Parametric Bootstrap Approach Research Articles

A parametric bootstrap approach for computing confidence intervals for genetic correlations with application to genetically determined protein-protein networks

Genetic correlation refers to the correlation between genetic determinants of a pair of traits. When using individual-level data, it is typically estimated based on a bivariate model specification where the correlation between the two variables is identifiable and can be estimated from a covariance model that incorporates the genetic relationship between individuals, e.g., using a pre-specified kinship matrix. Inference relying on asymptotic normality of the genetic correlation parameter estimates may be inaccurate when the sample size is low, when the genetic correlation is close to the boundary of the parameter space, and when the heritability of at least one of the traits is low. We address this problem by developing a parametric bootstrap procedure to construct confidence intervals for genetic correlation estimates. The procedure simulates paired traits under a range of heritability and genetic correlation parameters, and it uses the population structure encapsulated by the kinship matrix. Heritabilities and genetic correlations are estimated using the close-form, method of moment, Haseman-Elston regression estimators. The proposed parametric bootstrap procedure is especially useful when genetic correlations are computed on pairs of thousands of traits measured on the same exact set of individuals. We demonstrate the parametric bootstrap approach on a proteomics dataset from the Jackson Heart Study.

Multichannel detection of evoked responses using critical values corrected by a parametric bootstrap: Frequency-domain cholesky correction

Multivariate Objective Response Detection (MORD) techniques aim to detect evoked responses in multichannel electroencephalographic (EEG) recordings. They provide enhanced statistical power, allowing the detection of small signals in shorter or noisy recordings. However, the correlation between the signals in multichannel recordings can lead to false positive rates greater than the nominal significance level of the tests. To address this, we propose a parametric bootstrap approach that adjusts the critical values based on the correlation between EEG channels in the time domain, a method called time-domain Cholesky correction (TDCC). In that first approach, we assumed that correlation (or, more precisely, coherence) is constant across all frequency bands. However, this is unlikely to hold true, as signal-to-noise ratios (where the signal is the evoked response and noise all other signal components) may vary across frequencies. Thus, in the current work, we propose an alternative parametric bootstrap method for estimating the critical values of MORD techniques based on the correlation in the frequency domain (FDCC, frequency-domain Cholesky-corrected critical values). The proposed methods are evaluated using simulated data and an auditory steady-state response (ASSR) database in the 40 Hz range. The proposed method controlled the false positive rate well, with increased sensitivity compared to single-channel methods. When compared to TDCC, FDCC achieved similar performance but with the advantage of being, on average, 27 times faster in terms of computational time required to estimate the critical values.

Confidence intervals for functions of signal-to-noise ratio with application to economics and finance

PurposeConfidence intervals play a crucial role in economics and finance, providing a credible range of values for an unknown parameter along with a corresponding level of certainty. Their applications encompass economic forecasting, market research, financial forecasting, econometric analysis, policy analysis, financial reporting, investment decision-making, credit risk assessment and consumer confidence surveys. Signal-to-noise ratio (SNR) finds applications in economics and finance across various domains such as economic forecasting, financial modeling, market analysis and risk assessment. A high SNR indicates a robust and dependable signal, simplifying the process of making well-informed decisions. On the other hand, a low SNR indicates a weak signal that could be obscured by noise, so decision-making procedures need to take this into serious consideration. This research focuses on the development of confidence intervals for functions derived from the SNR and explores their application in the fields of economics and finance.Design/methodology/approachThe construction of the confidence intervals involved the application of various methodologies. For the SNR, confidence intervals were formed using the generalized confidence interval (GCI), large sample and Bayesian approaches. The difference between SNRs was estimated through the GCI, large sample, method of variance estimates recovery (MOVER), parametric bootstrap and Bayesian approaches. Additionally, confidence intervals for the common SNR were constructed using the GCI, adjusted MOVER, computational and Bayesian approaches. The performance of these confidence intervals was assessed using coverage probability and average length, evaluated through Monte Carlo simulation.FindingsThe GCI approach demonstrated superior performance over other approaches in terms of both coverage probability and average length for the SNR and the difference between SNRs. Hence, employing the GCI approach is advised for constructing confidence intervals for these parameters. As for the common SNR, the Bayesian approach exhibited the shortest average length. Consequently, the Bayesian approach is recommended for constructing confidence intervals for the common SNR.Originality/valueThis research presents confidence intervals for functions of the SNR to assess SNR estimation in the fields of economics and finance.

Parametric test based on the bootstrapping approach for the MANOVA under a Behrens-Fisher problem

This article presents a comparison of multivariate normal mean vectors under covariance positive definite matrices. We introduce an improved parametric bootstrap (IPB) approach for addressing the multivariate Behrens-Fisher problem, specifically focusing on cases with unequal covariance matrices. Additionally, we evaluate the performance of the IPB test by comparing it with three existing tests: the parametric bootstrap (PB) test, the generalized variable (GV) test, and the Johansen test. Through Monte Carlo simulation, our results demonstrate that both the IPB test and the PB test exhibit superior control over Type I error rates compared to the GV and Johansen tests. Notably, the IPB test outperforms the PB test in terms of controlling Type I error rates. Consequently, our study concludes that the IPB test represents a preferred statistical method for testing the equality of mean vectors in the multivariate Behrens-Fisher problem.

Parameter estimation and forecasting with quantified uncertainty for ordinary differential equation models using QuantDiffForecast: A MATLAB toolbox and tutorial.

Mathematical models based on systems of ordinary differential equations (ODEs) are frequently applied in various scientific fields to assess hypotheses, estimate key model parameters, and generate predictions about the system's state. To support their application, we present a comprehensive, easy-to-use, and flexible MATLAB toolbox, QuantDiffForecast, and associated tutorial to estimate parameters and generate short-term forecasts with quantified uncertainty from dynamical models based on systems of ODEs. We provide software ( https://github.com/gchowell/paramEstimation_forecasting_ODEmodels/) and detailed guidance on estimating parameters and forecasting time-series trajectories that are characterized using ODEs with quantified uncertainty through a parametric bootstrapping approach. It includes functions that allow the user to infer model parameters and assess forecasting performance for different ODE models specified by the user, using different estimation methods and error structures in the data. The tutorial is intended for a diverse audience, including students training in dynamic systems, and will be broadly applicable to estimate parameters and generate forecasts from models based on ODEs. The functions included in the toolbox are illustrated using epidemic models with varying levels of complexity applied to data from the 1918 influenza pandemic in San Francisco. A tutorial video that demonstrates the functionality of the toolbox is included.

SumVg: Total Heritability Explained by All Variants in Genome-Wide Association Studies Based on Summary Statistics with Standard Error Estimates.

Genome-wide association studies (GWAS) are commonly employed to study the genetic basis of complex traits/diseases, and a key question is how much heritability could be explained by all single nucleotide polymorphisms (SNPs) in GWAS. One widely used approach that relies on summary statistics only is linkage disequilibrium score regression (LDSC); however, this approach requires certain assumptions about the effects of SNPs (e.g., all SNPs contribute to heritability and each SNP contributes equal variance). More flexible modeling methods may be useful. We previously developed an approach recovering the "true" effect sizes from a set of observed z-statistics with an empirical Bayes approach, using only summary statistics. However, methods for standard error (SE) estimation are not available yet, limiting the interpretation of our results and the applicability of the approach. In this study, we developed several resampling-based approaches to estimate the SE of SNP-based heritability, including two jackknife and three parametric bootstrap methods. The resampling procedures are performed at the SNP level as it is most common to estimate heritability from GWAS summary statistics alone. Simulations showed that the delete-d-jackknife and parametric bootstrap approaches provide good estimates of the SE. In particular, the parametric bootstrap approaches yield the lowest root-mean-squared-error (RMSE) of the true SE. We also explored various methods for constructing confidence intervals (CIs). In addition, we applied our method to estimate the SNP-based heritability of 12 immune-related traits (levels of cytokines and growth factors) to shed light on their genetic architecture. We also implemented the methods to compute the sum of heritability explained and the corresponding SE in an R package SumVg. In conclusion, SumVg may provide a useful alternative tool for calculating SNP heritability and estimating SE/CI, which does not rely on distributional assumptions of SNP effects.

Statistical inference of a step-stress model with competing risks under time censoring for alpha power exponential distribution

Accelerated life testing in a reliability experiment allows test units to be under more stress than normal (expected). Step-stress tests are a subset of accelerated life tests that raise the stress levels at specific predetermined time periods to gather data on lifetime parameters more quickly than they would under normal operating settings. Additionally, there are frequently a number of risk factors connected to the root cause of a test unit failure (mechanical, electrical, etc.). In this article, we discuss the statistical inference of a step-stress model in the presence of time censoring assuming independent alpha power exponential distribution. The point estimates of the unknown scale and shape parameters of the various causes are determined using the maximum likelihood technique under the assumption of cumulative damage. We also go through creating confidence intervals for the parameters using asymptotic distributions and the parametric bootstrap approach. Extensive Monte Carlo simulations are used to evaluate the accuracy of the estimates and the performance of the confidence intervals, and finally, an example is used to explain the methods of inference presented here.

Parametric Bootstrap Confidence Interval Estimation for the Percentile and Difference between the Percentiles of Delta-Lognormal Distributions with Application to Rainfall Data in Thailand

In Thailand, flooding often occurs during the summer monsoon when many tropical storms affect the country. The motivation of this study was to plan for and mitigate the damage caused by flooding in the future. The confidence interval (CI) for the percentile of a precipitation dataset can be used to estimate the intensity of rainfall in a particular area whereas the CI for the difference between the percentiles of two datasets can be used to compare the rainfall intensities in two areas. To this end, the performances of several approaches to estimate the CI for the percentile and difference between the percentiles of delta-lognormal distributions were constructed and compared. These estimates were constructed based on the Bayesian (BS) and parametric bootstrap (PB) approaches, as well as two fiducial generalized confidence interval (FGCI) approaches. The performances of the methods were evaluated using Monte Carlo simulation, the results of which indicate that the PB approach for both CIs performed the best in all scenarios tested. Its suitability was confirmed via two illustrative examples using daily rainfall datasets for Chiang Mai and Lampang provinces in Thailand.

Confidence intervals for ratio of means of delta-lognormal distributions based on left-censored data with application to rainfall data in Thailand.

Thailand is a country that is prone to both floods and droughts, and these natural disasters have significant impacts on the country's people, economy, and environment. Estimating rainfall is an important part of flood and drought prevention. Rainfall data typically contains both zero and positive observations, and the distribution of rainfall often follows the delta-lognormal distribution. However, it is important to note that rainfall data can be censored, meaning that some values may be missing or truncated. The interval estimator for the ratio of means will be useful when comparing the means of two samples. The purpose of this article was to compare the performance of several approaches for statistically analyzing left-censored data. The performance of the confidence intervals was evaluated using the coverage probability and average length, which were assessed through Monte Carlo simulation. The approaches examined included several variations of the generalized confidence interval, the Bayesian, the parametric bootstrap, and the method of variance estimates recovery approaches. For (ξ1, ξ2) = (0.10,0.10), simulations showed that the Bayesian approach would be a suitable choice for constructing the credible interval for the ratio of means of delta-lognormal distributions based on left-censored data. For (ξ1, ξ2) = (0.10,0.25), the parametric bootstrap approach was a strong alternative for constructing the confidence interval. However, the generalized confidence interval approach can be considered to construct the confidence when the sample sizes are increase. Practical applications demonstrating the use of these techniques on rainfall data showed that the confidence interval based on the generalized confidence interval approach covered the ratio of population means and had the smallest length. The proposed approaches' effectiveness was illustrated using daily rainfall datasets from the provinces of Chiang Rai and Chiang Mai in Thailand.

Bridging the gap: how to adopt opportunistic plant observations for phenology monitoring.

Plant phenology plays a vital role in assessing climate change. To monitor this, individual plants are traditionally visited and observed by trained volunteers organized in national or international networks - in Germany, for example, by the German Weather Service, DWD. However, their number of observers is continuously decreasing. In this study, we explore the feasibility of using opportunistically captured plant observations, collected via the plant identification app Flora Incognita to determine the onset of flowering and, based on that, create interpolation maps comparable to those of the DWD. Therefore, the opportunistic observations of 17 species collected in 2020 and 2021 were assigned to "Flora Incognita stations" based on location and altitude in order to mimic the network of stations forming the data basis for the interpolation conducted by the DWD. From the distribution of observations, the percentile representing onset of flowering date was calculated using a parametric bootstrapping approach and then interpolated following the same process as applied by the DWD. Our results show that for frequently observed, herbaceous and conspicuous species, the patterns of onset of flowering were similar and comparable between both data sources. We argue that a prominent flowering stage is crucial for accurately determining the onset of flowering from opportunistic plant observations, and we discuss additional factors, such as species distribution, location bias and societal events contributing to the differences among species and phenology data. In conclusion, our study demonstrates that the phenological monitoring of certain species can benefit from incorporating opportunistic plant observations. Furthermore, we highlight the potential to expand the taxonomic range of monitored species for phenological stage assessment through opportunistic plant observation data.

A simulation study of the optimal experimental designs for a two-compartment kinetic model

The optimal design of nonlinear experiments is based on an optimality criterion that maximizes the Fisher information of an assumed model. In practice, however, we can be less certain about the actual performance or statistical efficiencies of the obtained designs that are jointly affected by the nonlinear model structure, the prior assumption, and the parameter estimation, all of which can make an optimal design underperform. For a realistic numerical evaluation of the designs, we implement a Monte Carlo simulation and parametric bootstrapping approach. In particular, we are interested in a classical second-order kinetic model, the structure of which is however unstable and vulnerable to random noises, as shown in our demonstration. As a result, the corresponding optimal designs are found to be inefficient, even so when the parameter prior is uninformative. Reasonable and robust model and prior assumptions are crucial for careful planning of future optimal design of experiments.

Regression-based rectangular multivariate normal prediction regions for setting reference regions

Reference intervals are among the most widely used decision-making tools in the medical field, and are invaluable in the interpretation of laboratory test results. Moreover, when several biochemical analytes are needed to diagnose the same condition, a multivariate reference region is necessary to take the correlations among the analytes into account. Traditionally, multivariate reference regions have been constructed as ellipsoidal in shape. Since such regions are difficult to interpret and cannot detect the outlyingness of a specific analyte, many authors prefer rectangular regions. Reference intervals and regions may also depend on covariates such as age and sex. The covariate values are often random quantities since they are typically not controlled in reference interval determination studies. In this study, we propose procedures to construct rectangular multivariate reference regions that incorporate random covariate information. The reference regions are computed in a multivariate normal setting, using a prediction region criterion. A parametric bootstrap approach is employed to compute the prediction factor. Numerical results show that the parametric bootstrap approach is quite accurate, with coverage probabilities close to the desired nominal value. Finally, we apply the proposed methods to real-life data from a study to compute covariate-dependent reference regions for insulin-like growth factors.

Statistical inference based on lower record values for the inverse Weibull distribution under the modified loss function

The main objective of this article is to develop a linear, exponential loss function (LXLF) to the dependability value and variables of the Inverse Weibull Distribution (IWD) according to Lowest Record Values. By weighting the LXLF to construct current function loss, the modified linear, exponential loss function (WLXLF) was named. Then use WLXLF to estimate the parameters and reliability functions of the (IWD). After that, we evaluated how well the prediction made in this article performed against the Bayesian estimator using the symmetric and asymmetric loss functions and maximum likelihood estimation (MLE). The credibility range for the values of the parameters and durability function has been created using the parametric bootstrap approach, and the outcomes have been contrasted via a Monte Carlo simulation. An actual data set from a realistic situation was utilized to explain the concept. The computer simulation results demonstrated that the suggested method, performed as expected, was the best for estimating the scale parameter and reliability function. The proposed technique performed well in estimating the shape parameter based on real data and had an acceptable performance for estimating scale parameters and reliability functions.

Confidence Intervals for Mean and Difference between Means of Delta-Lognormal Distributions Based on Left-Censored Data

A delta-lognormal distribution consists of zero and positive values. The positive values follow a lognormal distribution, which is an asymmetric distribution. It is well known that the logarithm of these values follows a normal distribution, which is a symmetric distribution. The delta-lognormal distribution is used in medical and environmental sciences. This study considers the challenges of constructing confidence intervals for the mean and difference between means of delta-lognormal distributions containing left-censored data and applies them to compare two daily rainfall average areas in Thailand. Three different approaches for constructing confidence intervals for the mean of the delta-lognormal distribution containing left-censored data, based on the generalized confidence interval approach, the Bayesian approach, and the parametric bootstrap approach, are developed. Moreover, four different approaches for constructing confidence intervals for the difference between means of delta-lognormal distributions containing left-censored data, based on the generalized confidence interval approach, the Bayesian approach, the parametric bootstrap approach, and the method of variance estimates recovery approach, are considered. The performance of the proposed confidence intervals is evaluated by Monte Carlo simulation. The simulation studies indicate that the Bayesian approach can be considered as an alternative to construct a credible interval for the mean of the delta-lognormal distribution containing left-censored data. Additionally, the generalized confidence interval and Bayesian approaches can be recommended as alternatives to estimate the confidence interval for the difference between means of delta-lognormal distributions containing left-censored data. All approaches are illustrated using the daily rainfall data from Chiang Mai and Lampang provinces in Thailand.

Identification of mechanism consistency for LFP/C batteries during accelerated aging tests based on statistical distributions

This study establishes a novel approach to investigate if accelerated aging tests can accurately model realistic cell aging in a short time while also maintaining the consistency of the involved aging mechanisms. As a trade-off between efficiency and consistent mechanism, the application of accelerated aging necessitates carefully selecting stress factors to identify the operational range and the significance of aging-related stress factors. Based on three levels of major stress factors designed for 43-month calendar aging tests and 10-month cyclic aging tests, this work aims at the stress ranking and indicating suitable operational intervals for commercial LFP/C batteries, taking two of the most popular lifetime distributions for batteries, namely log-normal and Weibull. Statistical distributions of lithium-ion batteries are attained from discharge capacity loss with nonlinear mixed-effects (NLME) models. Results prove that log-normal is the preferred model, and the right-skewed Weibull becomes more pronounced with deeper aging, especially in calendar aging. The evolution law of distribution parameters guided by the consistent acceleration factor was derived. The likelihood ratio parametric bootstrap approach based on the NLME model for life samples consistently yields that test conditions with the temperature above 47.5 °C and average state-of-charge (SOC) for cycling aging above 72.5% can result in different life behaviors. In contrast, the combination of SOC levels and higher temperatures does not lead to a change in the calendar aging mechanisms. The temperature is the most significant stress, followed by temperature-coupled cycle depth and SOC levels. This method can offer a reference to make reasonable test plans for detecting battery's performance to predict their life more accurately.

Comparison of the several two-parameter exponential distributed group means in the presence of outliers

The two-parameter exponential distribution is often used to model the lifetime of a product. The comparison of the mean lifetimes of several products is a main concern in reliability applications. In this study, the performance of the methods to compare the mean lifetimes of several products based on generalized p-value, parametric bootstrap, and fiducial approach are compared in the presence of outliers. The results of Monte-Carlo simulations clearly indicate that there is no uniformly powerful test. The parametric bootstrap test is superior to the others except in the case of the lower number of groups and the presence of outliers. An illustrative example of testing the equality lifetimes of a component is given to perform the proposed tests. The considered tests are implemented in an R package doex.

Model-based community health surveillance via multilevel small area estimation using state behavioral risk factor surveillance system (BRFSS): a case study in Connecticut

PurposeThe main objective of state behavioral risk factor surveillance system (BRFSS) is to produce reliable state-level estimates of various population health outcomes. A multilevel Regression and Post-stratification (MRP) methodology for small area estimation has been applied to the 500 Cities Project to provide population estimates at both city-level and census tract-level using national BRFSS data. To date, MRP has not been applied to any state BRFSS to produce health data at local geographic areas. In addition, the use of single year BRFSS might produce temporary inconsistency in small area estimates (SAEs). The predicted standard errors (SEs) and confidence intervals (CIs) of SAEs using Monte Carlo simulation could be substantially underestimated or overestimated. MethodsBy extending the current MRP approach and applying a parametric bootstrapping approach to Connecticut BRFSS (CT BRFSS), we were able to produce SAEs as well as SEs and CIs of SAEs for Connecticut counties and towns. We also applied this model to 5-year CT BRFSS (2011–2015) with an aim to improve the temporary consistency of SAEs. ResultsBoth single-year and 5-year estimates with SEs and CIs were generated for six selected population health indicators at town, county and state levels. Model-based SAEs were internally evaluated by comparing to single-year and 5-year direct BRFSS survey (2011–2015). SAEs were also externally validated when external data were available. ConclusionsModel-based SAEs are valid and could be used to characterize local geographic variations using single state BRFSS data.

Rectangular tolerance regions and multivariate normal reference regions in laboratory medicine.

Reference intervals are widely used in the interpretation of results of biochemical and physiological tests of patients. When there are multiple biochemical analytes measured from each subject, a multivariate reference region is needed. Because of their greater specificity against false positives, such reference regions are more desirable than separate univariate reference intervals that disregard the cross-correlations between variables. Traditionally, under multivariate normality, reference regions have been constructed as ellipsoidal regions. This approach suffers from a major drawback: it cannot detect component-wise extreme observations. In the present work, procedures are developed to construct rectangular reference regions in the multivariate normal setup. The construction is based on the criteria for tolerance intervals. The problems addressed include the computation of a rectangular tolerance region and simultaneous tolerance intervals. Also addressed is the computation of mixed reference intervals that include both two-sided and one-sided limits, simultaneously. A parametric bootstrap approach is used in the computations, and the accuracy of the proposed methodology is assessed using estimated coverage probabilities. The problem of sample size determination is also addressed, and the results are illustrated using examples that call for the computation of referenceregions.

Confidence Intervals Based on the Difference of Medians for Independent Log-Normal Distributions

In this paper, we study the inferences of the difference of medians for two independent log-normal distributions. These methods include traditional methods such as the parametric bootstrap approach, the normal approximation approach, the method of variance estimates recovery approach, and the generalized confidence interval approach. The simultaneous confidence intervals for the difference in the median for more than two independent log-normal distributions are also discussed. Our simulation studies evaluate the performances of the proposed confidence intervals in terms of coverage probabilities and average lengths. We find that the parametric bootstrap approach would be a suitable choice for smaller sample sizes for the two independent distributions and multiple independent distributions. However, the method of variance estimates recovery and normal approximation approaches are alternative competitors for constructing simultaneous confidence intervals, especially when the populations have large variance. We also include two practical applications demonstrating the use of the techniques on observed data, where one data set works for the PM2.5 mass concentrations in Bangkapi and Dindaeng in Thailand and the other data came from the study of nitrogen-bound bovine serum albumin produced by three groups of diabetic mice. Both applications show that the confidence intervals from the parametric bootstrap approach have the smallest length.

Rectangular multivariate normal prediction regions for setting reference regions in laboratory medicine

ABSTRACT Reference intervals are among the most widely used medical decision-making tools and are invaluable in the interpretation of laboratory results of patients. Moreover, when multiple biochemical analytes are measured on each patient, a multivariate reference region (MRR) is needed. Such regions are more desirable than separate univariate reference intervals since the latter disregard the cross-correlations among variables. Traditionally, assuming multivariate normality, MRRs have been constructed as ellipsoidal regions, which cannot detect componentwise extreme values. Consequently, MRRs are rarely used in actual practice. In order to address the above drawback of ellipsoidal reference regions, we propose a procedure to construct rectangular MRRs under multivariate normality. The rectangular MRR is computed using a prediction region criterion. However, since the population correlations are unknown, a parametric bootstrap approach is employed for computing the required prediction factor. Also addressed in this study is the computation of mixed reference intervals, which include both two-sided and one-sided prediction limits, simultaneously. Numerical results show that the parametric bootstrap procedure is quite accurate, with estimated coverage probabilities very close to the nominal level. Moreover, the expected volumes of the proposed rectangular regions are substantially smaller than the expected volumes obtained from Bonferroni simultaneous prediction intervals. We also explore the computation of covariate-dependent MRRs in a multivariate regression setting. Finally, we discuss real-life applications of the proposed methods, including the computation of reference ranges for the assessment of kidney function and for components of the insulin-like growth factor system in adults.