Bootstrap Confidence Intervals Research Articles

On the assessment of the ability of measurements, nowcasts, and forecasts to track changes.

Measurements, nowcasts, or forecasts ideally should correctly reflect changes in the values of interest. In this article, we focus on how to assess the ability of measurements, nowcasts, or forecasts to correctly predict the direction of changes in values - which we refer to as the ability to track changes (ATC). We review and develop visual techniques and quantitative measures to assess ATC. Extensions for noisy data and estimation uncertainty are implemented using bootstrap confidence intervals and exclusion areas. We exemplarily illustrate the proposed methods to assess the ability to track changes for nowcasting during the COVID-19 pandemic, patient admissions to an emergency department, and non-invasive blood pressure measurements. The proposed methods effectively evaluate ATC across different applications. The developed ATC assessment methods offer a comprehensive toolkit for evaluating the ATC of measurements, nowcasts, and forecasts. These techniques provide valuable insights into model performance, complementing traditional accuracy measures and enabling more informed decision-making in various fields, including public health, healthcare management, and medical diagnostics.

Prediction of electroconvulsive therapy outcome: A network analysis approach.

While electroconvulsive therapy (ECT) for the treatment of major depressive disorder is effective, individual response is variable and difficult to predict. These difficulties may in part result from heterogeneity at the symptom level. We aim to predict remission using baseline depression symptoms, taking the associations among symptoms into account, by using a network analysis approach. We combined individual patient data from two randomized controlled trials (total N = 161) and estimated a Mixed Graphical Model to estimate which baseline depression symptoms (corresponding to HRSD-17 items) uniquely predicted remission (defined as either HRSD≤7 or MADRS<10). We included study as moderator to evaluate study heterogeneity. For symptoms directly predictive of remission we computed odds ratios. Three baseline symptoms were uniquely predictive of remission: suicidality negatively predicted remission (OR = 0.75; bootstrapped confidence interval (bCI) = 0.44-1.00) whereas retardation (OR = 1.21; bCI = 1.00-2.02) and hypochondriasis (OR = 1.31; bCI = 1.00-2.25) positively predicted remission. The estimated effects did not differ across trials as no moderation effects were found. By using a network analysis approach this study identified that the presence of suicidal ideation predicts an overall worse treatment outcome. Psychomotor retardation and hypochondriasis, on the other hand, seem to be associated with a better outcome.

Optimal Estimation of Reliability Parameters for Modified Frechet-Exponential Distribution Using Progressive Type-II Censored Samples with Mechanical and Medical Data

The aim of this research is to estimate the parameters of the modified Frechet-exponential (MFE) distribution using different methods when applied to progressive type-II censored samples. These methods include using the maximum likelihood technique and the Bayesian approach, which were used to determine the values of parameters in addition to calculating the reliability and failure functions at time t. The approximate confidence intervals (ACIs) and credible intervals (CRIs) are derived for these parameters. Two bootstrap techniques of parametric type are provided to compute the bootstrap confidence intervals. Both symmetric loss functions such as the squared error loss (SEL) and asymmetric loss functions such as the linear-exponential (LINEX) loss are used in the Bayesian method to obtain the estimates. The Markov Chain Monte Carlo (MCMC) technique is utilized in the Metropolis–Hasting sampler approach to obtain the unknown parameters using the Bayes approach. Two actual datasets are utilized to examine the various progressive schemes and different estimation methods considered in this paper. Additionally, a simulation study is performed to compare the schemes and estimation techniques.

Confidence intervals of difference and ratio between two means of delta-Birnbaum-Saunders distributions

During the dry season, the northern region of Thailand consistently grapples with compromised air quality, notably an excessive level of particulate matter with a diameter of less than 2.5 microns (PM2.5), which poses implications for public health. Wind speed emerges as the primary factor that diminishes the concentration of PM2.5, making the evaluation of wind speed changes crucial in understanding and potentially mitigating the impact of air pollution on public health in the region. The wind speed data contain zero and positive values. This can be estimated through the confidence intervals of the difference and ratio between two means of delta-Birnbaum-Saunders distributions using various methods, including the generalized confidence interval (GCI), bootstrap confidence interval (BCI), and generalized fiducial confidence interval (GFCI). These methods rely on variance stabilizing transformations (VST), the Wilson and Hannig methods. According to the simulation, for small sample sizes, the GCI based on the VST and Hannig was the most effective method in terms of coverage probabilities and average lengths. For medium sample sizes, it was found that the performance of GFCI based on the VST method was superior to other methods. Additionally, when confronted with a large sample size, the BCI based on the VST method becomes relevant and will be introduced. To demonstrate the efficacy of our proposed methods, we applied them to wind speed data gathered from Chiang Mai Airport station in Thailand from January to February in both 2022 and 2023.

Updated CP*Trends: An Online Tool to Compare Cohort and Period Trends across Cancer Sites.

CP*Trends is a widely used SEER website used to explore temporal effects of period and cohort on cancer incidence and mortality. It provides a graphical display of smoothed rates, and a C-P Score that helps to assess the magnitude of the effect of cohort and period. This update provides results for African Americans and Whites. The C-P Score has an intrinsic bias favoring cohort because there are many more cohorts than periods. An adjusted C-P Score removes some of this advantage. Bootstrap confidence intervals are given, which allow one to see the effects of different sample sizes on the model results. Finally, users may control window size used in the smoothing algorithm, which helps to avoid over smoothing or masking of trends. The method is illustrated using data on cervical cancer incidence trends for African Americans and Whites, 1975-2018. Rates are higher for African Americans, and both races have contributions for cohort. However, the period effect is only strongly evident in Whites. Visual inspection of White trends suggests possible differences for those older and younger than age 50. These methods are applied in an interactive website displaying incidence and mortality trends for over 20 cancer sites in the US.

On the Replicability of the Thermodynamic Modeling of Spectroscopic Titration Data in the Nickel(II) En System

ABSTRACTCharacterizing complicated solution phase systems in situ requires advanced modeling techniques to capture the intricate balances between the many chemical species. Due to the error inherent in any scientific measurement, a spectrophotometric titration experiment with nickel(II) and ethylenediamine (en) was repeated six times using an autotitrator to test the replicability of the data and the consistency of the resulting thermodynamic model. All six datasets could be modeled very tightly (R2 &gt; 99.9999%) with the following eight complexes: [Ni]2+, [Ni2en]4+, [Nien]2+, [Ni2en3]4+, [Nien2]2+, [Ni2en5]4+, [Nien3]2+, and [Nien6]2+. The logK values for the stepwise associative reactions agree with existing literature values for the majority species ([Nienn = 1–3]2+) and matched expectations for the minority species; 95% confidence intervals for each logK value were determined via bootstrapping, which quantifies the variability in the binding constant value that is supported by a given dataset. The repeated experiments, which could not be successfully concatenated together, demonstrate that replication is crucial to capturing all the variability in the logK values. Conversely, bootstrapped confidence intervals across multiple experiments can be readily combined to generate an appropriate range for an experimentally determined binding constant.

Some Improvements of the Bootstrap over the Delta Method Probability Errors for Whittle Estimators

The purpose of this paper is to compare the coverage probability errors of the parametric bootstrap with that of the delta method for the covariance parameters of a regression model with auto-regressive fractionally integrated moving average (ARFIMA) errors. We consider the coverage probability errors of both confidence intervals (CIs) and tests based on the the plug-in Whittle maximum likelihood (PWML) estimators. We first show that, under some sets of conditions on the regression coefficients, the spectral density function, and the parameter values, the bounds on the coverage probability errors of the two-sided delta method and parametric bootstrap confidence intervals on the plug-in Whittle likelihood estimator or the covariance parameter are shown to be $O(n^{-1})$ and $o(n^{-3/2}\ln{n})$, respectively, where n is the sample size. Next, we show that those of the one-sided parametric bootstrap confidence intervals are shown to be $O(n^{-1/2})$ and $o(n^{-1}\ln{n})$, respectively. These results show that for both one-sided and two-sided confidence intervals and tests, the bootstrap provides a significant improvement over that of the delta method.

Estimation of Lifetime Performance Index for Generalized Inverse Lindley Distribution Under Adaptive Progressive Type-II Censored Lifetime Test

The lifetime performance index (LPI) is an important metric for evaluating product quality, and research on the statistical inference of the LPI is of great significance. This paper discusses both the classical and Bayesian estimations of the LPI under an adaptive progressive type-II censored lifetime test, assuming that the product’s lifetime follows a generalized inverse Lindley distribution. At first, the maximum likelihood estimator of the LPI is derived, and the Newton–Raphson iterative method is adopted to solve the numerical solution due to the log-likelihood equations having no analytical solutions. If the exact distribution of the LPI is not available, then the asymptotic confidence interval and bootstrap confidence interval of the LPI are constructed. For the Bayesian estimation, the Bayesian estimators of the LPI are derived under three different loss functions. Due to the complex multiple integrals involved in these estimators, the MCMC method is used to draw samples and further construct the HPD credible interval of the LPI. Finally, Monte Carlo simulations are used to observe the performance of these estimators in terms of the average bias and mean squared error, and two practical examples are used to illustrate the application of the proposed estimation method.

Estimation methods for the variance of Birnbaum-Saunders distribution containing zero values with application to wind speed data in Thailand.

Thailand is currently grappling with a severe problem of air pollution, especially from small particulate matter (PM), which poses considerable threats to public health. The speed of the wind is pivotal in spreading these harmful particles across the atmosphere. Given the inherently unpredictable wind speed behavior, our focus lies in establishing the confidence interval (CI) for the variance of wind speed data. To achieve this, we will employ the delta-Birnbaum-Saunders (delta-BirSau) distribution. This statistical model allows for analyzing wind speed data and offers valuable insights into its variability and potential implications for air quality. The intervals are derived from ten different methods: generalized confidence interval (GCI), bootstrap confidence interval (BCI), generalized fiducial confidence interval (GFCI), and normal approximation (NA). Specifically, we apply GCI, BCI, and GFCI while considering the estimation of the proportion of zeros using the variance stabilized transformation (VST), Wilson, and Hannig methods. To evaluate the performance of these methods, we conduct a simulation study using Monte Carlo simulations in the R statistical software. The study assesses the coverage probabilities and average widths of the proposed confidence intervals. The simulation results reveal that GFCI based on the Wilson method is optimal for small sample sizes, GFCI based on the Hannig method excels for medium sample sizes, and GFCI based on the VST method stands out for large sample sizes. To further validate the practical application of these methods, we employ daily wind speed data from an industrial area in Prachin Buri and Rayong provinces, Thailand.

The Mediation Role of Coping With Stress in the Relationship Between Psychological Flexibility and Posttraumatic Growth in Cancer Patients.

Objectives: Active and adaptive coping strategies have been identified as factors that can assist cancer patients in effectively managing and overcoming the crisis, leading to the potential for post-traumatic growth during the diagnosis and treatment stages. Psychological flexibility is another factor that can protect individuals and promote more adaptive reactions to traumatic situations. The study aims to examine the investigation of the mediation role of coping with stress in the relationship between psychological flexibility and posttraumatic growth in cancer patients. Methods: This study was conducted with 97 (63 women, 34 male) participants aged between 38 and 82 who are literate and diagnosed with breast cancer or gynecological cancers (endometrial, cervical, vulvar) undergoing radiotherapy planning at the Radiation Oncology Clinic of Zonguldak Bülent Ecevit University Hospital. Demographic Information Form, Psychological Flexibility Scale, Post-Traumatic Growth Inventory, and Coping Styles Scale were applied to the participants. The mediation effects were interpreted using bootstrap confidence intervals and VAF values. Results: This study showed that the active coping styles partially mediated the relationship between psychological flexibility and posttraumatic growth. Conclusion: In this regard, by organizing psychoeducational programs and interventions aimed at increasing psychological flexibility for individuals diagnosed with cancer or undergoing treatment, individuals can be enabled to cope with stress more actively, and thus post-traumatic growth can be achieved.

Classical and Bayesian inference of Cpc$\mathcal {C}_{pc}$ for Wilson–Hilferty distribution under progressively first‐failure type‐II censoring samples

AbstractThis study uses two frequentist approaches and the Bayesian method of estimation using progressively first‐failure type‐II censored data to estimate process capability index (PCI), , for the Wilson–Hilferty (WH) distribution. A competitive maximum product of spacing (MPS) method for estimation of is proposed in the frequentist method as an alternative to conventional likelihood (LK)‐based estimation. We have also taken into account the PS function in the Bayesian setup as an alternative to the conventional LK function, and both LK and PS‐based Bayesian estimates are given for . Further, the Bayes estimates are evaluated by applying Tierney–Kadane (TK) approximation method and Markov chain Monte Carlo (MCMC) method with the help of both LK and PS functions and Jeffrey's prior. Additionally, the approximate confidence intervals based on the suggested frequentist techniques as well as the Bayes highest posterior density (HPD) credible intervals are built for the index . In addition, two bootstrap confidence intervals are obtained. In the simulation exercise, the performance of the Bayes and traditional estimates of is assessed in terms of their mean squared errors, and the average width and coverage probabilities of the CIs and HPD intervals are compared. An actual data set from the electronic industries is reanalyzed in order to show the efficacy of the proposed index and estimation methodology.

Sensitivity analysis for unmeasured confounding in estimating the difference in restricted mean survival time.

The difference in restricted mean survival time has been increasingly used as an alternative measure to the hazard ratio in survival analysis. Although some statistical methods have been developed for estimating the difference in restricted mean survival time adjusted for measured confounders in observational studies, the impact of unmeasured confounding on the estimate has rarely been assessed. We develop a novel sensitivity analysis for the estimate of the difference in restricted mean survival time with respect to unmeasured confounding. After formulating the sensitivity analysis problem as an optimization problem, we explain how to obtain the sensitivity range of the difference in restricted mean survival time efficiently and assess its uncertainty using the percentile bootstrap confidence interval. Analytic results are provided for some important survival settings. Simulation studies show that the proposed methods perform well in various settings. We illustrate the proposed sensitivity analysis method by analyzing data from the German Breast Cancer Study Group study.

Multimedia: Multimodal Mediation Analysis of Microbiome Data.

Mediation analysis has emerged as a versatile tool for answering mechanistic questions in microbiome research because it provides a statistical framework for attributing treatment effects to alternative causal pathways. Using a series of linked regressions, this analysis quantifies how complementary data relate to one another and respond to treatments. Despite these advances, existing software's rigid assumptions often result in users viewing mediation analysis as a black box. We designed the multimedia R package to make advanced mediation analysis techniques accessible, ensuring that statistical components are interpretable and adaptable. The package provides a uniform interface to direct and indirect effect estimation, synthetic null hypothesis testing, bootstrap confidence interval construction, and sensitivity analysis, enabling experimentation with various mediator and outcome models while maintaining a simple overall workflow. The software includes modules for regularized linear, compositional, random forest, hierarchical, and hurdle modeling, making it well-suited to microbiome data. We illustrate the package through two case studies. The first re-analyzes a study of the microbiome and metabolome of Inflammatory Bowel Disease patients, uncovering potential mechanistic interactions between the microbiome and disease-associated metabolites, not found in the original study. The second analyzes new data about the influence of mindfulness practice on the microbiome. The mediation analysis highlights shifts in taxa previously associated with depression that cannot be explained indirectly by diet or sleep behaviors alone. A gallery of examples and further documentation can be found at https://go.wisc.edu/830110.

The Difference in Achilles Tendon Loading within Immobilizing Boots Based on Ankle Angle, Boot Type, and Walking Speed.

Achilles tendon rupture is an increasingly common injury treated with progressive rehabilitation in an immobilizing boot. However, it is poorly understood how ankle angle, boot type, and walking speed affect Achilles tendon loading. These different parameters would affect Achilles tendon loading in terms of (from greatest to least) ankle angle constraint, immobilization style, boot construction, and walking speed. Descriptive laboratory study. Ten healthy young adults (8 women and 2 men; age, 21 ± 2 years; body mass index, 21.5 ± 3.0 kg/m2) walked in 3 different immobilizing boots at self-selected slow, medium, and fast walking speeds. The authors estimated Achilles tendon loading using a 3-part instrumented insole within the immobilizing boot. The authors averaged tendon load across every stride for each condition and calculated 2-sided bootstrap confidence intervals. Peak tendon loading was compared across all boots, ankle angles, and walking speeds. All boots and immobilization styles decreased tendon loading with respect to shod walking. Immobilization angle had the largest effect on tendon loading, followed by boot construction, and finally walking speed. Ankle angle, boot type, and walking speed can be modified to change loading progression during rehabilitation. Understanding how immobilization affects tendon loading will enable clinicians to modify rehabilitation to improve functional outcomes.

Reliability inference for dual constant-stress accelerated life test with exponential distribution and progressively Type-II censoring

Accelerated life test provides a feasible and effective way to rapidly derive lifetime information by exposing products to higher-than-normal operating conditions. However, most of the previous research on accelerated life test has focused on the application of a single stress factor and a traditional censoring scheme. This article considers the reliability inference for a dual constant-stress accelerated life test model with exponential distribution and progressively Type-II censoring. Point estimates for model parameters are provided using maximum likelihood estimation and the weighted least squares method based on random variable transformation. In addition, we construct asymptotic confidence intervals, approximate confidence intervals, and bootstrap confidence intervals for the parameters of interest. Finally, extensive simulation studies and an illustrative example are presented to investigate the performance of the proposed methods.

Stress–strength reliability estimation of s-out-of-k multicomponent systems based on copula function for dependent strength elements under progressively censored sample

The main objective of this research is to determine the reliability of multicomponent stress–strength under progressive Type II censoring. The model comprises k independent strength components, and each component has two elements that are statistically dependent and exposed to the same random stress. To assess the correlation between their elements, we are utilizing the Gumbel copula and assuming that its parameter is unknown. The system is deemed operational only if at least certain number of strength variables s ( 1 ≤ s ≤ k ) surpass the random stress. We are using the Chen distribution to model the stress and strength variables, with varying shape parameters. Different methods are employed to estimate the unknown parameters, including maximum likelihood, maximum product of spacings, Cramér–von-Mises, and bootstrap confidence intervals. The effectiveness of these estimation techniques is evaluated through Monte Carlo simulation, and a real data set is analyzed to illustrate our procedures.

A Tidy Framework and Infrastructure to Systematically Assemble Spatio-temporal Indexes from Multivariate Data

Indexes are useful for summarizing multivariate information into single metrics for monitoring, communicating, and decision-making. While most work has focused on defining new indexes for specific purposes, more attention needs to be directed toward making it possible to understand index behavior in different data conditions, and to determine how their structure affects their values and the variability therein. Here we discuss a modular data pipeline recommendation to assemble indexes. It is universally applicable to index computation and allows investigation of index behavior as part of the development procedure. One can compute indexes with different parameter choices, adjust steps in the index definition by adding, removing, and swapping them to experiment with various index designs, calculate uncertainty measures, and assess indexes’ robustness. The article presents three examples to illustrate the usage of the pipeline framework: comparison of two different indexes designed to monitor the spatio-temporal distribution of drought in Queensland, Australia; the effect of dimension reduction choices on the Global Gender Gap Index (GGGI) on countries’ ranking; and how to calculate bootstrap confidence intervals for the Standardized Precipitation Index (SPI). The methods are supported by a new R package, called tidyindex. Supplemental materials for the article are available online.

115 Confidence intervals for validation statistics with data truncation in genomic prediction

Abstract Validation by data truncation is a common practice in genetic evaluations because of the interest in predicting the genetic merit of a set of young selection candidates. Two of the most used validation methods in genetic evaluations are predictivity (correlation between pre-adjusted phenotypes and EBV) divided by the square root of the heritability) and the linear regression (LR) method. Both methods compare predictions with the whole and partial datasets obtained by removing the information related to a set of validation individuals. Confidence intervals (CI) for predictivity and the LR method can be obtained by k-fold validation or bootstrapping. Analytical or frequentist CI are unavailable for predictivity and the LR method and would be beneficial to avoid running several validations. The analytical CI can also help test the quality of bootstrap intervals. This study aimed to derive analytical CI for predictivity, and statistics included in the LR method (bias, dispersion, ratio of accuracies, and reliability). The CI for the bias, dispersion, and reliability depends on the (co)variances of the EBV across the individuals in the validation set. The CI for the ratio of accuracies and predictivity were obtained through the Fisher transformation. We showed the adequacy of the analytical CI using simulation. The analytical CI were closer to the simulated ones. Bootstrap CI tend to be narrower than the simulated ones. Estimating the sampling variation of predictivity and the statistics in the LR method without replication or bootstrap is possible for any dataset with the method proposed in this study. All the formulas derived in this study were implemented in a new program belonging to the BLUPF90 suite called Validationf90.

B - 72 Cognitive Regulation as a Predictor of Parenting Distress

Abstract Objective To determine the relationship between adverse childhood events (ACE), executive function, and parenting. Method Pregnant individuals with and without a history of substance use were recruited to participate in a longitudinal study on perinatal reward processing and parenting. Data were collected from 111 pregnant participants, from which 43 contributed data at six months postpartum. Childhood trauma was collected via the ACE scale, and executive function (EF) challenges were measured using the Metacognition Index of the Behavior Ratings Inventory of Executive Functions for Adults (BRIEF-A). Parenting stress was assessed using the Parenting Stress Inventory, Short Form. The parental distress (PD) and parent perception of their child’s dysregulation (DC) scales were calculated from the PSI at the 6-month timepoint (N = 43 dyads, mean infant age = 27.14 (2.45) weeks.). A structural equation modeling approach was utilized to assess the direct and indirect effects of ACEs and EF challenges on PD and DC. A path mediation model was used. All models were estimated using the R Statistical Software Lavaan package. Bootstrapped confidence intervals were calculated for all paths. Missing data were handled using full information maximum likelihood. Results We found a significant indirect effect of ACEs on DC through metacognition (β = 0.1, 95% CI [0.01, 0.18], p = 0.026) and a significant indirect effect of ACEs on PD through metacognition (β = 0.13, 95% CI [0.02, 0.23], p = 0.019). There were no significant direct effects of ACE on PD or DC. Conclusion This analysis supports the hypothesis that EF, specifically cognitive regulation, impacts PS in the context of a history of ACE.

Confidence Intervals for the Mean and Difference of Means of Birnbaum-Saunders Distributions with Application to Wind Speed Data

This paper proposes the confidence intervals for the mean and difference of means of Birnbaum-Saunders (BirSau) distributions based on the Bootstrap confidence interval (BCI), Percentile bootstrap confidence interval (PBCI), Generalized confidence interval (GCI), Bayesian credible interval (BayCrI) and the highest posterior density (HPD). The simulation study used R statistical software to evaluate the coverage probabilities and average lengths. The concerning results of the mean suggest that HPD is the recommended method for constructing confidence intervals in the BirSau distributions, except for small sample sizes where the GCI method proves more efficient. For the difference of means, PBCI emerges as the preferred way to construct confidence intervals, except in some cases where small sample sizes with the HPD method are more efficient. Moreover, the average lengths of these proposed confidence intervals decreased as both sample size and shape parameters increased. To illustrate the effectiveness of the suggested confidence intervals, we applied them to wind speed datasets collected in Ayutthaya and Ratchaburi provinces, Thailand.