Nominal Coverage Research Articles

Inference for the generalized exponential stress-strength model

This study develops inferential procedures for the generalized exponential stress-strength model. A generalized confidence interval for the stress-strength reliability is derived when the stress and strength variables follow the generalized exponential distributions with the common rate parameters. Moreover, based on the Fisher Z transformation, a modified generalized confidence interval for the stress-strength reliability with the unequal rate parameters is proposed. The performance of the proposed procedures is evaluated by Monte Carlo simulation. The simulation results show that the coverage percentages of the proposed generalized confidence intervals are quite close to the nominal coverage probabilities, even for small sample sizes. Finally, an example is used to illustrate the proposed procedures.

Accounting for imperfect detection of groups and individuals when estimating abundance.

If animals are independently detected during surveys, many methods exist for estimating animal abundance despite detection probabilities <1. Common estimators include double‐observer models, distance sampling models and combined double‐observer and distance sampling models (known as mark‐recapture‐distance‐sampling models; MRDS). When animals reside in groups, however, the assumption of independent detection is violated. In this case, the standard approach is to account for imperfect detection of groups, while assuming that individuals within groups are detected perfectly. However, this assumption is often unsupported. We introduce an abundance estimator for grouped animals when detection of groups is imperfect and group size may be under‐counted, but not over‐counted. The estimator combines an MRDS model with an N‐mixture model to account for imperfect detection of individuals. The new MRDS‐Nmix model requires the same data as an MRDS model (independent detection histories, an estimate of distance to transect, and an estimate of group size), plus a second estimate of group size provided by the second observer. We extend the model to situations in which detection of individuals within groups declines with distance. We simulated 12 data sets and used Bayesian methods to compare the performance of the new MRDS‐Nmix model to an MRDS model. Abundance estimates generated by the MRDS‐Nmix model exhibited minimal bias and nominal coverage levels. In contrast, MRDS abundance estimates were biased low and exhibited poor coverage. Many species of conservation interest reside in groups and could benefit from an estimator that better accounts for imperfect detection. Furthermore, the ability to relax the assumption of perfect detection of individuals within detected groups may allow surveyors to re‐allocate resources toward detection of new groups instead of extensive surveys of known groups. We believe the proposed estimator is feasible because the only additional field data required are a second estimate of group size.

The performance of model averaged tail area confidence intervals

ABSTRACTWe investigate the exact coverage and expected length properties of the model averaged tail area (MATA) confidence interval proposed by Turek and Fletcher, CSDA, 2012, in the context of two nested, normal linear regression models. The simpler model is obtained by applying a single linear constraint on the regression parameter vector of the full model. For given length of response vector and nominal coverage of the MATA confidence interval, we consider all possible models of this type and all possible true parameter values, together with a wide class of design matrices and parameters of interest. Our results show that, while not ideal, MATA confidence intervals perform surprisingly well in our regression scenario, provided that we use the minimum weight within the class of weights that we consider on the simpler model.

Statistical design and analysis for plant cover studies with multiple sources of observation errors

AbstractEffective wildlife habitat management and conservation requires understanding the factors influencing distribution and abundance of plant species. Field studies, however, have documented observation errors in visually estimated plant cover including measurements which differ from the true value (measurement error) and not observing a species that is present within a plot (detection error). Unlike the rapid expansion of occupancy and N‐mixture models for analysing wildlife surveys, development of statistical models accounting for observation error in plants has not progressed quickly. Our work informs development of a monitoring protocol for managed wetlands within the National Wildlife Refuge System.Zero‐augmented beta (ZAB) regression is the most suitable method for analysing areal plant cover recorded as a continuous proportion but assumes no observation errors. We present a model extension that explicitly includes the observation process thereby accounting for both measurement and detection errors. Using simulations, we compare our approach to a ZAB regression that ignores observation errors (naïve model) and an “ad hoc” approach using a composite of multiple observations per plot within the naïve model. We explore how sample size and within‐season revisit design affect the ability to detect a change in mean plant cover between 2 years using our model.Explicitly modelling the observation process within our framework produced unbiased estimates and nominal coverage of model parameters. The naïve and “ad hoc” approaches resulted in underestimation of occurrence and overestimation of mean cover. The degree of bias was primarily driven by imperfect detection and its relationship with cover within a plot. Conversely, measurement error had minimal impacts on inferences. We found &gt;30 plots with at least three within‐season revisits achieved reasonable posterior probabilities for assessing change in mean plant cover.For rapid adoption and application, code for Bayesian estimation of our single‐species ZAB with errors model is included. Practitioners utilizing our R‐based simulation code can explore trade‐offs among different survey efforts and parameter values, as we did, but tuned to their own investigation. Less abundant plant species of high ecological interest may warrant the additional cost of gathering multiple independent observations in order to guard against erroneous conclusions.

Survival analysis with functions of mismeasured covariate histories: the case of chronic air pollution exposure in relation to mortality in the nurses' health study.

Environmental epidemiologists are often interested in estimating the effect of functions of time-varying exposure histories, such as the 12-month moving average, in relation to chronic disease incidence or mortality. The individual exposure measurements that comprise such an exposure history are usually mis-measured, at least moderately, and, often, more substantially. To obtain unbiased estimates of Cox model hazard ratios for these complex mis-measured exposure functions, an extended risk set regression calibration method for Cox models is developed and applied to a study of long-term exposure to the fine particulate matter (PM2.5) component of air pollution in relation to all-cause mortality in the Nurses' Health Study. Simulation studies under several realistic assumptions about the measurement error model and about the correlation structure of the repeated exposure measurements were conducted to assess the finite sample properties of this new method, and found that the method has good performance in terms of finite sample bias reduction and nominal confidence interval coverage.

Inference on the ratio of two coefficients of variation of two lognormal distributions

ABSTRACTThe coefficient of variation (CV) can be used as an index of reliability of measurement. The lognormal distribution has been applied to fit data in many fields. We developed approximate interval estimation of the ratio of two coefficients of variation (CsV) for lognormal distributions by using the Wald-type, Fieller-type, log methods, and method of variance estimates recovery (MOVER). The simulation studies show that empirical coverage rates of the methods are satisfactorily close to a nominal coverage rate for medium sample sizes.

Feasible Generalized Least Squares Using Machine Learning

In the presence of heteroskedastic errors, regression using Feasible Generalized Least Squares (FGLS) offers potential efficiency gains over Ordinary Least Squares (OLS). However, FGLS adoption remains limited, in part because the form of heteroskedasticity may be misspecified. We investigate machine learning methods to address this concern, focusing on Support Vector Regression. Monte Carlo results indicate the resulting estimator and an accompanying standard error correction offer substantially improved precision, nominal coverage rates, and shorter confidence intervals than OLS with heteroskedasticity-consistent (HC3) standard errors. Reductions in root mean squared error are over 90% of those achievable when the form of heteroskedasticity is known.

Modified confidence intervals for the Mahalanobis distance

Reiser (2001) proposes a method of forming confidence interval for a Mahalanobis distance that yields intervals which have exactly the nominal coverage, but sometimes the interval is (0,0). We consider the case where Mahalanobis distance quantifies the difference between an individual and a population mean, and suggest a modification that avoids implausible intervals.

Demographic transition and the dynamics of measles in six provinces in China: A modeling study.

BackgroundIndustrialization and demographic transition generate nonstationary dynamics in human populations that can affect the transmission and persistence of infectious diseases. Decades of increasing vaccination and development have led to dramatic declines in the global burden of measles, but the virus remains persistent in much of the world. Here we show that a combination of demographic transition, as a result of declining birth rates, and reduced measles prevalence, due to improved vaccination, has shifted the age distribution of susceptibility to measles throughout China.Methods and findingsWe fit a novel time-varying catalytic model to three decades of age-specific measles case reporting in six provinces in China to quantify the change in the age-specific force of infection for measles virus over time. We further quantified the impact of supplemental vaccination campaigns on the reduction of susceptible individuals. The force of infection of measles has declined dramatically (90%–97% reduction in transmission rate) in three industrialized eastern provinces during the last decade, driving a concomitant increase in both the relative proportion and absolute number of adult cases, while three central and western provinces exhibited dynamics consistent with endemic persistence (24%–73% reduction in transmission rate). The reduction in susceptible individuals due to supplemental vaccination campaigns is frequently below the nominal campaign coverage, likely because campaigns necessarily vaccinate those who may already be immune. The impact of these campaigns has significantly improved over time: campaigns prior to 2005 were estimated to have achieved less than 50% reductions in the proportion susceptible in the target age classes, but campaigns from 2005 onwards reduced the susceptible proportion by 32%–87%. A limitation of this study is that it relies on case surveillance, and thus inference may be biased by age-specific variation in measles reporting.ConclusionsThe age distribution of measles cases changes in response to both demographic and vaccination processes. Combining both processes in a novel catalytic model, we illustrate that age-specific incidence patterns reveal regional differences in the progress to measles elimination and the impact of vaccination controls in China. The shift in the age distribution of measles susceptibility in response to demographic and vaccination processes emphasizes the importance of progressive control strategies and measures to evaluate program success that anticipate and react to this transition in observed incidence.

Regression based circular error probable: An application to ballistic systems

ABSTRACTThis paper explores the computation of Circular Error Probable from a bivariate regression model as well as upper confidence limits computed at covariate values of interest. Upper confidence limits were computed based on a bootstrap methodology and a bootstrap calibration of the delta method. The bootstrap calibration provided an improvement in the nominal coverage for the delta method at smaller sample sizes. An example is provided using munition data from an Army test event to show how these approaches can be applied to data sets from test events with small sample sizes.

Two parts are better than one: modeling marginal means of semicontinuous data

In health services research, it is common to encounter semicontinuous data characterized by a point mass at zero followed by a continuous distribution with positive support. These are often analyzed using two-part mixtures that separately model the probability of use to account for the portion of the sample with zero values. Commonly, but not always, the second component models the continuous values conditional on them being positive. Prior work examining whether such two-part models are needed to appropriately draw inference from semicontinuous data compared to standard one-part regression models has found mixed results. However, prior studies have generally used only measures of model fit on a single dataset, leaving a definitive conclusion uncertain. This paper provides a detailed evaluation using simulations of the appropriateness of standard one-part generalized linear models (GLMs) compared to a recently developed marginalized two-part (MTP) model. The MTP model, unlike the one-part GLMs, explicitly accounts for the point mass at zero, yet takes the same form for the marginal mean as the commonly used GLM with log link, making the covariate effects directly comparable. We simulate data scenarios with varying sample sizes and percentages of zeros. One-part GLMs resulted in increased bias, lower than nominal coverage of confidence intervals, and inflated type I error rates, rendering them inappropriate for use with semicontinuous data. Even when distributional assumptions were violated, estimates of covariate effects and type I error rates under the MTP model remained robust.

Bioinspired Hierarchically Structured Surfaces for Efficient Capture and Release of Circulating Tumor Cells.

The development of novel bioinspired surfaces with hierarchical micro- and nanoscale topographic structures for efficient capture and release of circulating tumor cells (CTCs) is reported. The capture of CTCs, facilitated by surface-immobilized epithelial cell adhesion molecule antibodies (anti-EpCAM), was shown to be significantly enhanced in novel three-dimensional hierarchically structured surfaces that were fabricated by replicating the natural micro- and nanostructures of rose petals. Under static conditions, these hierarchical capture substrates exhibited up to 6 times higher cell capture ability at concentrations of 100 cells mL-1 in contrast to flat anti-EpCAM-functionalized polydimethylsiloxane (PDMS) surfaces. As indicated by scanning electron microscopy (SEM) and immunofluorescent images, this enhancement can be in large part attributed to the topographical interaction between nanoscale cell surface components and nanostructures on the substrate. Similarly, the increased surface area affords a higher nominal coverage of anti-EpCAM, which increases the number of available binding sites for cell capture. By treating the substrates with the biocompatible reductant glutathione (GSH), up to 85% of the captured cells were released, which displayed over 98% cell viability after culturing on tissue culture polystyrene (TCP) for 24 h. Therefore, these bioinspired hierarchically structured and functionalized substrates can be successfully applied to capture CTCs, as well as release CTCs for subsequent analysis. These findings provide new prospects for designing cell-material interfaces for advanced cell-based biomedical studies in the future.

Quantitative imaging biomarkers: Effect of sample size and bias on confidence interval coverage.

Introduction Quantitative imaging biomarkers (QIBs) are being increasingly used in medical practice and clinical trials. An essential first step in the adoption of a quantitative imaging biomarker is the characterization of its technical performance, i.e. precision and bias, through one or more performance studies. Then, given the technical performance, a confidence interval for a new patient's true biomarker value can be constructed. Estimating bias and precision can be problematic because rarely are both estimated in the same study, precision studies are usually quite small, and bias cannot be measured when there is no reference standard. Methods A Monte Carlo simulation study was conducted to assess factors affecting nominal coverage of confidence intervals for a new patient's quantitative imaging biomarker measurement and for change in the quantitative imaging biomarker over time. Factors considered include sample size for estimating bias and precision, effect of fixed and non-proportional bias, clustered data, and absence of a reference standard. Results Technical performance studies of a quantitative imaging biomarker should include at least 35 test-retest subjects to estimate precision and 65 cases to estimate bias. Confidence intervals for a new patient's quantitative imaging biomarker measurement constructed under the no-bias assumption provide nominal coverage as long as the fixed bias is <12%. For confidence intervals of the true change over time, linearity must hold and the slope of the regression of the measurements vs. true values should be between 0.95 and 1.05. The regression slope can be assessed adequately as long as fixed multiples of the measurand can be generated. Even small non-proportional bias greatly reduces confidence interval coverage. Multiple lesions in the same subject can be treated as independent when estimating precision. Conclusion Technical performance studies of quantitative imaging biomarkers require moderate sample sizes in order to provide robust estimates of bias and precision for constructing confidence intervals for new patients. Assumptions of linearity and non-proportional bias should be assessed thoroughly.

A new prediction-based variance estimator for two-stage model-assisted surveys of forest resources

Forest resource assessments utilizing remotely sensed auxiliary data are becoming increasingly important due to their ability to provide precise estimates of forest parameters at low cost. In presenting results from such surveys, it is important to provide not only estimates of the target parameters, but also their confidence intervals, which provide the range of values wherein the true value is located with a certain level of confidence. If such an interval is narrow the point estimates from the survey can be considered very reliable. In estimating the confidence interval the variance of an estimator must first be estimated. Unbiasedness, i.e. that an estimator on average coincides with the true value, is an important property also for variance estimators. Another important property is that the variance estimator itself has low variance, not least in cases when the variance estimates obtained with the estimator may not be strictly positive. One such important case is when two-stage designs are used to first allocate sample clusters in the form of strips from which auxiliary data, such as metrics derived from airborne laser scanning, are obtained; field data are then derived from sample plots beneath each sample strip in a second stage. In this article we compare two variance estimators for such surveys. The first estimator is a standard estimator suggested in reference textbooks on model-assisted sampling. The second estimator is proposed by the authors, and utilizes the auxiliary data to a larger extent. Through Monte Carlo simulation we show that both variance estimators are approximately unbiased, but that the new estimator is more stable (i.e., has lower empirical variance) and provides empirical confidence interval coverage rates that coincide more closely with the nominal coverage rates.

Using a network-based approach and targeted maximum likelihood estimation to evaluate the effect of adding pre-exposure prophylaxis to an ongoing test-and-treat trial.

Several cluster-randomized trials are underway to investigate the implementation and effectiveness of a universal test-and-treat strategy on the HIV epidemic in sub-Saharan Africa. We consider nesting studies of pre-exposure prophylaxis within these trials. Pre-exposure prophylaxis is a general strategy where high-risk HIV- persons take antiretrovirals daily to reduce their risk of infection from exposure to HIV. We address how to target pre-exposure prophylaxis to high-risk groups and how to maximize power to detect the individual and combined effects of universal test-and-treat and pre-exposure prophylaxis strategies. We simulated 1000 trials, each consisting of 32 villages with 200 individuals per village. At baseline, we randomized the universal test-and-treat strategy. Then, after 3 years of follow-up, we considered four strategies for targeting pre-exposure prophylaxis: (1) all HIV- individuals who self-identify as high risk, (2) all HIV- individuals who are identified by their HIV+ partner (serodiscordant couples), (3) highly connected HIV- individuals, and (4) the HIV- contacts of a newly diagnosed HIV+ individual (a ring-based strategy). We explored two possible trial designs, and all villages were followed for a total of 7 years. For each village in a trial, we used a stochastic block model to generate bipartite (male-female) networks and simulated an agent-based epidemic process on these networks. We estimated the individual and combined intervention effects with a novel targeted maximum likelihood estimator, which used cross-validation to data-adaptively select from a pre-specified library the candidate estimator that maximized the efficiency of the analysis. The universal test-and-treat strategy reduced the 3-year cumulative HIV incidence by 4.0% on average. The impact of each pre-exposure prophylaxis strategy on the 4-year cumulative HIV incidence varied by the coverage of the universal test-and-treat strategy with lower coverage resulting in a larger impact of pre-exposure prophylaxis. Offering pre-exposure prophylaxis to serodiscordant couples resulted in the largest reductions in HIV incidence (2% reduction), and the ring-based strategy had little impact (0% reduction). The joint effect was larger than either individual effect with reductions in the 7-year incidence ranging from 4.5% to 8.8%. Targeted maximum likelihood estimation, data-adaptively adjusting for baseline covariates, substantially improved power over the unadjusted analysis, while maintaining nominal confidence interval coverage. Our simulation study suggests that nesting a pre-exposure prophylaxis study within an ongoing trial can lead to combined intervention effects greater than those of universal test-and-treat alone and can provide information about the efficacy of pre-exposure prophylaxis in the presence of high coverage of treatment for HIV+ persons.

A coverage probability of bootstrap-t confidence interval for the variance

We examine one-sided confidence intervals for the population variance, based on the ordinary t-statistics. We derive an unconditional coverage probability of the bootstrap-t interval for unknown variance. For that purpose, we find an Edgeworth expansion of the distribution of t-statistic to an order n-2. We can see that a number of simulation, B, has the influence on coverage probability of the confidence interval for the variance. If B equals sample size then coverage probability and its limit (when B ? ?) disagree at the level O(n-2). If we want that nominal coverage probability of the interval would be equal to ?, then coverage probability and its limit agree to order n-3/2 if B is of larger order than the square root of the sample size. We present a modeling application in insurance property, where the purpose of analysis is to measure variability of a data set.

Multivariate Stochastic Volatility-Double Jump Model: An Application for Oil Assets

We propose a new multivariate model to capture the presence of jumps in mean and conditional variance in the returns of oil prices and companies in this sector. The model is based on the presence of common factors associated with jumps in mean and variance, as it performs a decomposition of the conditional variance of each asset as the sum of the common factor plus a specific transitory factor in a multivariate stochastic volatility structure. The estimation is made through Bayesian methods using Markov Chain Monte Carlo. The model allows recovering the changes in prices and volatility patterns observed in this sector, relating the jumps with the events observed in the period 2000-2015. We apply the model to estimate risk management measures, hedging and portfolio allocation and performing a comparison with other multivariate models of conditional volatility. Based on the results, we may conclude that the proposed model has a better performance when used to calculate portfolio VaR, since it does not reject the hypothesis of correct nominal coverage with certain specifications presented in this work. Furthermore, we conclude that the model can be used to hedge oil price risks, through the optimal hedge ratio for a portfolio containing an oil company as-set (stock) and the oil price contract. When compared to the standard methodology based on GARCH models, our model performs well in this application.

Confidence intervals for directly standardized rates using mid-p gamma intervals.

Directly standardized rates continue to be an integral tool for presenting rates for diseases that are highly dependent on age, such as cancer. Statistically, these rates are modeled as a weighted sum of Poisson random variables. This is a difficult statistical problem, because there are k observed Poisson variables and k unknown means. The gamma confidence interval has been shown through simulations to have at least nominal coverage in all simulated scenarios, but it can be overly conservative. Previous modifications to that method have closer to nominal coverage on average, but they do not achieve the nominal coverage bound in all situations. Further, those modifications are not central intervals, and the upper coverage error rate can be substantially more than half the nominal error. Here we apply a mid-p modification to the gamma confidence interval. Typical mid-p methods forsake guaranteed coverage to get coverage that is sometimes higher and sometimes lower than the nominal coverage rate, depending on the values of the parameters. The mid-p gamma interval does not have guaranteed coverage in all situations; however, in the (not rare) situations where the gamma method is overly conservative, the mid-p gamma interval often has at least nominal coverage. The mid-p gamma interval is especially appropriate when one wants a central interval, since simulations show that in many situations both the upper and lower coverage error rates are on average less than or equal to half the nominal error rate.

Controlling the exciton emission of gold coated GaAs–AlGaAs core–shell nanowires with an organic spacer layer

Excitons are the most prominent optical excitations and controlling their emission is an important step towards new optical devices. We have investigated the exciton emission from uncoated and gold/aluminum quinoline (Alq3) coated GaAs–AlGaAs–GaAs core–shell nanowires (NWs) using temperature-, intensity- and polarization dependent photoluminescence (PL). Plasmonic GaAs–AlGaAs–GaAs NWs with a ∼10 nm thick Au coating but without an Alq3 spacer layer reveal a significant reduction of the PL intensity of the exciton emission compared with the uncoated NW sample. Plasmonic NW samples with the same nominal Au coverage and an additional Alq3 interlayer of 3 or 6 nm thickness show a clearly stronger PL intensity which increases with rising Alq3 spacer thickness. Time-resolved (TR) PL measurements reveal an increase of the exciton decay rate by a factor of up to two with decreasing Alq3 spacer thickness suggesting the presence of Förster energy transfer from NW excitons to plasmon oscillations in the gold film. The weak change of the decay time, however, indicates that Förster energy-transfer is only partially responsible for the PL quenching in the gold coated NWs. The main reason for the reduction of the PL emission is attributed to a gold induced band-bending in the GaAs NW core which causes exciton dissociation. With increasing Alq3 spacer thickness the band-bending decreases leading to a reduction of the exciton dissociation and PL quenching. Our interpretation is supported by electron energy loss spectroscopy measurements which show a signal reduction and blue shift of defect (possibly EL2) transitions when gold particles are deposited on NWs compared with bare or Alq3 coated NWs.

Fractional order statistic approximation for nonparametric conditional quantile inference

Using and extending fractional order statistic theory, we characterize the O(n−1) coverage probability error of the previously proposed (Hutson, 1999) confidence intervals for population quantiles using L-statistics as endpoints. We derive an analytic expression for the n−1 term, which may be used to calibrate the nominal coverage level to get O(n−3/2[log(n)]3) coverage error. Asymptotic power is shown to be optimal. Using kernel smoothing, we propose a related method for nonparametric inference on conditional quantiles. This new method compares favorably with asymptotic normality and bootstrap methods in theory and in simulations. Code is provided for both unconditional and conditional inference.