Coverage Probability Research Articles

Confidence Intervals for Ratios of the Coefficients of Variation of the Delta-Birnbaum-Saunders Distributions

The Delta-Birnbaum-Saunders distribution is a combination of positive values that follow the Birnbaum-Saunders distribution and zeros that follow the binomial distribution, making it a relatively new distribution. The coefficient of variation is calculated as the ratio of the standard deviation to the mean. It is important for comparing the dispersion of datasets. Therefore, this paper aims to generate confidence intervals for ratios of coefficients of variation under the Delta-Birnbaum-Saunders distributions. We have proposed four methods for constructing confidence intervals, namely, the method of variance estimates recovery, the bootstrap confidence interval, the generalized confidence interval based on the variance stabilized transformation, and the generalized confidence interval based on the Wilson score method. The assessment of their performance relies on coverage probabilities and average widths obtained through Monte Carlo simulations. The overall study results reveal that the generalized confidence interval based on the variance stabilized transformation and the generalized confidence interval based on the Wilson score methods provide similar values in both the coverage probabilities and average widths, making them the two most efficient methods. Furthermore, it was found that the method of variance estimates recovery performs well when the shape parameters are small. Finally, all the proposed methods will be applied to wind speed data in Thailand.

A Bayesian Approach to Correcting the Attenuation Bias of Regression Using Polygenic Risk Score.

Polygenic risk score (PRS) has become increasingly popular for predicting the value of complex traits. In many settings, PRS is used as a covariate in regression analysis to study the association between different phenotypes. However, measurement error in PRS causes attenuation bias in the estimation of regression coefficients. In this paper, we employ a Bayesian approach to accounting for the measurement error of PRS and correcting the attenuation bias in linear and logistic regression. Through simulation, we show that our approach is able to obtain approximately unbiased estimation of coefficients and credible intervals with correct coverage probability. We also empirically compare our Bayesian measurement error model to the conventional regression model by analyzing real traits in the UK Biobank. The results demonstrate the effectiveness of our approach as it significantly reduces the error in coefficient estimates.

Obtaining a Bayesian Estimate of Coefficient Alpha Using a Posterior Normal Distribution.

A new alternative to obtain a Bayesian estimate of coefficient alpha through a posterior normal distribution is proposed and assessed through percentile, normal-theory-based, and highest probability density credible intervals in a simulation study. The results indicate that the proposed Bayesian method to estimate coefficient alpha has acceptable coverage probability performance across the majority of investigated simulation conditions.

Towards 6G Energy Sustainability: Effect of a Reduced UAV Power Control Factor on Downlink Transmission

Unmanned Aerial Vehicles (UAVs) have emerged as crucial components of 5G Internet of Things (IoT) networks, expanding coverage and capacity in various applications. While prior research has extensively examined the impact of power control factor adjustments on UAV uplink transmission, limited attention has been devoted to UAV downlink transmission, which is vital for seamless connectivity and quality of service. In this study, we address this research gap by investigating the effects of reduced power control factors on UAV downlink transmission. We use MATLAB simulations to model how user equipment (UE) is randomly placed in a UAV network. We then check the coverage probability and spectral efficiency for UAV altitudes between 200 and 500 m, taking into account different power control factors in the downlink transmission. Our findings show that a certain threshold of 0.05 for the power control factor keeps coverage probabilities at different heights, making sure that served UEs have enough signal strength. Surprisingly, there is no significant change in spectral efficiency when compared to the baseline results. This means that lowering the power control factor does not hurt spectral efficiency in UAV downlink transmission. These results help us figure out how to make UAV communication work better in 5G IoT networks. They also help us make smart choices about how to change the power to make up for lost downlink signals while keeping the quality of service high. Moreover, our study lays the groundwork for future research in UAV deployment and communication optimization within advanced wireless networks.

A Decade of Oocyte Cryopreservation: New Horizons in Patients Accessing Care.

Objective: Utilization of fertility preservation treatments has increased since the American Society for Reproductive Medicine lifted the "experimental" label for oocyte cryopreservation in 2012. This study characterizes changes in insurance coverage, clinical outcomes, and live birth probabilities over a span of a decade (2012-2022) in patients who underwent planned oocyte cryopreservation. Methods: Retrospective analysis of planned oocyte cryopreservation cycles using vitrification from 2012 to 2022. Medically indicated cycles were excluded. Age, anti-mullerian hormone (AMH), number of mature oocytes vitrified, and insurance coverage were evaluated by year of procedure. Comparative statistics were performed using Kruskal-Wallis and chi-square analysis. Linear regression models and Cochran-Armitage trend test were performed to determine the relationships between each variable and time. Result(s): A total of 4,544 planned oocyte cryopreservation cycles were included. Mean age at egg retrieval decreased significantly over time (37.9 ± 2.9 years versus 34.9 ± 3.3, p < 0.0001). Mature oocytes frozen per cycle rose significantly over time (10.7 ± 7.4 in 2012 versus 13.3 ± 8.6 in 2022, p ≤ 0.0001). Cycles with insurance coverage significantly increased, 0% covered in 2012 versus 46.9% covered in 2022 (p ≤ 0.0001). Conclusions: Since 2012, patient age at time of egg freezing has decreased, coinciding with a mean increase in AMH and number of mature oocytes frozen per cycle. Younger participation in extending fertility is likely driven by a boost in social awareness regarding reproductive aging, cryopreservation technologies, and improved access to treatment. Modern oocyte cryopreservation includes more access to insurance coverage, shown by nearly half of current cycles benefiting from plan support. Shifts in patient demographics and insurance coverage, paired with updates to stimulation protocols that optimize oocyte yield, are expected to improve the overall prognosis and future fertility of patients who utilize thawed oocytes.

Nonparametric simultaneous tolerance intervals for small dimensions based on kernel density estimates

The tolerance interval plays an important role in many applications. Its property of containing a specified proportion of sampled population values with high degree of confidence makes its computation meaningful. Whenever there are several populations, it may be of interest to perform simultaneous inference. For this reason, this study proposes methods to construct simultaneous tolerance intervals (STIs). Furthermore, since in many cases of practical applications the underlying distribution is unknown, the proposed STIs are derived under a nonparametric setting. The proposed procedures and algorithms are then assessed through performance metrics, such as estimated coverage probabilities and expected lengths. The performance of the proposed methodology is also compared with the Bonferroni correction approach. The proposed methods show accurate results, with coverage probabilities close to the nominal level. The nonparametric STIs computed using the proposed methods are generally better than the ones obtained through a Bonferroni-corrected approach. A real-life application on the assessment of liver function is presented to illustrate the use of the proposed method.

Methods to Adjust for Confounding in Test-Negative Design COVID-19 Effectiveness Studies: Simulation Study.

Real-world COVID-19 vaccine effectiveness (VE) studies are investigating exposures of increasing complexity accounting for time since vaccination. These studies require methods that adjust for the confounding that arises when morbidities and demographics are associated with vaccination and the risk of outcome events. Methods based on propensity scores (PS) are well-suited to this when the exposure is dichotomous, but present challenges when the exposure is multinomial. This simulation study aimed to investigate alternative methods to adjust for confounding in VE studies that have a test-negative design. Adjustment for a disease risk score (DRS) is compared with multivariable logistic regression. Both stratification on the DRS and direct covariate adjustment of the DRS are examined. Multivariable logistic regression with all the covariates and with a limited subset of key covariates is considered. The performance of VE estimators is evaluated across a multinomial vaccination exposure in simulated datasets. Bias in VE estimates from multivariable models ranged from -5.3% to 6.1% across 4 levels of vaccination. Standard errors of VE estimates were unbiased, and 95% coverage probabilities were attained in most scenarios. The lowest coverage in the multivariable scenarios was 93.7% (95% CI 92.2%-95.2%) and occurred in the multivariable model with key covariates, while the highest coverage in the multivariable scenarios was 95.3% (95% CI 94.0%-96.6%) and occurred in the multivariable model with all covariates. Bias in VE estimates from DRS-adjusted models was low, ranging from -2.2% to 4.2%. However, the DRS-adjusted models underestimated the standard errors of VE estimates, with coverage sometimes below the 95% level. The lowest coverage in the DRS scenarios was 87.8% (95% CI 85.8%-89.8%) and occurred in the direct adjustment for the DRS model. The highest coverage in the DRS scenarios was 94.8% (95% CI 93.4%-96.2%) and occurred in the model that stratified on DRS. Although variation in the performance of VE estimates occurred across modeling strategies, variation in performance was also present across exposure groups. Overall, models using a DRS to adjust for confounding performed adequately but not as well as the multivariable models that adjusted for covariates individually.

Comparative evaluation of four exome enrichment solutions in 2024: Agilent, Roche, Vazyme and Nanodigmbio

Whole exome sequencing (WES) is essential for identifying genetic variants linked to diseases. This study compares available to date four exome enrichment kits: Agilent SureSelect Human All Exon v8, Roche KAPA HyperExome, Vazyme VAHTS Target Capture Core Exome Panel, and Nanodigmbio NEXome Plus Panel v1. We evaluated target design, coverage statistics, and variant calling accuracy across these four different exome capture products. All kits showed high target coverage, with 10x coverage exceeding 97.5% and 20x coverage above 95%. Roche exhibited the most uniform coverage, indicated by the lowest fold-80 scores, while Nanodigmbio had more on-target reads due to fewer off-target reads. Variant calling performance, evaluated using in-lab standard E701 DNA sample, showed high recall rates for all kits, especially Agilent v8. All kits achieved an F-measure above 95.87%. Nanodigmbio had the highest precision with the fewest false positives but a slightly lower F-measure than other kits. This study also highlights the performance of new solutions from Vazyme (China) and Nanodigmbio (China), which were comparable to Agilent v8 and Roche KAPA kits. These findings assist researchers and clinicians in selecting appropriate exome capture solutions.

Bayesian method for comparing F1 scores in the absence of a gold standard

ABSTRACT In the field of medicine, evaluating the diagnostic performance of new diagnostic methods can be challenging, especially in the absence of a gold standard. This study proposes a methodology for assessing the performance of diagnostic tests by estimating the posterior distribution of the F 1 score using latent class analysis, without relying on a gold standard. The proposed method utilizes Markov Chain Monte Carlo sampling to estimate the posterior distribution of the F 1 score, enabling a comprehensive evaluation of diagnostic test methods. By applying this method to internet addiction, we demonstrate how latent class analysis can be effectively used to assess diagnostic performance, offering a practical solution for situations where no gold standard is available. The effectiveness of the proposed approach was evaluated through simulation studies by examining the coverage probability of the 95% highest density interval of the estimated posterior distributions.

Objective Bayesian inference for Birnbaum–Saunders distributions

This paper proposes a Bayesian analysis for the Birnbaum–Saunders distribution and develops noninformative priors for the scale and shape parameters. Probability matching and reference priors are derived for the shape parameter, finding that the second-order matching prior is a high posterior density (HPD) matching prior but not a cumulative density function (CDF) matching prior. For the scale parameter, the second-order matching prior is confirmed to be an HPD matching prior and CDF matching prior but does not match the alternative coverage probabilities up to the second order. The one-at-a-time reference prior and Jeffreys prior satisfy a first-order matching criterion but are not second-order matching priors. The developed priors cause improper posteriors; therefore, modified noninformative priors are suggested that use matching priors with desirable properties. A simulation study demonstrates that these modified matching priors accurately match the target coverage probabilities in a frequentist sense. Two actual examples are provided to illustrate the findings.

A comparison of confidence interval methods for the intraclass correlation coefficient based on the one-way random effects model

Abstract Intraclass correlation coefficients are widely used not only in medicine but also in various other fields. This study focuses on the intraclass correlation coefficient based on the one-way random effects model. We review the methods for constructing confidence intervals and compare their performance through simulations. Donner and Wells (Biometrics 42:401–412, 1986) and Ukoumunne (Stat Med 21(24):3757–3774, 2002) conducted simulation studies to compare some methods. However, in this study, we also include methods developed after their studies. These include a method based on the nonparametric bootstrap by Ukoumunne et al. (Stat Med 22(24):3805–3821, 2003), a method based on the restricted maximum likelihood (REML) by Burch (Comput Stat Data Anal 55(2):1018–1028, 2011), and a method based on the beta distribution by Demetrashvili et al. (Stat Methods Med Res 25(5):2359–2376, 2016). Our simulations reveal that under the normality of random effects and errors, the REML-based method performs best overall in terms of coverage probability of confidence intervals, upper and lower error rates, and mean interval width.

Objective Bayesian analysis of common quantiles of normal distributions

. Many procedures can assess the equivalence of the means or medians between groups when comparing several independent populations. However, neither the mean nor median captures the entire distribution. We propose a Bayesian approach for the quantiles of several normal distributions, focusing on developing non informative priors to compare the quantiles of multiple populations. Further, reference priors and first- and second-order matching priors are developed. The second-order matching prior does not exist, and the reference priors do not satisfy a first-order matching criterion. In addition, conditions for proper posterior distributions for general priors, including developed priors, are provided. Finally, simulations include a real-world example to demonstrate the proposed approach. The numerical studies indicate that the matching prior performs better than the reference prior and Jeffreys’ prior in terms of matching the frequentist target coverage probabilities, and shows good performance even in small sample sizes. Moreover, the matching prior is not affected by the values of parameters, the number of populations, and does not depend on the values of pth quantile

Bayesian doubly robust estimation of causal effects for clustered observational data

Observational data often exhibit clustered structure, which leads to inaccurate estimates of exposure effect if such structure is ignored. To overcome the challenges of modelling the complex confounder effects in clustered data, we propose a Bayesian doubly robust estimator of causal effects with random intercept BART to enhance the robustness against model misspecification. The proposed approach incorporates the uncertainty in the estimation of the propensity score, potential outcomes and the distribution of individual-level and cluster-level confounders into the exposure effect estimation, thereby improving the coverage probability of interval estimation. We evaluate the proposed method in the simulation study compared with frequentist doubly robust estimators with parametric and nonparametric multilevel modelling strategies. The proposed method is applied to estimate the effect of limited food access on the mortality of cardiovascular disease in the senior population.

Parametric bootstrap and fiducial inference for two-sample problems: two-parameter Maxwell distributions

Construction of confidence intervals (CIs) for the difference between means and for the ratio of means of two Maxwell distributions is considered. CIs based on the fiducial approach and parametric bootstrap method are proposed and compared with respect to coverage probability and precision. These methods are also extended to find CIs for a difference between percentiles and for a ratio of percentiles of two Maxwell distributions. In particular, CIs for the ratio of the 5th percentiles and for the ratio of the medians are developed and evaluated for accuracy in terms of coverage probability and compared in terms of precision. The methods are illustrated using two examples with real life data.

Reproducibility and repeatability of 18F-(2S, 4R)-4-fluoroglutamine PET imaging in preclinical oncology models.

Measurement of repeatability and reproducibility (R&R) is necessary to realize the full potential of positron emission tomography (PET). Several studies have evaluated the reproducibility of PET using 18F-FDG, the most common PET tracer used in oncology, but similar studies using other PET tracers are scarce. Even fewer assess agreement and R&R with statistical methods designed explicitly for the task. 18F-(2S, 4R)-4-fluoro-glutamine (18F-Gln) is a PET tracer designed for imaging glutamine uptake and metabolism. This study illustrates high reproducibility and repeatability with 18F-Gln for in vivo research. Twenty mice bearing colorectal cancer cell line xenografts were injected with ~9 MBq of 18F-Gln and imaged in an Inveon microPET. Three individuals analyzed the tumor uptake of 18F-Gln using the same set of images, the same image analysis software, and the same analysis method. Scans were randomly re-ordered for a second repeatability measurement 6 months later. Statistical analyses were performed using the methods of Bland and Altman (B&A), Gauge Reproducibility and Repeatability (Gauge R&R), and Lin's Concordance Correlation Coefficient. A comprehensive equivalency test, designed to reject a null hypothesis of non-equivalence, was also conducted. In a two-way random effects Gauge R&R model, variance among mice and their measurement variance were 0.5717 and 0.024. Reproducibility and repeatability accounted for 31% and 69% of the total measurement error, respectively. B&A repeatability coefficients for analysts 1, 2, and 3 were 0.16, 0.35, and 0.49. One-half B&A agreement limits between analysts 1 and 2, 1 and 3, and 2 and 3 were 0.27, 0.47, and 0.47, respectively. The mean square deviation and total deviation index were lowest for analysts 1 and 2, while coverage probabilities and coefficients of the individual agreement were highest. Finally, the definitive agreement inference hypothesis test for equivalency demonstrated that all three confidence intervals for the average difference of means from repeated measures lie within our a priori limits of equivalence (i.e. ± 0.5%ID/g). Our data indicate high individual analyst and laboratory-level reproducibility and repeatability. The assessment of R&R using the appropriate methods is critical and should be adopted by the broader imaging community.

Effects of Anti-Seizure Medications on Resting-State Functional Networks in Juvenile Myoclonic Epilepsy: An EEG Microstate Analysis

ObjectiveJuvenile myoclonic epilepsy (JME) is associated with large-scale brain network dysfunction. This study aims to investigate how anti-seizure medication (ASM) treatment alters resting-state functional networks in JME patients through resting-state EEG microstate analysis. MethodsNinety-six subjects participated in this study: 24 healthy controls (HC), 29 newly diagnosed JME patients who had not started ASMs therapy (JME-NM), and 43 JME patients on ASMs treatment with effective seizure control (JME-M). EEG data were collected for 10 minutes while participants were awake and resting with their eyes closed, using a standard 19-channel recording system. EEG topographies were categorized into four microstate classes (A, B, C, D), and parameters such as mean duration, occurrence rate, time coverage, and transition probabilities between microstates were computed and compared among the three groups. Advanced statistical methods were employed to ensure the robustness and validity of the findings. ResultsSignificant alterations in EEG microstate characteristics were observed in untreated JME patients (JME-NM) compared to both healthy controls and treated patients. Microstate B had a markedly reduced mean duration in the JME-NM group, while microstate A displayed an increased occurrence rate and greater time coverage. Transition probabilities between specific microstates, such as from A to C, A to D, and B to C, were also significantly different in the JME-NM group. The normalization of these parameters in the JME-M group suggests that ASMs effectively stabilize altered brain networks, potentially mitigating the pathophysiological disruptions associated with JME. ConclusionThis study demonstrates that ASMs effectively normalize disruptions in sensory-motor and visual networks in JME patients. EEG microstate analysis provides a dynamic view of brain network alterations and offers potential as a biomarker for the diagnosis and monitoring of JME, as well as for evaluating treatment response. These findings advance our understanding of the neurophysiological mechanisms underlying JME.

Coverage Probability of RIS-Assisted Wireless Communication Systems with Random User Deployment over Nakagami-$m$ Fading Channel

Coverage Probability of RIS-Assisted Wireless Communication Systems with Random User Deployment over Nakagami-$m$ Fading Channel

Uncertainty prediction of wind speed based on improved multi-strategy hybrid models

&lt;p&gt;Accurate interval prediction of wind speed plays a vital role in ensuring the efficiency and stability of wind power generation. Due to insufficient traditional wind speed interval prediction methods for mining nonlinear features, in this paper, a novel interval prediction method was proposed by combining improved wavelet threshold and deep learning (BiTCN-BiGRU) with the nutcracker optimization algorithm (NOA). First, NOA was used to optimize the wavelet transform (WT) and BiTCN-BiGRU. Second, we applied NOA-WT to smooth the wind speed data. Then, to capture nonlinear features of time series, phase space reconstruction (PSR) was utilized to identify chaotic characteristics of the processed data. Finally, the NOA-BiTCN-BiGRU model was built to perform wind speed interval prediction. Under the same hyperparameters and network structure settings, a comparison with other deep learning methods showed that the prediction interval coverage probability (PICP) and prediction interval mean width (PIMW) of NOA-WT-BiTCN-BiGRU model achieves the best balance, with good prediction accuracy and generalization performance. This research can provide reference and guidance for nonlinear time-series interval prediction in the real world.&lt;/p&gt;

CooccurrenceAffinity: An R package for computing a novel metric of affinity in co-occurrence data that corrects for pervasive errors in traditional indices.

1. Analysis of co-occurrence data with traditional indices has led to many problems such as sensitivity of the indices to prevalence and the same value representing either a strong positive or strong negative association across different datasets. In our recent study (Mainali et al 2022), we revealed the source of the problems that make the traditional indices fundamentally flawed and unreliable-namely that the indices in common use have no target of estimation quantifying degree of association in the non-null case-and we further developed a novel parameter of association, alpha, with complete formulation of the null distribution for estimating the mechanism of affinity. We also developed the maximum likelihood estimate (MLE) of alpha in our previous study. 2. Here, we introduce the CooccurrenceAffinity R package that computes the MLE for alpha. We provide functions to perform the analysis based on a 2×2 contingency table of occurrence/co-occurrence counts as well as a m×n presence-absence matrix (e.g., species by site matrix). The flexibility of the function allows a user to compute the alpha MLE for entity pairs on matrix columns based on presence-absence states recorded in the matrix rows, or for entity pairs on matrix rows based on presence-absence recorded in columns. We also provide functions for plotting the computed indices. 3. As novel components of this software paper not reported in the original study, we present theoretical discussion of a median interval and of four types of confidence intervals. We further develop functions (a) to compute those intervals, (b) to evaluate their true coverage probability of enclosing the population parameter, and (c) to generate figures. 4. CooccurrenceAffinity is a practical and efficient R package with user-friendly functions for end-to-end analysis and plotting of co-occurrence data in various formats, making it possible to compute the recently developed metric of alpha MLE as well as its median and confidence intervals introduced in this paper. The package supplements its main output of the novel metric of association with the three most common traditional indices of association in co-occurrence data: Jaccard, Sørensen-Dice, and Simpson.

Understanding and overcoming geographical barriers for scaling up dog vaccinations against rabies

Rabies causes 59,000 human deaths annually in over 150 countries. Mass dog vaccination (MDV) is key to controlling dog rabies, requiring 70% coverage in the susceptible dog population to eliminate rabies deaths. MDV campaigns must achieve geographical homogeneity of coverage. Although rabies elimination is feasible, operation challenges exist, especially in hard-to-reach areas. We conducted geospatial modelling to identify geographical factors affecting MDV success in terms of campaign completeness and vaccination coverage across 25 districts in south-eastern Tanzania. From October 2016 to January 2017, about 81,000 dogs were vaccinated in 1,379 (68%) villages within these districts. Multivariable regression analysis revealed that land cover, residence, poverty, and elevation were associated with campaign completeness. The odds of achieving completeness in croplands were 1.75 times higher compared to forests. Vaccination coverage was influenced by residence, area, poverty index, and elevation, with urban areas having lower odds of achieving coverage compared to rural areas. Coverage probabilities exceeding 70% were lower on islands, highlands, urban areas, and areas bordering protected areas. As the 2030 deadline for "zero dog-mediated human rabies deaths" approaches, operational and logistical challenges in MDV campaigns persist. Our data provide insights into MDV success and failure, guiding future control efforts to improve their effectiveness.