Detecting Item Preknowledge Using a Predictive Checking Method.

Calibration of thermoluminescent dosimeters for low exposure rates

ABSTRACTDue to wide applicability and simplicity, the exponential distribution is the most commonly used distribution in reliability engineering and other life testing experiments. In this paper a test statistic for testing upper and lower outliers simultaneously in an exponential sample is proposed. However, the distribution of test statistic under the alternative is rather intricate, the null distribution is derived and critical values are obtained. A simulation study is also carried out to compare the performance of test and is found that the test based on this statistic is more powerful than the other two selected tests.

The detection of nanoHertz gravitational waves through pulsar timing arrays hinges on identifying a common stochastic process affecting all pulsars in a correlated way across the sky. In the presence of other deterministic and stochastic processes affecting the time-of-arrival of pulses, a detection claim must be accompanied by a detailed assessment of the various physical or phenomenological models used to describe the data. In this study, we propose posterior predictive checks as a model-checking tool that relies on the predictive performance of the models with regards to new data. We derive and study predictive checks based on different components of the models, namely the Fourier coefficients of the stochastic process, the correlation pattern, and the timing residuals. We assess the ability of our checks to identify model misspecification in simulated datasets. We find that they can accurately flag a stochastic process spectral shape that deviates from the common power-law model as well as a stochastic process that does not display the expected angular correlation pattern. Posterior predictive likelihoods derived under different assumptions about the correlation pattern can further be used to establish detection significance. In the era of nanoHertz gravitational wave detection from different pulsar-timing datasets, such tests represent an essential tool in assessing data consistency and supporting astrophysical inference.

This article develops a method for testing the goodness-of-fit of a given parametric autoregressive conditional duration model against unspecified nonparametric alternatives. The test statistics are functions of the residuals corresponding to the quasi maximum likelihood estimate of the given parametric model, and are easy to compute. The limiting distributions of the test statistics are not free from nuisance parameters. Hence, critical values cannot be tabulated for general use. A bootstrap procedure is proposed to implement the tests, and its asymptotic validity is established. The finite sample performances of the proposed tests and several other competing ones in the literature, were compared using a simulation study. The tests proposed in this article performed well consistently throughout, and they were either the best or close to the best. None of the tests performed uniformly the best. The tests are illustrated using an empirical example.

In randomized clinical trials with a time-to-event outcome, the intervention effect could be quantified by a difference in restricted mean survival time (ΔRMST) between the intervention and control groups, defined as the expected survival duration gain due to the intervention over a fixed follow-up period. In cluster randomized trials (CRTs), social units are randomized to intervention or control groups; the correlation between survival times of the individuals within the same cluster must be taken into account in the statistical analysis. In a previous work, we proposed the use of pseudo-values regression, based on generalized estimating equations (GEEs), for estimating ΔRMST in CRTs. We showed that this method correctly estimated the ΔRMST and controlled the type I error rate in CRTs with at least 50 clusters. Here, we propose methods for CRTs with a small number of clusters (<50). We evaluated the performance of four bias-corrections of the GEE sandwich variance estimator of the intervention effect. We also considered the use of a Student t distribution as an alternative to the normal distribution of the GEE Wald test statistic for testing the intervention effect and constructing the confidence interval. With a simulation study, assuming proportional or non-proportional hazards, we showed that the Student t distribution outperformed the normal distribution in terms of type I error rate, and the Fay and Graubard bias-corrected variance led to an appropriate type I error rate whatever the number of clusters. Therefore, we recommend the use of the Fay and Graubard variance estimator combined with a Student t distribution for the pseudo-values regression to correctly estimate the variance of the intervention effect. Finally, we provide an illustrative analysis of the DEMETER trial evaluating the use of a specific endotracheal tube for subglottic secretion drainage to prevent ventilator-associated pneumonia, by comparing each of the methods considered.

ABSTRACTAlthough count data are collected in many experiments, their analysis remains challenging, especially in small sample sizes. Until now, linear or generalized linear models in Poisson or Negative Binomial distributional families have often been used. However, these data frequently show signs of over‐, underdispersion, or even zero‐inflation, casting doubt on these distributional assumptions and leading to inaccurate test results. Since their distributions are usually skewed, data transformations (e.g., log‐transformation) are not unusual. This underscores the need for statistical methods not to hinge on specific distributional assumptions. We delve into multiple contrast tests that allow general contrasts (e.g., many‐to‐one or all‐pairs comparisons) to analyze count data in multi‐arm trials. The methods vary in their effect and variance estimation, as well as in approximating the joint distribution of multiple test statistics, including frequently used methods such as linear and generalized linear models, and data transformations. An extensive simulation study demonstrates that a resampling version effectively controls the Type I error rate in various situations, while also highlighting the method's limitations, including overly liberal Type I error rates. Some standard methods, which have inflated Type I error rates, further underscore the need for alternative approaches. Real data applications further emphasize the applicability of these methods.

Counting of pulses and averaged photo-conduction in CdS crystals, with either DC or AC, have been compared. A slow increase of pulse height and duration limits the counting method. At low rates of exposure AC gives shorter times for decay, and susceptance is found to decay more rapidly than conductance; all rates of growth are nearly equal. Absence of drift in amplifiers is the main advantage of AC. Crystals respond in 3 min to 2·3 mR/hr, with 10 mR/hr of ` biassing ' radiation. Although this biassing exaggerates the effect of temperature, measurements in the range 0-50°C show that the biassing is acceptable at 20±10°C. The connection between DC photo-conduction and AC conductance and susceptance is discussed. The higher dark conductance found with AC may be due to dielectric loss in the crystal.A simple apparatus consisting of an oscillator, bridge, amplifier and crystal is described.

Most of the existing methodologies for evaluating heterogeneity in zero-inflated Poisson (ZIP) models are often assuming that the Poisson mean is a function of nuisance parameters. However, these nuisance parameters can be misspecified when performing these methodologies, the validity and the power of the test may be affected. In this article, we primarily focus on investigating the impact of misspecification on the performance of score test for homogeneity in ZIP models. Through an intensive simulation study, we find that: 1) under misspecification, the limiting distribution of the score test statistic under the null no longer follows a distribution. A parametric bootstrap methodology is suggested to use to find the true null limiting distribution of the score test statistic; 2) the power of the test decreases as the number of covariates in the Poisson mean increases. The test with a constant Poisson mean has the highest power, even compared to the test with a well-specified mean. At last, simulation results are applied to the Wuhan Inpatient Care Insurance data which contain excess zeros.

This dissertation includes three papers with each distributed in one chapter. In chapter 1, we use extensive simulation studies and real data studies to evaluate the performance of using the linkage disequilibrium score regression (LDSC) for controlling population stratification. In chapter 2, we propose a gene-based statistical method that leverage gene expression (GE) measurements and polygenic risk scores (PRS) to identify genes that are associated with a phenotype of interest. In simulation studies, the proposed method has correct type I error rates and can boost power comparing to other methods that use either gene expression or PRS in association tests. The real data analysis based on UK Biobank data for the asthma disease shows that the proposed method is also applicable to GWAS. In chapter 3, we analytically derive the distribution of TOW test statistics and modify TOW to utilize GWAS summary statistics (TOW-S). Simulation studies show that TOW-S has correct type I error rates and can retain power among all scenarios.

In this paper we consider the problem of testing for a parameter change in regression models with ARCH errors based on the residual cusum test. It is shown that the limiting distribution of the residual cusum test statistic is the sup of a Brownian bridge. Through a simulation study, it is demonstrated that the proposed test circumvents the drawbacks of Kim et al.’s (2000) cusum test. For illustration, we apply the residual cusum test to the return of yen/dollar exchange rate data.

The likelihood ratio test for hidden Markov models in two-sample problems

Approximating a class of goodness-of-fit test statistics

Comparing two suppliers for linear profiles is a very important task for supplier management. The difference test statistic based on the process-yield index is proposed to tackle the better process selection for linear profiles. A simple form of the sampling distribution of the process-yield index is derived by a simulation study. Therefore, the asymptotic normal distribution of the difference test statistic is established. The results provide useful information to practitioners. An example from the leather industry is presented to illustrate the applicability of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.

To assess the effect of exposure to evidence-based medication after hospital discharge for Medicare beneficiaries with acute myocardial infarction (AMI). A discrete-time hazard model was used to estimate time to outcome associated with exposure to four drug classes (angiotensin-converting enzyme inhibitors (ACEIs)/angiotensin-II receptor blockers (ARBs), beta-blockers (BBs), statins, and clopidogrel) used for post-AMI secondary prevention of cardiovascular events and mortality. Medicare administrative data for a 5% random sample of beneficiaries. Medicare beneficiaries (N=9,538) hospitalized for an AMI between April 1, 2006, and December 31, 2007, who survived for at least 30days after discharge. The cohort was followed until death or December 31, 2008. Time-varying exposure was measured as proportion of days covered (PDC) for each quarter during the follow-up period. PDC was classified into five categories (0-0.2, 0.2-0.4, 0.4-0.6, 0.6-0.8, 0.8-1.0). Outcomes were mortality and a composite outcome of death or post-AMI hospitalization. Over a median follow-up of 18months, mean PDC rates ranged from 0.37 (clopidogrel) to 0.50 (statins). When comparing the highest versus lowest categories of exposure, the hazard of the composite outcome was significantly lower for all drug classes except BBs (statins, adjusted hazard ratio (aHR)=0.71, ACEIs/ARBs, aHR=0.81, clopidogrel, aHR=0.85, BBs, aHR=0.93). All four drug classes were significantly associated with reductions in mortality; the magnitude of effect for the mortality outcome was largest for statins and smallest for BBs. Age modified the effect of statins on mortality. Use of evidence-based medications for secondary prevention after AMI is suboptimal in the Medicare population, and low exposure rates are associated with significantly higher risk for subsequent hospitalization and death.

Purpose: It is now commonplace to handle treatments of hyperthyroidism using iodine-131 as an outpatient procedure due to lower costs and less stringent federal regulations. The Nuclear Regulatory Commission has currently updated release guidelines for these procedures, but there is still a large uncertainty in the dose to the public. Current guidelines to minimize dose to the public require patients to remain isolated after treatment. The purpose of this study was to use a low-cost common device, such as a cell phone, to estimate exposure emitted from a patient to the general public. Methods: Measurements were performed using an Apple iPhone 3GS and a Cs-137 irradiator. The charge-coupled device (CCD) camera on the phone was irradiated to exposure rates ranging from 0.1 mR/hr to 100 mR/hr and 30-sec videos were taken during irradiation with the camera lens covered by electrical tape. Interactions were detected as white pixels on a black background in each video. Both single threshold (ST) and colony counting (CC) methods were performed using MATLAB®. Calibration curves were determined by comparing the total pixel intensity output from each method to the known exposure rate. Results: The calibration curve showed a linear relationship above 5 mR/hr for both analysis techniques. The number of events counted per unit exposure rate within the linear region was 19.5 ± 0.7 events/mR and 8.9 ± 0.4 events/mR for the ST and CC methods respectively. Conclusion: Two algorithms were developed and show a linear relationship between photons detected by a CCD camera and low exposure rates, in the range of 5 mR/hr to 100-mR/hr. Future work aims to refine this model by investigating the dose-rate and energy dependencies of the camera response. This algorithm allows for quantitative monitoring of exposure from patients treated with iodine-131 using a simple device outside of the hospital.