Probability Interval Research Articles

Bayesian analysis of diagnostic sensitivity and specificity for detecting infectious salmon anaemia virus (ISAV) using IFAT and real-time RT-PCR testing from laboratories in Atlantic Canada

Infectious Salmon Anaemia virus (ISAV) is the causative agent of Infectious Salmon Anaemia (ISA), an economically important disease in farmed Atlantic salmon (Salmo salar L.). Immunofluorescence antibody test (IFAT) and real-time reverse transcription polymerase chain reaction (qRT-PCR) are commonly used diagnostic tests for ISAV active surveillance in Atlantic Canada; however, their diagnostic accuracy is not well reported. In the absence of a reference test, we used Bayesian latent class analysis methods to estimate diagnostic sensitivity (DSe) and specificity (DSp) of IFAT and qRT-PCR. We compared diagnostic performance of qRT-PCR, performed at two laboratories, and IFAT (performed at another laboratory) using field samples obtained from two separate salmon populations (total n = 130) in province of Newfoundland and Labrador, Canada. Conditional independence models for two tests (IFAT and qRT-PCR) and two populations (low and high prevalence) were run separately on datasets from each laboratory. Informative priors were used for DSe and DSp of qRT-PCR and IFAT based on prior knowledge, while flat priors (beta 1,1) were used for prevalence. qRT-PCRs had similarly high DSe (>91%). IFAT was the least sensitive method (DSe range, 56.9%–60.4%). Both IFAT (DSp > 98.8%) and qRT-PCRs (DSp > 97.9%) showed high DSp. Real-time RT-PCR provided the greatest DSe for routine surveillance of Atlantic salmon farms while not sacrificing DSp. Sample size for the study was not likely adequate to estimate all parameters with very high confidence, which could have influenced the posterior probability interval calculated for DSe, resulting in less diagnostic confidence in the results (posterior probability for Sensitivities for the tests within 10% of the true population value instead of 5%). Although IFAT provided a high DSp, the qRT-PCR performed similarly in this regard. The findings indicate that the qRT-PCR is fit for ISAV surveillance programs.

Asymptotic expansions for a class of Fredholm Pfaffians and interacting particle systems

Motivated by the phenomenon of duality for interacting particle systems, we introduce two classes of Pfaffian kernels describing a number of Pfaffian point processes in the “bulk” and at the “edge.” Using the probabilistic method due to Mark Kac, we prove two Szegő-type asymptotic expansion theorems for the corresponding Fredholm Pfaffians. The idea of the proof is to introduce an effective random walk with transition density determined by the Pfaffian kernel, express the logarithm of the Fredholm Pfaffian through expectations with respect to the random walk, and analyse the expectations using general results on random walks. We demonstrate the utility of the theorems by calculating asymptotics for the empty interval and noncrossing probabilities for a number of examples of Pfaffian point processes: coalescing/annihilating Brownian motions, massive coalescing Brownian motions, real zeros of Gaussian power series and Kac polynomials, and real eigenvalues for the real Ginibre ensemble.

Insights on attenuating autophagy cellular and molecular pathways versus methotrexate-induced toxicity via liposomal turmeric therapy

BackgroundMethotrexate (MX), a competitive inhibitor of dihydrofolate reductase, can inhibit DNA and RNA production and is a powerful anticancer agent widely utilized in clinical practice for treating nonneoplastic maladies, as psoriasis and rheumatoid arthritis; meanwhile, its probable prescription dose and interval of administration are strictly limited due to dose-related organ damage. Former studies verified that kidney, brain, liver, and lung harms are prospective obstacles of methotrexate administration. To understand the machinery of methotrexate-prompt toxicity, various mechanisms were investigated. The former is an autophagy defense mechanism; autophagy is a self-digesting mechanism responsible for the removal of damaged organelles and malformed proteins by lysosome. The contemporary article hypothesized that turmeric or its liposomal analog could defeat autophagy of MX-induced acute toxicity. Methotrexate, in a dose of 1.5 mg/kg, was administered intravenously followed by turmeric and liposomal turmeric treatment in a dose of 5 mg/kg for 30 days in rats. ResultsIncrement in autophagy (AUTP) consent by MX administration was attenuated by concurrent treatment via turmeric and liposomal turmeric that was reliable on the alteration in apoptotic markers. The assembly of FOXO-3 in serum post methotrexate administration was suppressed by concurrent treatment via liposomal turmeric. Apoptosis/autophagic marker investigation was evaluated through the gene expression of Bax (BCL2-associated X protein)/Bcl2 (B-cell lymphoma 2)/P53 (tumor protein P53)/SiRT-1 (sirtuin silent mating-type information regulation 2 homolog 1) and FOXO-3 (forkhead box transcription factor-3)/ERDJ-4 (endoplasmic reticulum localized DnaJ homologs)/BNP (brain natriuretic peptide B) signaling. The cell death of all cells was categorized to achieve autophagy. Interestingly, Bax/Bcl2/P53/SiRT-1 signaling pathways were downregulated, contributing to inhibiting the initiation of autophagy. Meanwhile, FOXO-3/BNP/ERDJ-4 reduction-implicated noncanonical autophagy pathways were involved in methotrexate-induced autophagy, whereas this change was suppressed when turmeric was administered in liposomal form. ConclusionThese outcomes recommended that liposomal turmeric prevents MX-induced acute toxicity through its autophagy, antioxidant, and antiapoptotic properties.

Bayesian multilevel logistic regression models: a case study applied to the results of two questionnaires administered to university students

Bayesian multilevel models—also known as hierarchical or mixed models—are used in situations in which the aim is to model the random effect of groups or levels. In this paper, we conduct a simulation study to compare the predictive ability of 1-level Bayesian multilevel logistic regression models with that of 2-level Bayesian multilevel logistic regression models by using the prior Scaled Beta2 and inverse-gamma distributions to model the standard deviation in the 2-level. Then, these models are employed to estimate the correct answers in two questionnaires administered to university students throughout the first academic semester of 2018. The results show that 2-level models have a better predictive ability and provide more precise probability intervals than 1-level models, particularly when the prior Scaled Beta2 distribution is used to model the standard deviation in the second level. Moreover, the probability intervals of 1-level Bayesian multilevel logistic regression models proved to be more precise when Scaled Beta2 distributions, rather than an inverse-gamma distribution, are employed to model the standard deviation or when 1-level Bayesian multilevel logistic regression models, are used.

Residual Strength Estimation Method of Soft Coal Based on Equivalent Residual Strain Ratio

In underground mining engineering, the residual strength of surrounding rock has an important influence on the secondary stress distribution caused by excavation. Generally, the residual strength of coal can be measured by experiments, but for soft coal, due to its large postpeak deformation characteristics and the limitation of strain sensor range, it is difficult to measure residual strength. Therefore, it is of great practical significance to estimate the residual strength of soft coal with incomplete stress-strain curves. In this paper, a method for estimating residual strength of soft coal based on the ratio of equivalent residual strain to peak strain is proposed. Taking advantage of the characteristics that the strain-softening curve of soft coal decreases approximately linearly in the initial stage, keeping the drop modulus unchanged, the endpoint of the extension line can be determined based on the ratio of equivalent residual strain to peak strain, which is estimated residual strength. There are 342 groups of typical complete stress-strain curves analyzed to determine the value range of the ratio of equivalent residual strain to peak strain. It is concluded that for briquette composed of soft coal, the ratio of equivalent residual strain to peak strain is between 1 and 3.35 when the confining pressure is 0-6 MPa, and the maximum probability interval of the ratio value under different confining pressures is further calculated. When the confining pressure is higher than 6 MPa, the briquette composed of soft coal tends to ideal plastic state after peak. The feasibility of the residual strength estimation method is verified by comparing the numerical simulation results of triaxial compression of coal pillars with the experimental results.

Characterization and propagation of RTD uncertainty for continuous powder blending processes

Residence time distribution (RTD) is a probability density function that describes the time materials spend inside a system. It is a promising tool for mixing behavior characterization, material traceability, and real-time quality control in pharmaceutical manufacturing. However, RTD measurements are accompanied with some degree of uncertainties because of process fluctuation and variation, measurement error, and experimental variation among different replicates. Due to the strict quality control requirements of drug manufacturing, it is essential to consider RTD uncertainty and characterize its effects on RTD-based predictions and applications. Towards this end, two approaches were developed in this work, namely model-based and data-based approaches. The model-based approach characterizes the RTD uncertainty via RTD model parameters and uses Monte Carlo sampling to propagate and analyze the effects on downstream processes. To avoid bias and possible reduction of uncertainty during model fitting, the data-based approach characterizes RTD uncertainty using the raw experimental data and utilizes interval arithmetic for uncertainty propagation. A constrained optimization approach was also proposed to overcome the drawback of interval arithmetic in the data-based approach. Results depict probability intervals around the upstream disturbance tracking profile and the funnel plot, facilitating better decision-making for quality control under uncertainty.

Optimal dispatching method for integrated energy system based on robust economic model predictive control considering source–load power interval prediction

Effective source–load prediction and reasonable dispatching are crucial to realize the economic and reliable operations of integrated energy systems (IESs). They can overcome the challenges introduced by the uncertainties of new energies and various types of loads in the IES. Accordingly, a robust optimal dispatching method for the IES based on a robust economic model predictive control (REMPC) strategy considering source–load power interval prediction is proposed. First, an operation model of the IES is established, and an interval prediction model based on the bidirectional long short-term memory network optimized by beetle antenna search and bootstrap is formulated and applied to predict the photovoltaic power and the cooling, heating, and electrical loads. Then, an optimal dispatching scheme based on REMPC is devised for the IES. The source–load interval prediction results are used to improve the robustness of the REPMC and reduce the influence of source–load uncertainties on dispatching. An actual IES case is selected to conduct simulations; the results show that compared with other prediction techniques, the proposed method has higher prediction interval coverage probability and prediction interval normalized averaged width. Moreover, the operational cost of the IES is decreased by the REMPC strategy. With the devised dispatching scheme, the ability of the IES to handle the dispatching risk caused by prediction errors is enhanced. Improved dispatching robustness and operational economy are also achieved.

Study of interactions between CFH gene polymorphism and retinal pigment epithelium phenotype in age-related macular degeneration

Annotation. AMD (age-related macular degeneration) is one of the leading causes of blindness in the world, associated with the formation of extracellular deposits called drusen in the macula, i.e. in the central part of the retina. These drusen contain cellular debris and proteins, including components of the complement system, such as the regulator CFH (complement factor H). Complement dysregulation is believed to play a major role in the development of AMD. CFH acts through its ability to recognize polyanionic structures (eg, sulfated GAGs (glycosaminoglycans)) found in host tissues, and thus CFH inactivates any complement system (C3b) that is deposited. Importantly, the common CFH (Y402H) polymorphism was strongly associated with an increased risk of AMD. Recent studies have shown that the disease-associated allotype 402H interacts more poorly (compared to 402Y) with binding sites in the macula (eg, Bruch's membrane), where GAGs (glycosaminoglycans), heparan sulfate, and dermatan sulfate play a major role in mediating the interaction with CFH. Decreased binding of the 402H allotype may lead to complement dysregulation, leading to chronic local inflammation that may contribute to drusen accumulation and thus the initiation, development, and progression of AMD. That is why the goal of our study was to highlight the effect of the rs1061170 polymorphism of the CFH gene on the occurrence and development of age-related macular degeneration and to clarify the intensity of this pathological effect. The study group consisted of 291 people suffering from AMD (89 – with the “dry” form, 97 – with the “wet” form), the comparison group – 105 people without a history of ophthalmic pathology of the corresponding age. Optical coherence tomography (SOCT Copernicus “Optopol”) of the macular area of the retina was used in the study. We used the parameter ILM-RPE (internal limiting membrane-retinal pigmented epithelium). DNA was isolated from the biological material obtained by the buccal scraping method using the Bio-Rad Chelex ® 100 kit. Polymerase chain reaction was used to detect the rs1061170 polymorphism of the CFH gene. Statistical processing of the obtained results was carried out using Statistica 10 (StatSoft, Inc., USA) and SPSS 23.0 programs. The following were used: Hardy-Weinberg equilibrium (Hardy–Weinberg); Kruskal-Wallis test ANOVA by Ranks and Friedman ANOVA and Kendall Coeff. of Concordance; H-criterion; indicators of the odds ratio (OR; Odds Ratio – OR) and 95% probable interval (±95% CI; Confidence limit for means Interval – CI); used the method of analysis of operating characteristic curves (ROC – Receiver Operating Characteristic curve analysis); used special formulas using 2x2 tables. Our results confirm the high prognostic significance of the rs1061170 polymorphism of the CFH gene on the development and progression of AMD in the Ukrainian population. Indicators of specificity and sensitivity of SNP genotypes are ambiguous.

Intermittent MEK inhibition for the treatment of metastatic uveal melanoma.

IntroductionUveal melanoma (UM) is associated with poor outcomes in the metastatic setting and harbors activating mutations resulting in upregulation of MAPK signaling in almost all cases. The efficacy of selumetinib, an oral allosteric inhibitor of MEK1/2, was limited when administered at a continual dosing schedule of 75 mg BID. Preclinical studies demonstrate that intermittent MEK inhibition reduces compensatory pathway activation and promotes T cell activation. We hypothesized that intermittent dosing of selumetinib would reduce toxicity, allow for the administration of increased doses, and achieve more complete pathway inhibition, thus resulting in improved antitumor activity.MethodsWe conducted a phase Ib trial of selumetinib using an intermittent dosing schedule in patients with metastatic UM. The primary objective was to estimate the maximum tolerated dose (MTD) and assess safety and tolerability. Secondary objectives included assessment of the overall response rate (RR), progression-free survival (PFS) and overall survival (OS). Tumor biopsies were collected at baseline, on day 3 (on treatment), and between days 11-14 (off treatment) from 9 patients for pharmacodynamic (PD) assessments.Results29 patients were enrolled and received at least one dose of selumetinib across 4 dose levels (DL; DL1: 100 mg BID; DL2: 125 mg BID; DL3: 150 mg BID; DL4: 175 mg BID). All patients experienced a treatment-related adverse event (TRAE), with 5/29 (17%) developing a grade 3 or higher TRAE. Five dose limiting toxicities (DLT) were observed: 2/20 in DL2, 2/5 in DL3, 1/1 in DL4. The estimated MTD was 150 mg BID (DL3), with an estimated probability of toxicity of 29% (90% probability interval 16%-44%). No responses were observed; 11/29 patients achieved a best response of stable disease (SD). The median PFS and OS were 1.8 months (95% CI 1.7, 4.5) and 7.1 months (95% CI 5.3, 11.5). PD analysis demonstrated at least partial pathway inhibition in all samples at day 3, with reactivation between days 11-14 in 7 of those cases.ConclusionsWe identified 150 mg BID as the MTD of intermittent selumetinib, representing a 100% increase over the continuous dose MTD (75 mg BID). However, no significant clinical efficacy was observed using this dosing schedule.

Bayesian Evaluation of Three Serological Tests for Diagnosis of Brucella infections in Dromedary Camels Using Latent Class Models

Brucellosis is a zoonotic disease with significant economic and public health impacts. The disease has been found in ruminants, including camels, but clinical diagnosis of camel brucellosis is difficult due to the lack of clinical signs. Thus, this study aimed to estimate the sensitivity (Se) and specificity (Sp) of the Buffered Plate Antigen Test (BPAT), Rose Bengal Test (RBT), and indirect ELISA (i-ELISA) for the diagnosis of Brucella infection in dromedary camels imported from Sudan to Egypt. The secondary objective of the study was to calculate the animal-level true prevalence of Brucella infection in imported camels. A cross-sectional study was carried out on 921 apparently healthy camels randomly selected from those imported from Sudan and kept in the quarantine stations in the Shalateen area of the Red Sea Governorate, Egypt, between June 2018 and January 2019. Serum samples were collected and analyzed using BPAT, RBT, and i-ELISA. The posterior estimates [medians and 95% Bayesian probability intervals (95% BPI)] for Se and Sp of the three serological tests were obtained using Bayesian latent class models (BLCMs). The BLCM was fitted with the assumption that the BPAT and RBT tests were conditionally dependent on the true brucellosis status of camels. All tests had comparable and high Se (>86%) and Sp (>98%). The animal-level true prevalence of Brucella infection in imported camels was 8.6% (95% BPI: 6.8 – 10.7). Based on these findings, the three assays could be used for the initial screening of Brucella infection in camels. However, the BPAT and RBT are more suitable for use in camel brucellosis control and eradication program in Egypt because of their low unit cost and fast turnaround time compared to the i-ELISA. In addition, BPAT and RBT could be performed in the field where in-vivo tests are rarely used due to logistic and management constraints.

Statistical Inference for Odds Ratio of Two Proportions in Bilateral Correlated Data

Bilateral correlated data frequently arise in medical clinical studies such as otolaryngology and ophthalmology. Based on an equal correlation coefficient model, this paper mainly aimed to investigate the statistical inference for the odds ratio of two proportions in bilateral correlated data, including not only three test procedures but also four confidence interval (CI) constructions. Through iterative algorithms, all unknown parameters are estimated in order to construct the likelihood ratio, score and Wald-type tests. Furthermore, the profile likelihood CI, score CI, and Wald-type CI are obtained by the bisection root-finding algorithm. We provided another Wald-type CI based on an asymptotic normality property. The performance of the proposed tests were investigated with regard to empirical type I error rate and power, and CI methods were compared in terms of mean coverage probability and mean interval width. Numerical simulations show that the score test is more robust, and has higher power than other tests. The score CI also has a shorter interval width, and its coverage probability is closer to 0.95. A real example is used to illustrate the proposed methods.

Cautious weighted random forests

Random forest is an efficient and accurate classification model, which makes decisions by aggregating a set of trees, either by voting or by averaging class posterior probability estimates. However, tree outputs may be unreliable in presence of scarce data. The imprecise Dirichlet model (IDM) provides workaround, by replacing point probability estimates with interval-valued ones. This paper investigates a new tree aggregation method based on the theory of belief functions to combine such probability intervals, resulting in a cautious random forest classifier. In particular, we propose a strategy for computing tree weights based on the minimization of a convex cost function, which takes both determinacy and accuracy into account and makes it possible to adjust the level of cautiousness of the model. The proposed model is evaluated on 25 UCI datasets and is demonstrated to be more adaptive to the noise in training data and to achieve a better compromise between informativeness and cautiousness.

A Partial Multiplicative Dimensional Reduction-Based Reliability Estimation Method for Probabilistic and Non-Probabilistic Hybrid Structural Systems

A new reliability estimation method based on partial multiplicative dimensional reduction is proposed for probabilistic and non-probabilistic hybrid structural systems. The proposed method is characterized by decorrelating interval input variables from random input variables using the partial multiplicative dimensional reduction method in conjunction with the weakest-link theory. In this method, the failure statistics of the original performance function are equivalent to a statical chain of two elements, in which one of the two elements represents the failures due to random input variables and the other represents the failures due to interval variables. Rather than yielding an estimated interval of failure probability, the proposed method produces a single value for failure probability, which is more meaningful for engineering. In addition, the accuracy, validity, and superiority of the proposed method are demonstrated, and the error-related properties of the proposed method are investigated.

Inference in a Class of Optimization Problems: Confidence Regions and Finite Sample Bounds on Errors in Coverage Probabilities

This article describes three methods for carrying out nonasymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation under shape restrictions, estimation of models of discrete games, and estimation based on grouped data. The partially identified parameters are characterized by restrictions that involve the unknown population means of observed random variables in addition to structural parameters. Inference consists of finding confidence intervals for functions of the structural parameters. Our theory provides finite-sample lower bounds on the coverage probabilities of the confidence intervals under three sets of assumptions of increasing strength. With the moderate sample sizes found in most economics applications, the bounds become tighter as the assumptions strengthen. We discuss estimation of population parameters that the bounds depend on and contrast our methods with alternative methods for obtaining confidence intervals for partially identified parameters. The results of Monte Carlo experiments and empirical examples illustrate the usefulness of our method.

Cost savings associated with a web-based physical activity intervention for COPD.

To estimate the cost savings associated with a pedometer-based, web-mediated physical activity intervention in a cohort of US veterans with chronic obstructive pulmonary disease (COPD). Economic analysis. We constructed a decision tree from the health care system perspective incorporating adjusted relative risk of a pedometer-based, web-mediated intervention for COPD-related acute exacerbations, acute exacerbation-related costs (ie, emergency department visits and hospitalizations), and intervention-related costs. Total COPD-related costs were estimated per patient across 12 months. Probabilistic sensitivity analysis with Monte Carlo simulation was used to estimate uncertainty in the model findings. In the deterministic (base case) model, the model estimated costs to be $4236 per participant who used the pedometer-based, web-mediated intervention compared with $7913 per participant in the control group (estimated $3677 saved in 1 year compared with the control group). The model findings were robust to probabilistic sensitivity analysis, with a difference in mean costs of $4582 (95% probability interval, $4084-$5080; P < .001). Cost savings in the model were driven by the adjusted relative risk of the web-based intervention, probability of a COPD-related acute exacerbation, rate of hospitalization, probability of hospitalization, and cost of hospitalization. A pedometer-based, web-mediated physical activity intervention yielded substantial cost savings. Increased implementation of the intervention could markedly reduce the economic burden of COPD for payers and patients.

Failure Probability and Inspection Interval of Pressure Safety Valves: Case Study of a Gas Processing Plant

Inspection of pressure safety valves (PSVs) is critical for the safety of process plants which also involves cost. API proposes a Risk-Based Inspection (RBI) method that includes consequences and probability of failure. In this work, PSVs installed in different pressurized equipment of a gas processing plant located in Comilla, Bangladesh, have been studied in order to establish and implement a risk-based inspection planning process in the facility in accordance with API 580 and 581. The probability of failure and consequence of failure have been assessed separately and then combined to determine the risk of failure. The results have been used to assess the acceptability of the current inspection schedule in the facility and present some inspection planning guidelines in order to manage risks. The outcome indicates that a large fraction of the overall risk is concentrated in a relatively limited number of PSVs. These potentially high-risk PSVs should require greater consideration through an amended inspection plan in which more regular inspections are to be scheduled for these devices while inspection intervals may be extended for PSVs identified as having lower risk.

Analysis of an empirical seismic fragility prediction model of wooden roof truss buildings

To explore the vulnerability of wood roof truss buildings (WRTBs) under earthquake action, the empirical damage typical characteristics of 12,343.4 × 104 m2 and 21,490 buildings of this type of building that suffered different degrees of loss in 22 typical destructive earthquakes in China from 1993 to 2013 were observed and analysed. Based on the analysis methods of the nonlinear vulnerability model, probability statistics, and prediction model, a novel fragility probability matrix, plane, surface, nonlinear regression curve, and function model of different intensity zones under the latest Chinese macrointensity standard (GB/T 17742–2020, CMS-20) assessment were established, and vulnerability curve models were employed based on the damage ratio (DR) and actual cumulative damage probability (ACDP) parameters. According to 1993–1999, 2000–2010, and after 2011, the time-varying fragility specimen data were classified and censusly analysed. The fragility prediction curve models of DR and ACDP were performed using the probabilistic demand modal analysis method. Combined with the matrix probability and confidence interval calculation model, a novel regional mean fragility index domain model for typical structural (WRTB) vulnerability assessment was developed.

Normal cones corresponding to credal sets of lower probabilities

Credal sets are one of the most important models for describing probabilistic uncertainty. They usually arise as convex sets of probabilistic models compatible with judgments provided in terms of coherent lower previsions or more specific models such as coherent lower probabilities or probability intervals. In finite spaces, credal sets usually take the form of convex polytopes. Many properties of convex polytopes can be derived from their normal cones, which form polyhedral complexes called normal fans. We analyze the properties of normal cones corresponding to credal sets of coherent lower probabilities. For two important classes of coherent lower probabilities, 2-monotone lower probabilities and probability intervals, we provide a detailed description of the normal fan structure. These structures are related to the structure of the extreme points of the credal sets. To arrive at our main results, we provide some general results on triangulated normal fans of convex polyhedra and their adjacency structure.

A new approach to constructing confidence intervals for population means based on small samples.

This paper presents a new approach to constructing the confidence interval for the mean value of a population when the distribution is unknown and the sample size is small, called the Percentile Data Construction Method (PDCM). A simulation was conducted to compare the performance of the PDCM confidence interval with those generated by the Percentile Bootstrap (PB) and Normal Theory (NT) methods. Both the convergence probability and average interval width criterion are considered when seeking to find the best interval. The results show that the PDCM outperforms both the PB and NT methods when the sample size is less than 30 or a large population variance exists.

Confidence Intervals for Seroprevalence

This paper concerns the construction of confidence intervals in standard seroprevalence surveys. In particular, we discuss methods for constructing confidence intervals for the proportion of individuals in a population infected with a disease using a sample of antibody test results and measurements of the test’s false positive and false negative rates. We begin by documenting erratic behavior in the coverage probabilities of standard Wald and percentile bootstrap intervals when applied to this problem. We then consider two alternative sets of intervals constructed with test inversion. The first set of intervals are approximate, using either asymptotic or bootstrap approximation to the finite-sample distribution of a chosen test statistic. We consider several choices of test statistic, including maximum likelihood estimators and generalized likelihood ratio statistics. We show with simulation that, at empirically relevant parameter values and sample sizes, the coverage probabilities for these intervals are close to their nominal level and are approximately equi-tailed. The second set of intervals are shown to contain the true parameter value with probability at least equal to the nominal level, but can be conservative in finite samples.