Jackknife Variance Estimator Research Articles

Heavy alcohol use and the HIV care continuum in Kenya: a population-based study

ABSTRACT Heavy alcohol use (HAU) can destabilize engagement along the HIV care continuum. Population-based studies assessing associations of HAU with HIV treatment outcomes are lacking, especially in sub-Saharan Africa. We leveraged data from the Kenya Population-based HIV Impact Assessment to identify associations of self-reported HAU, assessed using two items measuring the frequency and quantity of past-year alcohol consumption, with serum biomarkers for HIV serostatus unawareness, antiretroviral therapy (ART) non-use, and HIV viremia (≥1000 RNA copies/mL). Overall and sex-stratified survey-weighted logistic regression with jackknife variance estimation modeled adjusted odds ratios (adjOR) of HIV treatment indicators by HAU. Overall, 1491 persons living with HIV aged 15–64 years (68.4% female) were included. The prevalence of HAU was 8.9% (95% confidence interval [95%CI]: 6.8–11.0%) and was significantly more pronounced in males than females (19.6% vs. 4.0%, p < 0.001). In multivariable analysis, HAU was significantly (p < 0.001) associated with HIV serostatus unawareness (adjOR = 3.65, 95%CI: 2.14–6.23), ART non-use (adjOR = 3.81, 95%CI: 2.25–6.43), and HIV viremia (adjOR = 3.13, 95%CI: 1.85–5.32). Incorporating sex-specific alcohol use screening into HIV testing and treatment services in populations where HAU is prevalent could optimize clinical outcomes along the HIV care continuum.

Stationary Jackknife

Variance estimation is an important aspect in statistical inference, especially in the dependent data situations. Resampling methods are ideal for solving this problem since these do not require restrictive distributional assumptions. In this paper, we develop a novel resampling method in the Jackknife family called the stationary jackknife. It can be used to estimate the variance of a statistic in the cases where observations are from a general stationary sequence. Unlike the moving block jackknife, the stationary jackknife computes the jackknife replication by deleting a variable length block and the length has a truncated geometric distribution. Under appropriate assumptions, we can show the stationary jackknife variance estimator is a consistent estimator for the case of the sample mean and, more generally, for a class of nonlinear statistics. Further, the stationary jackknife is shown to provide reasonable variance estimation for a wider range of expected block lengths when compared with the moving block jackknife by simulation.

SleepMore

The availability of commercial wearable trackers equipped with features to monitor sleep duration and quality has enabled more useful sleep health monitoring applications and analyses. However, much research has reported the challenge of long-term user retention in sleep monitoring through these modalities. Since modern Internet users own multiple mobile devices, our work explores the possibility of employing ubiquitous mobile devices and passive WiFi sensing techniques to predict sleep duration as the fundamental measure for complementing long-term sleep monitoring initiatives. In this paper, we propose SleepMore, an accurate and easy-to-deploy sleep-tracking approach based on machine learning over the user's WiFi network activity. It first employs a semi-personalized random forest model with an infinitesimal jackknife variance estimation method to classify a user's network activity behavior into sleep and awake states per minute granularity. Through a moving average technique, the system uses these state sequences to estimate the user's nocturnal sleep period and its uncertainty rate. Uncertainty quantification enables SleepMore to overcome the impact of noisy WiFi data that can yield large prediction errors. We validate SleepMore using data from a month-long user study involving 46 college students and draw comparisons with the Oura Ring wearable. Beyond the college campus, we evaluate SleepMore on non-student users of different housing profiles. Our results demonstrate that SleepMore produces statistically indistinguishable sleep statistics from the Oura ring baseline for predictions made within a 5% uncertainty rate. These errors range between 15-28 minutes for determining sleep time and 7-29 minutes for determining wake time, proving statistically significant improvements over prior work. Our in-depth analysis explains the sources of errors.

Interpoint distance-based two-sample tests for functional data

This study examines interpoint distance-based tests for random elements from probability distributions in infinite-dimensional space. Some asymptotic properties such as the limiting distributions and the asymptotic power of the Biswas–Ghosh type test (Biswas and Ghosh in J Multivar Anal 123: 160–171, 2014) are presented using the theory of U-statistic. In addition, the p-value approximation based on the jackknife variance estimators and the Welch–Satterthwaite equation is proposed. Simulation studies are conducted to evaluate the performance of the proposed test statistics in functional data analysis. The proposed tests are shown to have better power than the existing method for functional data in some situations.

A Bootstrap Variance Procedure for the Generalised Regression Estimator

SummaryThe generalised regression estimator (GREG) uses auxiliary data that are available from the finite population to improve the efficiency of the estimator of a total (mean). Estimators of the variance of GREG that have been proposed in the sampling literature include those based on Taylor linearisation and the jackknife techniques. Approximations based on Taylor expansions are reasonable for large samples. However, when the sample size is small, the Taylor‐based variance estimator has a large negative bias. The jackknife variance estimators overestimate the variance of GREG for small sample sizes. We offset these setbacks using a bootstrap procedure for estimating the variance of the GREG. The method uses a bootstrap population constructed with the model underlying the GREG estimator. Repeated samples are selected in the bootstrap population according to the design used to select the initial sample, and the variability associated with these bootstrap samples is used to compute the proposed bootstrap variance estimator. Simulations show that the new bootstrap estimator has a small bias for samples that have few observations.

Inverse weighting method with jackknife variance estimator for differential expression analysis of single-cell RNA sequencing data

Single-cell RNA sequencing (scRNA-seq) data exhibit an unusual abundance of zero counts with a considerable fraction due to the dropout events, which introduces challenges to differential expression analysis. To correct biases in differential expression due to the informative dropouts, an inverse non-dropout-probability weighting method is proposed given that the dropout rate is negatively dependent on the underlying gene expression magnitude in scRNA-seq data. The weights are estimated using the maximum likelihood method where dropout values are integrated out using the Gauss-Hermite quadrature. Linear, generalized linear and mixed regressions with the estimated weights are fitted on original or transformed scRNA-seq data. Variances of coefficient estimators from the weighted regressions are estimated using the jackknife method. Extensive simulation studies are carried out to compare the proposed method to five cutting-edge methods (Limma, edgeR, MAST, ZIAQ and scImpute), where the proposed method performs among the best under all scenarios in terms of AUC, sensitivity, specificity and FDR. Rate of detecting true positives is examined for the proposed method and five comparison methods using mouse embryonic stem cells and fibroblasts where differentially expressed (DE) genes detected in bulk RNA-seq data on the same set of genes under the same conditions from independent source serve as true positives. Specificity is compared for these methods on true negative data by random splitting of a real dataset. Furthermore, the proposed method is illustrated on a lineage study where cells in the same embryo are correlated and genes differentially expressed between cell division lineages are identified.

Weighted U-statistics for likelihood-ratio ordering of bivariate data

Characterisation of marginal distribution and density functions is of interest where data on a pair of random variables (X, Y) are observed. Stochastic orderings between (X, Y) have been studied in statistics and economics. Likelihood-ratio ordering is useful in understanding the behaviour of the random variables. In this article, tests based on U-statistics are proposed to test for equality of marginal density functions against the alternative of likelihood-ratio ordered when (X, Y) are dependent. The tests can be used when the data are either completely observed or subjected to independent univariate right censoring. The asymptotic variances of these tests are complicated and hence, are estimated using jackknife variance estimators. Validity of the jackknife variance estimators in statistical inference based on the proposed tests is demonstrated using simulation studies. The test for uncensored setting has desired size and good power for small sample. The performance of the tests for censored case depends on the sample size, proportion of censoring and the measure of dependence between X and Y. The tests are illustrated on three real data sets chosen in order to bring out various aspects of the tests.

Quantifying uncertainty of subsampling-based ensemble methods under a U-statistic framework

ABSTRACT This paper addresses the problem of variance estimation of predictions obtained from a subsampling-based ensemble estimator, such as subbagging and sub-random forest. We first recognize that a subsampling-based ensemble can be written as an infinite-order U-statistic of degree , where is the subsample size that may depend on the learning sample size n. As a result, one can study the uncertainty of predictions obtained from a subsampling-based ensemble under a U-statistic framework, such as approximating its asymptotic variance. However, existing methods used to estimate the asymptotic variance relies on some regularity conditions. In addition, they tend to yield variance estimations with large bias in finite sample scenarios. Motivated by the work of Wang and Lindsay (2014), we propose to construct an unbiased variance estimator for a subsampling-based ensemble. It is efficient to realize with the help of a partition-resampling scheme. We show by simulation studies that the proposed variance estimator yields better performance in terms of mean, standard deviation, and mean squared error compared to both the infinitesimal jackknife and internal variance estimation methods under either a simple linear regression model or a multivariate adaptive regression splines model. Furthermore, we present how to construct an asymptotic confidence interval for the expected prediction at a given test instance using the proposed variance estimator, and compare its coverage probability to that of competing methods. In the end, we demonstrate the practical applications of the methodology using two real data examples.

Jackknife winsorized variance estimator under imputed data

Abstract In the present study, we consider the problem of missing and extreme values for the estimation of population variance. The presence of extreme values either in the study variable, or the auxiliary variable, or in both of them, can adversely affect the performance of the estimation procedure. We consider three different situations for the presence of extreme values and also consider jackknife variance estimators for the population variance by handling these extreme values under stratified random sampling. Bootstrap technique ABB is carried out to understand the relative relationship more precisely.

Characteristics of users of HIV self-testing in Kenya, outcomes, and factors associated with use: results from a population-based HIV impact assessment, 2018

Background and settingAbout 20% of persons living with HIV aged 15–64 years did not know their HIV status in Kenya, by 2018. Kenya adopted HIV self-testing (HIVST) to help close this gap. We examined the sociodemographic characteristics and outcomes of self-reported users of HIVST as our primary outcome.MethodsWe used data from a 2018 population-based cross-sectional household survey in which we included self-reported sociodemographic and behavioral characteristics and HIV test results. To compare weighted proportions, we used the Rao-Scott χ-square test and Jackknife variance estimation. In addition, we used logistic regression to identify associations of sociodemographic, behavioral, and HIVST utilization.ResultsOf the 23,673 adults who reported having ever tested for HIV, 937 (4.1%) had ever self-tested for HIV. There were regional differences in HIVST, with Nyanza region having the highest prevalence (6.4%), p < 0.001. Factors independently associated with having ever self-tested for HIV were secondary education (adjusted odds ratio [aOR], 3.5 [95% (CI): 2.1–5.9]) compared to no primary education, being in the third (aOR, 1.7 [95% CI: 1.2–2.3]), fourth (aOR, 1.6 [95% CI: 1.1–2.2]), or fifth (aOR, 1.8 [95% CI: 1.2–2.7]) wealth quintiles compared to the poorest quintile and having one lifetime sexual partner (aOR, 1.8 [95% CI: 1.0–3.2]) or having ≥ 2 partners (aOR, 2.1 [95% CI: 1.2–3.7]) compared to none. Participants aged ≥ 50 years had lower odds of self-testing (aOR, 0.6 [95% CI: 0.4–1.0]) than those aged 15–19 years.ConclusionKenya has made progress in rolling out HIVST. However, geographic differences and social demographic factors could influence HIVST use. Therefore, more still needs to be done to scale up the use of HIVST among various subpopulations. Using multiple access models could help ensure equity in access to HIVST. In addition, there is need to determine how HIVST use may influence behavior change towardsaccess to prevention and HIV treatment services.

Estimation of genetic correlation with summary association statistics

SummaryGenome-wide association studies have identified thousands of genetic variants that are associated with complex traits. Many complex traits are shown to share genetic etiology. Although various genetic correlation measures and their estimators have been developed, rigorous statistical analysis of their properties, including their robustness to model assumptions, is still lacking. We develop a method of moments estimator of genetic correlation between two traits in the framework of high-dimensional linear models. We show that the genetic correlation defined based on the regression coefficients and the linkage disequilibrium matrix can be decomposed into both the pleiotropic effects and correlations due to linkage disequilibrium between the causal loci of the two traits. The proposed estimator can be computed from summary association statistics when the raw genotype data are not available. Theoretical properties of the estimator in terms of consistency and asymptotic normality are provided. The proposed estimator is closely related to the estimator from the linkage disequilibrium score regression. However, our analysis reveals that the linkage disequilibrium score regression method does not make full use of the linkage disequilibrium information, and its jackknife variance estimate can be biased when the model assumptions are violated. Simulations and real data analysis results show that the proposed estimator is more robust and has better interpretability than the linkage disequilibrium score regression method under different genetic architectures.

Jackknife empirical likelihood: small bandwidth, sparse network and high-dimensional asymptotics

Summary This article aims to shed light on inference problems for statistical models under alternative or nonstandard asymptotic frameworks from the perspective of the jackknife empirical likelihood. Examples include small-bandwidth asymptotics for semiparametric inference and goodness-of-fit testing, sparse-network asymptotics, many-covariates asymptotics for regression models, and many-weak-instruments asymptotics for instrumental variable regression. We first establish Wilks’ theorem for the jackknife empirical likelihood statistic in a general semiparametric inference problem under the conventional asymptotics. We then show that the jackknife empirical likelihood statistic may lose asymptotic pivotalness in the above nonstandard asymptotic frameworks, and argue that this phenomenon can be understood in terms of the emergence of Efron &amp; Stein (1981)’s bias of the jackknife variance estimator at first order. Finally, we propose a modification of the jackknife empirical likelihood to recover asymptotic pivotalness under both conventional and nonstandard asymptotics. Our modification works for all of the above examples and provides a unified framework for investigating nonstandard asymptotic problems.

An efficient variance estimator of AUC and its applications to binary classification.

The area under the ROC (receiver operating characteristic) curve, AUC, is one of the most commonly used measures to evaluate the performance of a binary classifier. Due to sampling variation, the model with the largest observed AUC score is not necessarily optimal, so it is crucial to assess the variation of AUC estimate. We extend the proposal by Wang and Lindsay and devise an unbiased variance estimator of AUC estimate that is of a two-sample U-statistic form. The proposal can be easily generalized to estimate the variance of a K-sample U-statistic (K ≥ 2). To make our developed variance estimator more applicable, we employ a partition-resampling scheme that is computationally efficient. Simulation studies suggest that the developed AUC variance estimator yields much better or comparable performance to jackknife and bootstrap variance estimators, and computational times that are about 10 to 30 times faster than the times of its counterparts. In practice, the proposal can be used in the one-standard-error rule for model selection, or to construct an asymptotic confidence interval of AUC in binary classification. In addition to conducting simulation studies, we illustrate its practical applications using two real datasets in medical sciences.

Methods for the robust computation of the long-period seismic spectrum of broad-band arrays

SUMMARY We describe array methods to search for low signal-to-noise ratio (SNR) signals in long-period seismic data using Fourier analysis. This is motivated by published results that find evidence of solar free oscillations in the Earth's seismic hum. Previous work used data from only one station. In this paper, we describe methods for computing spectra from array data. Arrays reduce noise level through averaging and provide redundancy that we use to distinguish coherent signal from a random background. We describe two algorithms for calculating a robust spectrum from seismic arrays, an algorithm that automatically removes impulsive transient signals from data, a jackknife method for estimating the variance of the spectrum, and a method for assessing the significance of an entire spectral band. We show examples of their application to data recorded by the Homestake Mine 3-D array in Lead, SD and the Piñon Flats PY array. These are two of the quietest small aperture arrays ever deployed in North America. The underground Homestake data has exceptionally low noise, and the borehole sensors of the PY array also have very low noise, making these arrays well suited to finding very weak signals. We find that our methods remove transient signals effectively from the data so that even low-SNR signals in the seismic background can be found and tested. Additionally, we find that the jackknife variance estimate is comparable to the noise floor, and we present initial evidence for solar g-modes in our data through the T2 test, a multivariate generalization of Student's t-test.

Jackknife variance estimation for general two-sample statistics and applications to common mean estimators under ordered variances

We study the jackknife variance estimator for a general class of two-sample statistics. As a concrete application, we consider samples with a common mean but possibly different, ordered variances as arising in various fields such as interlaboratory experiments, field studies, or the analysis of sensor data. Estimators for the common mean under ordered variances typically employ random weights, which depend on the sample means and the unbiased variance estimators. They take different forms when the sample estimators are in agreement with the order constraints or not, which complicates even basic analyses such as estimating their variance. We propose to use the jackknife, whose consistency is established for general smooth two-sample statistics induced by continuously Gâteux or Frechet-differentiable functionals, and, more generally, asymptotically linear two-sample statistics, allowing us to study a large class of common mean estimators. Furthermore, it is shown that the common mean estimators under consideration satisfy a central limit theorem (CLT). We investigate the accuracy of the resulting confidence intervals by simulations and illustrate the approach by analyzing several data sets.

Adjustments of multi-sample [formula omitted]-statistics to right censored data and confounding covariates

U-statistics that can be used for comparing distribution of outcomes in two groups are considered. Adjustments to the classical U-statistics are proposed for overcoming potential biases arising from right-censoring of the outcomes and presence of confounding covariates. These newly proposed U-statistics are appropriate when, in addition to right censored outcomes, some fixed covariates are observed and deemed as confounders in an observational study. The summands of U-statistics are re-weighted and normalized based on a combination of inverse probability of censoring weights and propensity score based weights. Censoring times may depend on the group membership, confounders or some potentially observed time-dependent covariates, which may result in censoring mechanisms of varying degrees of complexity. In total, four censoring mechanisms are considered for the two-group comparison. Simulation results are used to illustrate the impact of right-censoring and confounding covariates on the performance of the newly proposed U-statistics under different censoring mechanisms. It is also demonstrated that large sample inferences for the adjusted U-statistics are valid using jackknife variance estimator. Comparisons of more than two groups are also considered from certain ways of pairwise two-group comparisons. The procedure is applied to analyze two real data sets for comparing two or more groups of event times. R codes of our procedure are available under supplementary material.

Informal Caregivers' Use of Internet-Based Health Resources: An Analysis of the Health Information National Trends Survey.

BackgroundInformal caregivers express strong interest in technology innovations to help them in their caregiving role; however, divides across sociodemographic characteristics in internet and technology access may preclude the most vulnerable caregivers from accessing such resources.ObjectiveThis study aims to examine caregivers’ internet use, both generally and for seeking health-related information, and whether usage differs as a function of caregivers’ characteristics.MethodsData were analyzed from the Health Information National Trends Survey 5 Cycle 1. Participants were included in analyses if they self-identified as providing uncompensated care to a close individual. Caregivers reported internet use factors, age, education, rurality, general health, distress, and objective caregiving burden. We used chi-square tests of independence with jackknife variance estimation to compare whether internet use factors differed by caregivers’ characteristics.ResultsA total of 77.5% (303/391) caregivers surveyed reported ever using the internet. Of internet users, 88.1% (267/303) accessed from a home computer and 83.2% (252/303) from a mobile device. Most caregivers accessed health information for themselves (286/391, 73.1%) or others (264/391, 67.5%); fewer communicated with a doctor over the Web (148/391, 37.9%) or had a wellness app (171/391, 43.7%). Caregivers reporting younger age, more education, and good health were more likely to endorse any of these activities. Furthermore, two-thirds of caregivers (258/391, 66.0%) endorsed trust in health information from the internet.ConclusionsComputers and mobile devices are practical platforms for disseminating caregiving-related information and supportive services to informal caregivers; these modalities may, however, have a more limited reach to caregivers who are older, have less education, and are in poorer health.

Standard errors and confidence intervals for variable importance in random forest regression, classification, and survival.

Random forests are a popular nonparametric tree ensemble procedure with broad applications to data analysis. While its widespread popularity stems from its prediction performance, an equally important feature is that it provides a fully nonparametric measure of variable importance (VIMP). A current limitation of VIMP, however, is that no systematic method exists for estimating its variance. As a solution, we propose a subsampling approach that can be used to estimate the variance of VIMP and for constructing confidence intervals. The method is general enough that it can be applied to many useful settings, including regression, classification, and survival problems. Using extensive simulations, we demonstrate the effectiveness of the subsampling estimator and in particular find that the delete-d jackknife variance estimator, a close cousin, is especially effective under low subsampling rates due to its bias correction properties. These 2 estimators are highly competitive when compared with the .164 bootstrap estimator, a modified bootstrap procedure designed to deal with ties in out-of-sample data. Most importantly, subsampling is computationally fast, thus making it especially attractive for big data settings.

Grouping Effects on Jackknifed Variance Estimation for Item Response Theory Scaling and Equating With Cluster‐Based Assessment Data

AbstractEducational assessment data are often collected from a set of test centers across various geographic regions, and therefore the data samples contain clusters. Such cluster‐based data may result in clustering effects in variance estimation. However, in many grouped jackknife variance estimation applications, jackknife groups are often formed by a random grouping method that ignores the cluster structures of the data. In this study, we constructed both random and cluster‐based jackknife groups for data known to have cluster structures and compared the jackknifed standard errors, yielded by two different grouping methods, of item response theory (IRT) scaling coefficient estimates and equated scores. Three independent data samples from an international test of English were used for the study. The cluster‐based jackknife group results showed relatively larger jackknifed standard errors of scaling coefficient estimates and scale scores than the results of the random jackknife groups for all three data samples. For cluster‐based assessment data, the cluster‐based jackknife approach provides a more appropriate way to estimate the standard errors of the parameters of IRT calibration, scaling, and equating analyses.

Estimation of the volume under the receiver-operating characteristic surface adjusting for non-ignorable verification bias.

The receiver-operating characteristic surface is frequently used for presenting the accuracy of a diagnostic test for three-category classification problems. One common problem that can complicate the estimation of the volume under receiver-operating characteristic surface is that not all subjects receive the verification of the true disease status. Estimation based only on data from subjects with verified disease status may be biased, which is referred to as verification bias. In this article, we propose new verification bias correction methods to estimate the volume under receiver-operating characteristic surface for a continuous diagnostic test. We assume the verification process is missing not at random, which means the missingness might be related to unobserved clinical characteristics. Three classes of estimators are proposed, namely, inverse probability weighted, imputation-based, and doubly robust estimators. A jackknife estimator of variance is derived for all the proposed volume under receiver-operating characteristic surface estimators. The finite sample properties of the new estimators are examined via simulation studies. We illustrate our methods with data collected from Alzheimer's disease research.