary factors. Research on the effects of oral vitamin supplements on arterial stiffness and/or endothelial function has produced controversial results. Therefore, the aim of this network meta-analysis was to comparatively assess the effect of different types of oral vitamin supplements on arterial stiffness in the adult population. We searched the PubMed, Embase, Cochrane Library, and Web of Science databases for randomized controlled trials from their inception to 30 September 2021. A network meta-analysis using a frequentist perspective was conducted to assess the effects of different types of oral vitamin supplements on arterial stiffness, as determined by pulse wave velocity. In total, 22 studies were included, with a total of 1318 participants in the intervention group and 1115 participants in the placebo group. The included studies were listed in an ad hoc table describing direct and indirect comparisons of the different types of vitamins. Our findings showed that, in both pairwise comparison and frequentist network meta-analysis, the different types of oral vitamin supplements did not show statistically significant effects on arterial stiffness. However, when oral vitamin supplementation was longer than 12 weeks, vitamin D3 showed a significant reduction in arterial stiffness, compared with the placebo (ES: −0.15; 95% CI: −0.30, −0.00; −60.0% m/s) and vitamin D2 (ES: −0.25; 95% CI: −0.48, −0.02, −52.0% m/s). In summary, our study confirms that oral vitamin D3 supplementation for more than 12 weeks could be an effective approach to reduce arterial stiffness and could be considered a useful approach to improve vascular health in patients at high risk of cardiovascular disease.

Bland–Altman Limits of Agreement from a Bayesian and Frequentist Perspective

Bland–Altman agreement analysis has gained widespread application across disciplines, last but not least in health sciences, since its inception in the 1980s. Bayesian analysis has been on the rise due to increased computational power over time, and Alari, Kim, and Wand have put Bland–Altman Limits of Agreement in a Bayesian framework (Meas. Phys. Educ. Exerc. Sci. 2021, 25, 137–148). We contrasted the prediction of a single future observation and the estimation of the Limits of Agreement from the frequentist and a Bayesian perspective by analyzing interrater data of two sequentially conducted, preclinical studies. The estimation of the Limits of Agreement θ1 and θ2 has wider applicability than the prediction of single future differences. While a frequentist confidence interval represents a range of nonrejectable values for null hypothesis significance testing of H0: θ1 ≤ −δ or θ2 ≥ δ against H1: θ1 &gt; −δ and θ2 &lt; δ, with a predefined benchmark value δ, Bayesian analysis allows for direct interpretation of both the posterior probability of the alternative hypothesis and the likelihood of parameter values. We discuss group-sequential testing and nonparametric alternatives briefly. Frequentist simplicity does not beat Bayesian interpretability due to improved computational resources, but the elicitation and implementation of prior information demand caution. Accounting for clustered data (e.g., repeated measurements per subject) is well-established in frequentist, but not yet in Bayesian Bland–Altman analysis.

A novel statistical test for treatment differences in clinical trials using a response-adaptive forward-looking Gittins Index Rule.

The most common objective for response-adaptive clinical trials is to seek to ensure that patients within a trial have a high chance of receiving the best treatment available by altering the chance of allocation on the basis of accumulating data. Approaches that yield good patient benefit properties suffer from low power from a frequentist perspective when testing for a treatment difference at the end of the study due to the high imbalance in treatment allocations. In this work we develop an alternative pairwise test for treatment difference on the basis of allocation probabilities of the covariate-adjusted response-adaptive randomization with forward-looking Gittins Index (CARA-FLGI) Rule for binary responses. The performance of the novel test is evaluated in simulations for two-armed studies and then its applications to multiarmed studies are illustrated. The proposed test has markedly improved power over the traditional Fisher exact test when this class of nonmyopic response adaptation is used. We also find that the test's power is close to the power of a Fisher exact test under equalrandomization.

Radiography and Clinical Decision-Making in Chiropractic.

The concern over x-ray exposure risks can overshadow the potential benefit of radiography, especially in cases where manual therapy is employed. Spinal malalignment cannot be accurately visualized without imaging. Manual therapy and the load tolerances of injured spinal tissues raise different criteria for the use of x-rays for spinal disorders than in medical practice. Current regulatory bodies rely on radiography risk assessments based on Linear-No-Threshold (LNT) risk models. There is a need to consider radiography guidelines for chiropractic which are different from those for medical practice. Radiography practice guidelines are summaries dominated by frequentist interpretations in the analysis of data from studies. In contrast, clinicians often employ a pseudo-Bayesian form of reasoning during the clinical decision-making process. The overrepresentation of frequentist perspectives in evidence-based practice guidelines alter decision-making away from practical assessment of a patient’s needs, toward an overly cautious standard applied to patients without regard to their risk/benefit likelihoods relating to radiography. Guidelines for radiography in chiropractic to fully assess the condition of the spine and spinal alignment prior to manual therapy, especially with high velocity, low amplitude spinal manipulation (HVLA-SM), should necessarily differ from those used in medical practice.

Standard Tone Stability as a Manipulation of Precision in the Oddball Paradigm: Modulation of Prediction Error Responses to Fixed-Probability Deviants

Electrophysiological sensory deviance detection signals, such as the mismatch negativity (MMN), have been interpreted from the predictive coding framework as manifestations of prediction error (PE). From a frequentist perspective of the classic oddball paradigm, deviant stimuli are unexpected because of their low probability. However, the amount of PE elicited by a stimulus can be dissociated from its probability of occurrence: when the observer cannot make confident predictions, any event holds little surprise value, no matter how improbable. Here we tested the hypothesis that the magnitude of the neural response elicited to an improbable sound (D) would scale with the precision of the prediction derived from the repetition of another sound (S), by manipulating repetition stability. We recorded the Electroencephalogram (EEG) from 20 participants while passively listening to 4 types of isochronous pure tone sequences differing in the probability of the S tone (880 Hz) while holding constant the probability of the D tone [1,046 Hz; p(D) = 1/11]: Oddball [p(S) = 10/11]; High confidence (7/11); Low confidence (4/11); and Random (1/11). Tones of 9 different frequencies were equiprobably presented as fillers [p(S) + p(D) + p(F) = 1]. Using a mass-univariate non-parametric, cluster-based correlation analysis controlling for multiple comparisons, we found that the amplitude of the deviant-elicited ERP became more negative with increasing S probability, in a time-electrode window consistent with the MMN (ca. 120–200 ms; frontal), suggesting that the strength of a PE elicited to an improbable event indeed increases with the precision of the predictive model.

Exact equal-tailed β-expectation tolerance intervals for sample variances

The sample variance of the quality characteristic shows the variation of a product or process. When the precision is a concern, a tolerance interval (TI) for sample variances is needed. In this paper, we construct β-expectation TIs for the population of sample variances, assuming normality of the data, from the frequentist and Bayesian perspectives. The accuracy level of each TI, which is the probability that the actual coverage falls into a specified range, is calculated to evaluate the performance of the TI. Besides, the determination of the minimum number of subgroups and the minimum subgroup size is discussed to achieve the desired accuracy level. When the accuracy level, the number of subgroups and subgroup size are known, the maximum variation is also calculated to measure the goodness of the proposed TI. Comparison results show that a Bayesian TI outperforms the corresponding frequentist TI. A real example is used to demonstrate the applicability and implementations of the proposed TIs.

1215Considerations for using multiple imputation in propensity score-weighted analysis

1215Considerations for using multiple imputation in propensity score-weighted analysis

Influence Diagnostics for Correlated Binomial Regression Models: An Application to a Data Set on High-Cost Health Services Occurrence

This paper considers a frequentist perspective to deal with the class of correlated binomial regression models (Pires &amp; Diniz, 2012), thus providing a new approach to analyze correlated binary response variables. Model parameters are estimated by direct maximization of the log-likelihood function. We also consider a diagnostic analysis under the correlated binomial regression model setup, which is performed considering residuals based on predictive values and deviance residuals (Cook &amp; Weisberg, 1982) to check for model assumptions, and global in˛uence measure based on case-deletion (Cook, 1977) to detect in˛uential observations. Moreover, a sensitivity analysis is carried out to detect possible in˛uential observations that could a˙ect the inferential results. This is done using local in˛uence metrics (Cook, 1986) with case-weight, response, and covariate perturbation schemes. A simulation study is conducted to assess the frequentist properties of model parameter estimates and check the performance of the considered diagnostic metrics under the correlated binomial regression model. A data set on high-cost claims made to a private health care provider in Brazil is analyzed to illustrate the proposed methodology.

Is convalescent plasma futile in COVID-19? A Bayesian re-analysis of the RECOVERY randomized controlled trial

BackgroundRandomized trials are generally performed from a frequentist perspective, which can conflate absence of evidence with evidence of absence. The RECOVERY trial evaluated convalescent plasma for patients hospitalized with coronavirus disease 2019 (COVID-19) and concluded that there was no evidence of an effect. Re-analysis from a Bayesian perspective is warranted. MethodsOutcome data were extracted from the RECOVERY trial by serostatus and time of presentation. A Bayesian re-analysis with a wide variety of priors (vague, optimistic, sceptical, and pessimistic) was performed, calculating the posterior probability for: any benefit, an absolute risk difference of 0.5% (small benefit, number needed to treat 200), and an absolute risk difference of one percentage point (modest benefit, number needed to treat 100). ResultsAcross all patients, when analysed with a vague prior, the likelihood of any benefit or a modest benefit with convalescent plasma was estimated to be 64% and 18%, respectively. The estimated chance of any benefit was 95% if presenting within 7 days of symptoms, or 17% if presenting after this. In patients without a detectable antibody response at presentation, the chance of any benefit was 85%. However, it was only 20% in patients with a detectable antibody response at presentation. ConclusionsBayesian re-analysis suggests that convalescent plasma reduces mortality by at least one percentage point among the 39% of patients who present within 7 days of symptoms, and that there is a 67% chance of the same mortality reduction in the 38% who are seronegative at the time of presentation. This is in contrast to the results in people who already have antibodies when they present. This biologically plausible finding bears witness to the advantage of Bayesian analyses over misuse of hypothesis tests to inform decisions.