Jackknife Variance Research Articles

Improving External Validity of Epidemiologic Cohort Analyses: A Kernel Weighting Approach.

For various reasons, cohort studies generally forgo probability sampling required to obtain population representative samples. However, such cohorts lack population-representativeness, which invalidates estimates of population prevalences for novel health factors only available in cohorts. To improve external validity of estimates from cohorts, we propose a kernel weighting (KW) approach that uses survey data as a reference to create pseudo-weights for cohorts. A jackknife variance is proposed for the KW estimates. In simulations, the KW method outperformed two existing propensity-score-based weighting methods in mean-squared error while maintaining confidence interval coverage. We applied all methods to estimating US population mortality and prevalences of various diseases from the non-representative US NIH-AARP cohort, using the sample from US-representative National Health Interview Survey (NHIS) as the reference. Assuming that the NHIS estimates are correct, the KW approach yielded generally less biased estimates compared to the existing propensity-score-based weighting methods.

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.

Practical issues in using generalized estimating equations for inference on transitions in longitudinal data: What is being estimated?

Generalized estimating equations (GEEs) are commonly used to estimate transition models. When the Markov assumption does not hold but first-order transition probabilities are still of interest, the transition inference is sensitive to the choice of working correlation. In this paper, we consider a random process transition model as the true underlying data generating mechanism, which characterizes subject heterogeneity and complex dependence structure of the outcome process in a very flexible way. We formally define two types of transition probabilities at the population level: "naive transition probabilities" that average across all the transitions and "population-average transition probabilities" that average the subject-specific transition probabilities. Through asymptotic bias calculations and finite-sample simulations, we demonstrate that the unstructured working correlation provides unbiased estimators of the population-average transition probabilities while the independence working correlation provides unbiased estimators of the naive transition probabilities. For population-average transition estimation, we demonstrate that the sandwich estimator fails for unstructured GEE and recommend the use of either jackknife or bootstrap variance estimates. The proposed method is motivated by and applied to the NEXT Generation Health Study, where the interest is in estimating the population-average transition probabilities of alcohol use in adolescents.

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.

How are multifactorial beliefs about the role of genetics and behavior in cancer causation associated with cancer risk cognitions and emotions in the US population?

People who believe that cancer has both genetic and behavioral risk factors have more accurate mental models of cancer causation and may be more likely to engage in cancer screening behaviors than people who do not hold such multifactorial causal beliefs. This research explored possible health cognitions and emotions that might produce such differences. Using nationally representative cross-sectional data from the US Health Information National Trends Survey (N=2719), we examined whether endorsing a multifactorial model of cancer causation was associated with perceptions of risk and other cancer-related cognitions and affect. Data were analyzed using linear regression with jackknife variance estimation and procedures to account for the complex survey design and weightings. Bivariate and multivariable analyses indicated that people who endorsed multifactorial beliefs about cancer had higher absolute risk perceptions, lower pessimism about cancer prevention, and higher worry about harm from environmental toxins that could be ingested or that emanate from consumer products (Ps<.05). Bivariate analyses indicated that multifactorial beliefs were also associated with higher feelings of risk, but multivariable analyses suggested that this effect was accounted for by the negative affect associated with reporting a family history of cancer. Multifactorial beliefs were not associated with believing that everything causes cancer or that there are too many cancer recommendations to follow (Ps>.05). Holding multifactorial causal beliefs about cancer are associated with a constellation of risk perceptions, health cognitions, and affect that may motivate cancer prevention and detection behavior.

Multiply robust imputation procedures for zero-inflated distributions in surveys.

Item nonresponse in surveys is usually treated by some form of single imputation. In practice, the survey variable subject to missing values may exhibit a large number of zero-valued observations. In this paper, we propose multiply robust imputation procedures for treating this type of variable. Our procedures may be based on multiple imputation models and/or multiple nonresponse models. An imputation procedure is said to be multiply robust if the resulting estimator is consistent when all models but one are misspecified. The variance of the imputed estimators is estimated through a generalized jackknife variance estimation procedure. Results from a simulation study suggest that the proposed procedures perform well in terms of bias, efficiency and coverage rate.

Extrapolation techniques in U-statistic variance estimation

ABSTRACTThis article considers the problem of variance estimation of a U-statistic. Following the proposal of a linearly extrapolated variance estimator in Wang and Chen (2015), we consider a second-order extrapolation technique and devise a variance estimator that is nearly second-order unbiased. Simulation studies confirm that the second-order extrapolated variance estimator has smaller bias than the linearly extrapolated variance estimator and the jackknife variance estimator across a wide selection of distributions. In addition, the proposal also yields a smaller mean squared error than its counterparts. In the end, we discuss the advantages of the proposed variance estimator in regression analysis and model selection.

Fusing photovoltaic data for improved confidence intervals

Characterizing and testing photovoltaic modules requires carefully made measurements on important variables such as the power output under standard conditions. When additional data is available, which has been collected using a different measurement system and therefore may be of different accuracy, the question arises how one can combine the information present in both data sets. In some cases one even has prior knowledge about the ordering of the variances of the measurement errors, which is not fully taken into account by commonly known estimators. We discuss several statistical estimators to combine the sample means of independent series of measurements, both under the assumption of heterogeneous variances and ordered variances. The critical issue is then to assess the estimator’s variance and to construct confidence intervals. We propose and discuss the application of a new jackknife variance estimator devised by [1] to such photovoltaic data, in order to assess the variability of common mean estimation under heterogeneous and ordered variances in a reliable and nonparametric way. When serial correlations are present, which usually a ect the marginal variances, it is proposed to construct a thinned data set by downsampling the series in such a way that autocorrelations are removed or dampened. We propose a data adaptive procedure which downsamples a series at irregularly spaced time points in such a way that the autocorrelations are minimized. The procedures are illustrated by applying them to real photovoltaic power output measurements from two different sun light flashers. In addition, focusing on simulations governed by real photovoltaic data, we investigate the accuracy of the jackknife approach and compare it with other approaches. Among those is a variance estimator based on Nair’s formula for Gaussian data and, as a parametric alternative, two Bayesian models. We investigate the statistical accuracy of the resulting confidence resp. credible intervals used in practice to assess the uncertainty present in the data.

OUP accepted manuscript

SummaryItem nonresponse in surveys is often treated through some form of imputation. We introduce multiply robust imputation in finite population sampling. This is closely related to multiple robustness, which extends double robustness. In practice, multiple nonresponse models and multiple imputation models may be fitted, each involving different subsets of covariates and possibly different link functions. An imputation procedure is said to be multiply robust if the resulting estimator is consistent when all models but one are misspecified. A jackknife variance estimator is proposed and shown to be consistent. Random and fractional imputation procedures are discussed. A simulation study suggests that the proposed estimation procedures have low bias and high efficiency.

Variance estimation of DEE and regression estimator when a first-phase cluster sample is restratified

ABSTRACTWe consider a variance estimation when a stratified single stage cluster sample is selected in the first phase and a stratified simple random element sample is selected in the second phase. We propose explicit formulas of (asymptotically), we propose explicit formulas of (asymptotically) unbiased variance estimators for the double expansion estimator and regression estimator. We perform a small simulation study to investigate the performance of the proposed variance estimators. In our simulation study, the proposed variance estimator showed better or comparable performance to the Jackknife variance estimator. We also extend the results to a two-phase sampling design in which a stratified pps with replacement cluster sample is selected in the first phase.

Vertically Weighted Averages in Hilbert Spaces and Applications to Imaging: Fixed-Sample Asymptotics and Efficient Sequential Two-Stage Estimation

We discuss fixed-sample asymptotics and jackknife variance estimation for vertically weighted averages and the construction of related sequential two-stage confidence intervals. Those vertically weighted averages represent a class of nonlinear smoothers that are commonly applied to denoise observations without corrupting details (such as jumps in a time series or object boundaries in an image), detect those details, and design segmentation procedures. In addition to their extensive use in imaging, they have been also successfully applied in signal processing and financial data analysis. This article extends this approach to general functional data taking values in a Hilbert space and establishes the related asymptotic distribution theory in terms of central limit theorems and their sequential generalizations. In addition, focusing on real-valued data, the problems of variance estimation by the jackknife and two-stage estimation are studied. We show that the jackknife is consistent and asymptotically unbiased, thus providing an easy-to-use approach to evaluate the estimator's precision. Because the inhomogeneous variance of vertically weighted averages is a drawback when denoising data, we study the construction of fixed-width confidence intervals based on a two-stage sampling procedure in the spirit of Stein's (1945) seminal article. The proposed procedure can be shown to be consistent for the asymptotic optimal fixed-sample solution as well as asymptotically first-order efficient.

A Border Versus Non-Border Comparison of Food Environment, Poverty, and Ethnic Composition in Texas Urban Settings

The goal was to examine the relationship between the food environment and selected socioeconomic variables and ethnic/racial makeup in the eight largest urban settings in Texas so as to gain a better understanding of the relationships among Hispanic composition, poverty, and urban foodscapes, comparing border to non-border urban environments. Census-tract level data on (a) socioeconomic factors, like percentage below the poverty line and number of households on foodstamps, and (b) ethnic variables, like percent of Mexican origin and percent foreign born, were obtained from the U.S. Census. Data at the census-tract level on the total number of healthy (e.g., supermarkets) and less-healthy (e.g., fast food outlets) food retailers were acquired from the CDC's modified retail food environment index (mRFEI). Variation among urban settings in terms of the relationship between mRFEI scores and socioeconomic and ethnic context was tested using a mixed-effect model, and linear regression was used to identify significant factors for each urban location. A jackknife variance estimate was used to account for clustering and autocorrelation of adjacent census tracts. Average census-tract mRFEI scores exhibited comparatively small variation across Texas urban settings, while socioeconomic and ethnic factors varied significantly. The only covariates significantly associated with mRFEI score were percent foreign born and percent Mexican origin. Compared to the highest-population county (Harris, which incorporates most of Houston), the only counties that had significantly different mRFEI scores were Bexar, which is analogous to San Antonio (2.12 lower), El Paso (2.79 higher), and Neuces, which encompasses Corpus Christi (2.90 less). Significant interaction effects between mRFEI and percent foreign born (El Paso, Tarrant - Fort Worth, Travis - Austin), percent Mexican origin (Hidalgo - McAllen, El Paso, Tarrant, Travis), and percent living below the poverty line (El Paso) were observed for some urban settings. Percent foreign born and percent Mexican origin tended to be positively associated with mRFEI in some locations (Hidalgo, El Paso) and negatively associated in others (Tarrant, Travis). Findings are consistent with other studies that suggest the effects of Hispanic concentration on the foodscape may be positive (beneficially healthy) in border urban settings and negative in non-border. The evidence implies that the effects of Hispanic ethnic composition on the food environment are location-dependent, reflecting the unique attributes (e.g., culture, infrastructure, social networks) of specific urban settings.

A general class of linearly extrapolated variance estimators

A general class of linearly extrapolated variance estimators was developed as an extension of the conventional leave-one-out jackknife variance estimator. In the context of U-statistic variance estimation, the proposed variance estimator is first-order unbiased. After showing the equivalence between the Hoeffding decomposition (Hoeffding, 1948) and the ANOVA decomposition (Efron and Stein, 1981), we study the bias property of the proposed variance estimator in comparison to the conventional jackknife method. Simulation studies indicate that the proposal has comparable performance to the jackknife method when assessing the variance of the sample variance in various distributions. An application to half-sampling cross-validation indicates that the proposal is more computationally efficient and shows better performance than its jackknife counterpart in the context of regression analysis.

Doubly robust imputation procedures for finite population means in the presence of a large number of zeros

AbstractSingle imputation is often used in surveys to compensate for item nonresponse. In some cases, the variable requiring imputation contains a large amount of zeros. This is especially frequent in business surveys that collect economic variables. Motivated by a mixture regression model, we propose three imputation procedures and study their properties in terms of bias and variance. We show that these procedures are doubly robust, leading to consistent estimators of the finite population mean if either the imputation model or the nonresponse model is well specified. For the proposed procedures, we consider a jackknife variance estimator, which is consistent for the true variance, provided the overall sampling fraction is negligible. Finally, the results of a simulation study comparing the performance of point and variance estimators in terms of relative bias and mean square error are presented. The Canadian Journal of Statistics 42: 650–669; 2014 © 2014 Statistical Society of Canada

Replication Variance Estimation under Two-phase Sampling in the Presence of Non-response

Kim and Yu (2011) discussed replication variance estimator for two-phase stratified sampling. In this paper estimators for mean have been proposed in two-phase stratified sampling for different situation of existence of non-response at first phase and second phase. The expressions of variances of these estimators have been derived. Furthermore, replication-based jackknife variance estimators of these variances have also been derived. Simulation study has been conducted to investigate the performance of the suggested estimators.

Jackknife variance of the partial area under the empirical receiver operating characteristic curve.

Receiver operating characteristic analysis provides an important methodology for assessing traditional (e.g., imaging technologies and clinical practices) and new (e.g., genomic studies, biomarker development) diagnostic problems. The area under the clinically/practically relevant part of the receiver operating characteristic curve (partial area or partial area under the receiver operating characteristic curve) is an important performance index summarizing diagnostic accuracy at multiple operating points (decision thresholds) that are relevant to actual clinical practice. A robust estimate of the partial area under the receiver operating characteristic curve is provided by the area under the corresponding part of the empirical receiver operating characteristic curve. We derive a closed-form expression for the jackknife variance of the partial area under the empirical receiver operating characteristic curve. Using the derived analytical expression, we investigate the differences between the jackknife variance and a conventional variance estimator. The relative properties in finite samples are demonstrated in a simulation study. The developed formula enables an easy way to estimate the variance of the empirical partial area under the receiver operating characteristic curve, thereby substantially reducing the computation burden, and provides important insight into the structure of the variability. We demonstrate that when compared with the conventional approach, the jackknife variance has substantially smaller bias, and leads to a more appropriate type I error rate of the Wald-type test. The use of the jackknife variance is illustrated in the analysis of a data set from a diagnostic imaging study.

How does working on university–industry collaborative projects affect science and engineering doctorates’ careers? Evidence from a UK research-based university

This paper examines the impact of industrial involvement in doctoral projects on the particular nature of the training and careers of doctorates. We draw on an original survey of job histories of doctorates in physical sciences and engineering from a research-based university in the UK. Using multivariate probit analysis and linearised (robust) and resampling (jackknife) variance estimation techniques, we found that projects with industrial involvement are associated with higher degree of socialisation with industry. There is some evidence showing that these projects are also more likely to focus on solving firm-specific technical problems or developing firm-specific specifications/prototypes, rather than exploring high-risk concepts or generating knowledge in the subject areas. Crucially, these projects result in fewer journal publications. Not surprisingly, in line with existing literature, we found that engaging in projects with industrial involvement (in contrast to projects without industrial involvement) confers advantages on careers in the private sector. Nevertheless, there is also a hint that engaging in projects with industrial involvement may have a negative effect on careers in academia or public research organisations. While acknowledging that the modelling results are based on a small sample from a research-based university and that therefore the results need to be treated with caution, we address implications for doctorates, universities and policymakers.