Nonparametric Confidence Intervals Research Articles

Phenotypic Characterization of Patients with Polycystic Ovary Syndrome in a Population from the Ecuadorian Andes: A Cross-Sectional Study.

Background: Polycystic ovary syndrome (PCOS) is a highly prevalent endocrine-metabolic disorder in women of reproductive age. Diagnosis is based on the evidence-based international guideline 2018 and the Rotterdam Consensus to classify PCOS phenotypes. This study aims to characterize the biodemographic, clinical, metabolic, and reproductive variables and their relationship with PCOS phenotypes in a population from the Ecuadorian Andes. Methodology: A cross-sectional study was conducted with a non-random consecutive sample of 92 women who attended the outpatient gynecology and endocrinology clinic at the Hospital of the Technical University of Loja (UTPL)-Santa Inés, Loja, Ecuador, between January 2022 and July 2023. Descriptive statistics, mean calculations, standard deviation, parametric and nonparametric tests, odds ratios (OR), confidence intervals (CI), and p-values were employed. Results: The average age was 22 ± 3.4 years, with a predominantly mestizo, urban, single, highly educated, and medium-high socioeconomic level population. It was identified that phenotypes A + B are at a higher risk of developing oligomenorrhea and hypertriglyceridemia compared to phenotypes C + D, with statistically significant differences (p < 0.05). Furthermore, in terms of reproductive variables, phenotypes A + B exhibit a significantly higher frequency of elevated anti-Müllerian hormone (AMH) compared to phenotypes C + D, also with statistical significance (p < 0.05). Conclusions: The classical phenotypes A and B of PCOS are the most common in Ecuadorian Andean women and carry a higher risk of insulin resistance, anovulation, metabolic disorders, and elevated triglyceride levels compared to phenotypes C and D. Ethnic diversity and sociocultural habits influence the prevalence and clinical manifestations of these phenotypes.

Adaptive inference procedures for the concentration parameter of a Fisher-von Mises-Langevin distribution

This paper focuses on the estimation and testing of a shape parameter or concentration parameter κ of a directional distribution named Fisher-von Mises- Langevin distribution. The estimators for κ using standard procedures cannot be obtained in closed or explicit forms. We derive asymptotic expressions up to first order for the bias, mean squared error and variance of the maximum likelihood estimator of κ when its mean direction is unknown. Using these expressions in a selective manner, several nearly-unbiased estimators for κ are proposed. A simulation study is carried out to compare the biases and percentage risk improvement of these new proposed estimators. The proposed estimators are seen to offer substantial improvements in terms of bias and percentage risk improvement over the earlier ones. The simulation study shows that these tests achieve size quite close to their nominal values and have quite good power performances. A nonparametric bootstrap confidence intervals for κ is presented. Finally these estimators and test procedures are applied on a real data set. ‘MATLAB’ functions are developed for practical use.

Nonparametric Bootstrap Confidence Intervals for the Population Mean of a Zero-Truncated Poisson-Lindley Distribution and Their Application

Recently, the zero-truncated Poisson-Lindley distribution has been proposed for studying count data containing non-zero values. However, the nonparametric bootstrap confidence interval estimation of the population mean has not yet been studied. In this study, confidence interval estimation based on percentile, simple, and biased-corrected bootstrap methods was compared in terms of coverage probability and average interval length via Monte Carlo simulation. The true values of parameter () were set as 0.25, 0.5, 1, 1.5, and 2, and the population means are approximate 7.7586, 4.0909, 2.4000, 1.8817, and 1.6364, respectively. The bootstrap samples (=1,000) of size were generated from the original sample, and each simulation was repeated 1,000 times. The results indicate that attaining the nominal confidence level using the bootstrap confidence intervals was impossible for small sample sizes regardless of the other settings. Moreover, when the sample size was large, the performance of the nonparametric bootstrap confidence intervals was not substantially different. Overall, the bias-corrected bootstrap confidence interval outperformed the others, even for small sample sizes. Last, the nonparametric bootstrap confidence intervals were used to calculate the confidence interval for the population mean of the zero-truncated Poisson-Lindley distribution via two numerical examples, the results of which match those from the simulation study.

The effect of date fruit consumption on early postpartum hemorrhage: a randomized clinical trial

BackgroundPostpartum hemorrhage, anemia, and iron deficiency are important health problems. Using safe, cheap, and available methods to reduce the amount of hemorrhage after childbirth can be effective for the mother's health during this period. Therefore, this study was conducted to determine the effect of date fruit consumption on the amount of hemorrhage after natural childbirth.MethodsThis randomized clinical trial was conducted on 98 women referred to the maternity ward of Al-Zahra Hospital in Rasht using the available sampling method. The primary outcome was postpartum hemorrhage, measured using the Pictorial Blood Loss Assessment Chart (PBLAC). Two hours after delivery, 100 g of date fruits were given to the intervention group, and the amount of hemorrhage was recorded during the first 24 h. Comparison between the two groups was done with the Mann–Whitney test with the Hodges–Lehmann estimator and corresponding exact conditional nonparametric confidence interval (CI) as effect estimate. A P < 0.05 was considered significant.ResultsThe median of postpartum hemorrhage after normal delivery in the date and control groups was 35.0 [interquartile range (IQR): 22.0 to 39.8] and 39.0 [IQR: 27.5 to 64.5], respectively. Using the Hodges–Lehmann estimator, on average, the median postpartum hemorrhage in the date group was 9.0 (95% CI: 2.00–18.0) units lower than the control group (P = 0.009).ConclusionConsumption of dates effectively reduces the amount of hemorrhage after natural childbirth; thus, consuming this fruit during postpartum period is recommended. Also to confirm the findings, it is recommended to conduct similar studies in this field.Trial registrationThis trial was registered with the Iranian Registry of Clinical Trials; https://www.irct.ir/trial/59197 (IRCT20210607051505N2) on 31/10/2021.

Monte Carlo confidence intervals for the indirect effect with missing data.

Missing data is a common occurrence in mediation analysis. As a result, the methods used to construct confidence intervals around the indirect effect should consider missing data. Previous research has demonstrated that, for the indirect effect in data with complete cases, the Monte Carlo method performs as well as nonparametric bootstrap confidence intervals (see MacKinnon et al., Multivariate Behavioral Research, 39(1), 99-128, 2004; Preacher & Selig, Communication Methods and Measures, 6(2), 77-98, 2012; Tofighi & MacKinnon, Structural Equation Modeling: A Multidisciplinary Journal, 23(2), 194-205, 2015). In this manuscript, we propose a simple, fast, and accurate two-step approach for generating confidence intervals for the indirect effect, in the presence of missing data, based on the Monte Carlo method. In the first step, an appropriate method, for example, full-information maximum likelihood or multiple imputation, is used to estimate the parameters and their corresponding sampling variance-covariance matrix in a mediation model. In the second step, the sampling distribution of the indirect effect is simulated using estimates from the first step. A confidence interval is constructed from the resulting sampling distribution. A simulation study with various conditions is presented. Implications of the results for applied research are discussed.

Is the Kimchi premium a speculative bubble?

This study investigates whether the Kimchi premium, the phenomenon in which the Bitcoin price in Korea is persistently higher than the United States price, reflects a speculative bubble. Eom (2021) argued that the Kimchi premium is a bubble, evidenced by its positive relationship with trading volume and price volatility estimated from unconditional regressions. We re-examine this evidence by estimating and testing time-varying coefficients using nonparametric regressions and bootstrap confidence intervals. Our results show that the positive relationship is not robust over time, suggesting that we do not yet have clear evidence to conclude that the Kimchi premium is a bubble.

Confidence intervals of the process capability index Cpc$C_{pc}$ revisited via modified bootstrap technique and ROC curves

AbstractWe consider the process capability index (PCI), a widely used quality‐related statistic used to assess the quality of products and performance of monitored processes in various industries. It is widely known that the conventional PCIs perform well when the quality process being monitored has a normal distribution. Unfortunately, using the indices to evaluate a non‐normally distributed process often leads to inaccurate results. In this article, we consider a new PCI, , that can be used in both normal and non‐normal scenarios. The objective of this article is threefold: (i) We provide a corrected form of the confidence interval for . (ii) We compare the performance of three nonparametric bootstrap confidence intervals (BCIs) for . Specifically, the standard bootstrap, percentile bootstrap, and bias‐corrected percentile bootstrap. Under various distributional assumptions such as the normal, chi‐square, Student t, Laplace, and two‐parameter exponential distributions, the estimated coverage probabilities and average width of the confidence intervals and BCIs for are compared. (iii) The power of the respective bootstrap approaches is evaluated by using the equivalence relation between confidence interval construction and two‐sided hypothesis testing. We also provide the receiver operating characteristic curves to evaluate their performance. Finally, as an illustrative example, an actual data set related to groove dimensions (in inches) measured from a manufacturing process of ignition keys is re‐analyzed to illustrate the utility of the proposed methods.

The use of fractional order statistics for estimating nonparametric confidence intervals for quantiles of the fatigue damage computed in service random loadings

This paper deals with the statistical variability of fatigue damage in random loadings as caused by the inherent randomness of the loading. It examines the use of a nonparametric method based on fractional order statistics as a tool for constructing confidence intervals for the quantile of fatigue damage, regardless of the knowledge of the damage probability distribution. The approach here discussed relies on a statistical method existing in the literature. After a short review of this method, with also an emphasis on possible advantages and limitations, the paper presents a numerical benchmark, followed by a practical application to time-histories measured on a mountain-bike in off-road tracks. The paper concludes with some critical remarks and an outlook.

Valid inferences about soil carbon in heterogeneous landscapes

Using soil organic carbon (SOC) to generate carbon offsets requires reliably quantifying SOC sequestration. However, accuracy of SOC measurement is limited by inherent spatial heterogeneity, variability of laboratory assays, unmet statistical assumptions, and the relatively small magnitude of SOC changes over time, among other things. Most SOC measurement protocols currently used to generate offsets for C markets do not adequately address these issues, threatening to undermine climate change mitigation efforts. Using analyses and simulations from 1,117 soil samples collected from California crop and rangelands, we quantified measurement errors and sources of uncertainty to optimize SOC measurement. We demonstrate that (1) spatial heterogeneity is a primary driver of uncertainty; (2) dry combustion assays contribute little to uncertainty, although inorganic C can increase error; (3) common statistical methods—Student’s t-test and its relatives—can be unreliable for SOC (e.g. at low to medium sample sizes or when the distribution of SOC is skewed), which can lead to incorrect interpretations of SOC sequestration; and (4) common sample sizes (10–30 cores) are insufficiently powered to detect the modest SOC changes expected from management in heterogeneous agricultural landscapes. To reduce error and improve the reliability of future SOC offsets, protocols should: (1) require power analyses that include spatial heterogeneity to determine minimum sample sizes, rather than allowing arbitrarily small sample sizes; (2) minimize the use of compositing; (3) require dry combustion analysis, by the same lab for all assays; and (4) use nonparametric statistical tests and confidence intervals to control Type I error rates. While these changes might increase costs, they will make SOC estimates more accurate and more reliable, adding credibility to soil management as a climate change mitigation strategy.

Parametric and nonparametric methods for confidence intervals and sample size planning for win probability in parallel-group randomized trials with Likert item and Likert scale data.

Data on the Likert scale are ubiquitous in medical research, including randomized trials. Statistical analysis of such data may be conducted using the means of raw scores or the rank information of the scores. In the context of parallel-group randomized trials, we quantify treatment effects by the probability that a subject in the treatment group has a better score than (or a win over) a subject in the control group. Asymptotic parametric and nonparametric confidence intervals for this win probability and associated sample size formulas are derived for studies with only follow-up scores, and those with both baseline and follow-up measurements. We assessed the performance of both the parametric and nonparametric approaches using simulation studies based on real studies with Likert item and Likert scale data. The simulation results demonstrate that even without baseline adjustment, the parametric methods did not perform well, in terms of bias, interval coverage percentage, balance of tail error, and assurance of achieving a pre-specified precision. In contrast, the nonparametric approach performed very well for both the unadjusted and adjusted win probability. We illustrate the methods with two examples: one using Likert item data and the other using Like scale data. We conclude that non-parametric methods are preferable for two-group randomization trials with Likert data. Illustrative SAS code for the nonparametric approach using existing procedures is provided.

Improving an old way to measure moderation effect in standardized units.

Moderation effects in multiple regression, tested usually by the inclusion of a product term, are frequently investigated in health psychology. However, several issues in presenting the moderation effects in standardized units and their associated confidence intervals are commonly observed. While an old method had been proposed to standardize variables in moderated regression before fitting a moderated regression model, this method was rarely used due to inconvenience and even when used, the confidence intervals derived were biased. Here, we attempt to solve these two problems by providing a tool to conveniently conduct standardization in moderated regression without the step of standardizing the variables beforehand and to accurately form the nonparametric bootstrapping confidence intervals for this standardized measure of moderation effects. Health psychology researchers are now equipped with a tool that can be used to report and interpret standardized moderation effects correctly. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

The number needed to treat adjusted for explanatory variables in regression and survival analysis: Theory and application.

The number needed to treat (NNT) is an efficacy index commonly used in randomized clinical trials. The NNT is the average number of treated patients for each undesirable patient outcome, for example, death, prevented by the treatment. We introduce a systematic theoretically‐based framework to model and estimate the conditional and the harmonic mean NNT in the presence of explanatory variables, in various models with dichotomous and nondichotomous outcomes. The conditional NNT is illustrated in a series of four primary examples; logistic regression, linear regression, Kaplan‐Meier estimation, and Cox regression models. Also, we establish and prove mathematically the exact relationship between the conditional and the harmonic mean NNT in the presence of explanatory variables. We introduce four different methods to calculate asymptotically‐correct confidence intervals for both indices. Finally, we implemented a simulation study to provide numerical demonstrations of the aforementioned theoretical results and the four examples. Numerical analysis showed that the parametric estimators of the NNT with nonparametric bootstrap‐based confidence intervals outperformed other examined combinations in most settings. An R package and a web application have been developed and made available online to calculate the conditional and the harmonic mean NNTs with their corresponding confidence intervals.

An application of the interval estimation for the At-Risk-of-Poverty Rate assessment

In the document [Eurostat (Your Key to European Statistics) 2020], At-Risk-of-Poverty Rate (ARPR in short) is defined as the percentage of population with an income not exceeding 60% of the general population median income. Extensive and thorough research on the estimation of this measure has been conducted since its introduction. For example, in the paper of [Zieliński 2009a] a non-parametric, distribution-free confidence interval for ARPR has been constructed. An example of application of the confidence interval proposed by [Zieliński 2009a] has been given in [Zieliński 2009b]. Some other interesting approach regarding the interval estimation of ARPR has been proposed in [Luo and Qin 2017], where the authors introduced new concepts of the interval estimation for the so-called Low-Income Proportion (LIP) measure, which is a generalization of ARPR. The LIP measure and thus, the ARPR parameter in particular, are important indexes describing the inequality in an income distribution. Based on the construction of the point smoothed kernel estimate for LIP, [Luo and Qin 2017] established a smoothed jackknife empirical likelihood approach leading to the introduction of some new non-parametric confidence intervals for the LIP measure and consequently, for the ARPR index as well. In our work, we aim to apply the most interesting ideas of LIP and ARPR point and interval estimation for data consisting of observations concerning an equalised disposable income of households in Poland from 2003. We also discuss the accuracy and adequacy of the empirical results relating to the ARPR interval estimation, obtained by the implementation of the constructed confidence intervals.

Multicomponent stress-strength reliability estimation for the standard two-sided power distribution

A system of $k$ components that functions as long as at least $s$ components survive is termed as $s$-out-of-$k$:G system, where G refers to "good". In this study, we consider the $s$-out-of-$k$:G system when $X_{1}, X_{2},\cdots, X_{k}$ are independent and identically distributed strength components and each component is exposed to common random stress $Y$ when the underlying distributions all belong to the standard two-sided power distribution. The system is regarded as surviving only if at least $s$ out of $k$ $1&amp;lt;s&amp;lt;k$ strengths exceed the stress. The reliability of such a system is the surviving probability and is estimated by using the maximum likelihood and Bayesian approaches. Parametric and nonparametric bootstrap confidence intervals for the maximum likelihood estimates and the highest posterior density confidence intervals for Bayes estimates by using the Markov Chain Monte Carlo technique are obtained. A real data set is also analyzed to illustrate the performances of the estimators.

DIY bootstrapping: Getting the nonparametric bootstrap confidence interval in SPSS for any statistics or function of statistics (when this bootstrapping is appropriate).

Researchers can generate bootstrap confidence intervals for some statistics in SPSS using the BOOTSTRAP command. However, this command can only be applied to selected procedures, and only to selected statistics in these procedures. We developed an extension command and prepared some sample syntax files based on existing approaches from the Internet to illustrate how researchers can (a) generate a large number of nonparametric bootstrap samples, (b) do desired analysis on all these samples, and (c) form the bootstrap confidence intervals for selected statistics using the OMS commands. We developed these tools to help researchers apply nonparametric bootstrapping to any statistics for which this method is appropriate, including statistics derived from other statistics, such as standardized effect size measures computed from the t test results. We also discussed how researchers can extend the tools for other statistics and scenarios they encounter.

On the resilience of health systems: A methodological exploration across countries in the WHO African Region.

The need for resilient health systems is recognized as important for the attainment of health outcomes, given the current shocks to health services. Resilience has been defined as the capacity to “prepare and effectively respond to crises; maintain core functions; and, informed by lessons learnt, reorganize if conditions require it”. There is however a recognized dichotomy between its conceptualization in literature, and its application in practice. We propose two mutually reinforcing categories of resilience, representing resilience targeted at potentially known shocks, and the inherent health system resilience, needed to respond to unpredictable shock events. We determined capacities for each of these categories, and explored this methodological proposition by computing country-specific scores against each capacity, for the 47 Member States of the WHO African Region. We assessed face validity of the computed index, to ensure derived values were representative of the different elements of resilience, and were predictive of health outcomes, and computed bias-corrected non-parametric confidence intervals of the emergency preparedness and response (EPR) and inherent system resilience (ISR) sub-indices, as well as the overall resilience index, using 1000 bootstrap replicates. We also explored the internal consistency and scale reliability of the index, by calculating Cronbach alphas for the various proposed capacities and their corresponding attributes. We computed overall resilience to be 48.4 out of a possible 100 in the 47 assessed countries, with generally lower levels of ISR. For ISR, the capacities were weakest for transformation capacity, followed by mobilization of resources, awareness of own capacities, self-regulation and finally diversity of services respectively. This paper aims to contribute to the growing body of empirical evidence on health systems and service resilience, which is of great importance to the functionality and performance of health systems, particularly in the context of COVID-19. It provides a methodological reflection for monitoring health system resilience, revealing areas of improvement in the provision of essential health services during shock events, and builds a case for the need for mechanisms, at country level, that address both specific and non-specific shocks to the health system, ultimately for the attainment of improved health outcomes.

Questing benchmarks for the current ratio: An analysis of the Warsaw Stock Exchange firms

Objective: The first objective of the article is to assess the benchmarks for the current ratio commonly provided in the accounting and financial analysis literature. The minor objective is to arrange a research methodology permitting the accomplishment of the first objective. Research Design &amp; Methods: The paper, apart from the literature review and its critique, presents the results of descriptive, quantitative research. The research sample consists of 5 148 firm-years. Data were retrieved from Worldscope Database via Refinitiv Eikon for domestic, going concern, non-financial companies listed on the Warsaw Stock Exchange from 2005 to 2021. For comparison, the U.S.-related data was retrieved from Internet resources as ready-made ratios. Methods used in the analysis include descriptive statistics, parametric and nonparametric ANOVA, confidence intervals, and linear and parabolic trend analysis. Findings: The tests show that identifying a benchmark for the current ratio is problematic. Benchmarks vary between countries and industries; universal standards do not exist. The benchmark for the current ratio commonly suggested, 1.2-2.0, may be used only as a rough evaluation of the desired value. The findings indicate that the acceptable range for CR is much broader, from 1.1 (the first quartile) to 2.3 (the third quartile) for the total sample. Moreover, the SIC division's quartiles vary from 0.7 to 1.2 (the first) and from 1.6 to 3.6 (the third). Statistical tests indicate that benchmarks do not vary annually. However, the distribution's median and the third quartile change slowly over time toward higher values. The Covid-19 pandemic resulted in a substantial increase. On the contrary, the first quartile of about 1 remains relatively stable over time, indicating the reasonable lower bound for CR. The mean of the distribution is useless as a benchmark because of its sensitivity to outliers. Various techniques must be used to assess the benchmark. Implications &amp; Recommendations: Since there are material between-industry and between-country differences in benchmarks, analysts and investors should be very sensitive to the standards suggested in the literature and interpret them cautiously. Variability over time exists but is low unless a shock in the economy appears. Contribution &amp; Value Added: The main contribution of the paper is empirical verification of the benchmarks for the current ratio provided in the literature. Tests show that suggested benchmarks are not universal. Seeking a benchmark, an analyst must compare the firm's financial standing with other firms from the same country, industry, and period.

Implementation of sigmoidal models with different functional forms to estimate length at 50% maturity: A case study of the Pacific red snapper Lutjanus peru

To estimate mean size at sexual maturity (L50), a particular model is usually selected arbitrarily, and this decision does not consider the functional form (FF) of both the model (FFM) and the observed data (FFD). In this study, the performance of different sigmoidal models was evaluated by using data sources with different FF. To illustrate this, five sigmoidal models—Gompertz (GoM), logistic (LoM), Hill (HiM), Weibull (WeM), and gamma (GaM)—were used to estimate L50 for each sex and for the combined sexes of Lutjanus peru captured in the Eastern Central Pacific. To avoid redundancy, the models were selected based on different statistical properties: parameters in common L50; the same number of parameters (2); non-nested; different FF including symmetric or asymmetric; and asymptotic maturity equal to 1. Each model was fit to minimize the negative log likelihood by using a binomial probabilistic density function. Bias-corrected non-parametric confidence intervals CI were estimated for the parameters and predictions. The model average (AvM) and their CI were calculated by using the multi-model inference approach. According to the FFD, the best-fitting model was different for females (WeM), males (HiM), and the combined sexes (GaM). The comparison among the models revealed three features: i) the CI values overlapped among the data sets; ii) the estimate of L50 showed a gradient from right-skewed to left-skewed FF, which increases its value by ca. 7 cm; and iii) according to the selected model, it was possible to identify a marked variability in the computed L50. According to the multi-model approach, AvM was estimated for: i) females, L50 = 42.3 cm standard length LS computed from the WeM and LoM; ii) males, L50 = 37.4 cm LS computed from the GoM and WeM; and iii) the combined sexes, L50 = 39.5 cm LS estimated from the GaM as the unique model. The results show the importance of considering the FFD when L50 is estimated. By following this procedure, the AvM could be more informative regarding L50 estimates. This study proposes the implementation of sigmoidal models with different FF so that they can be fit to different FFD; this procedure exhibits the potential uncertainty linked to the candidate models.

Confidence interval estimation for the Mantel–Haenszel estimator of the risk ratio and risk difference in rare event meta-analysis with emphasis on the bootstrap

This paper takes a deeper look into uncertainty assessment of the Mantel–Haenszel estimator (MHE). In the homogeneity case, all developed confidence intervals for the risk ratio and risk difference behave acceptably, even in therare events situation. For heterogeneity, the non-parametric bootstrap approachprovides confidence intervals for the risk difference with acceptable coverage,depending on the number of studies. For the risk ratio, the situation is morecomplex as typically distributions for the log-relative risk are considered. TheMHE overestimates the expected value of the distribution of the log-relativerisk whatever it may be. However, if we consider as true value the estimand ofMHE, reasonable coverage probabilities can be achieved with the bootstrap. Asource of this problem is that the moments of a non-linearly transformedrelative risk variable are not equal to the non-linearly transformed moments ofthe respective relative risk variable.

On the Admissibility of Simultaneous Bootstrap Confidence Intervals

Simultaneous confidence intervals are commonly used in joint inference of multiple parameters. When the underlying joint distribution of the estimates is unknown, nonparametric methods can be applied to provide distribution-free simultaneous confidence intervals. In this note, we propose new one-sided and two-sided nonparametric simultaneous confidence intervals based on the percentile bootstrap approach. The admissibility of the proposed intervals is established. The numerical results demonstrate that the proposed confidence intervals maintain the correct coverage probability for both normal and non-normal distributions. For smoothed bootstrap estimates, we extend Efron’s (2014) nonparametric delta method to construct nonparametric simultaneous confidence intervals. The methods are applied to construct simultaneous confidence intervals for LASSO regression estimates.