Joint inference about sensitivity and specificity at the optimal cut-off point associated with Youden index

Youden index estimation based on group-tested data

Youden index, a linear function of sensitivity and specificity, provides a direct measurement of the highest diagnostic accuracy achievable by a biomarker. It is maximized at the cut-off point that optimizes the biomarker's overall classification rate while assigning equal weight to sensitivity and specificity. In this paper, we consider the problem of estimating the Youden index when only group-tested data are available. The unavailability of individual disease statuses poses a challenge, especially when there is differential false positives and negatives in disease screening. We propose both parametric and nonparametric procedures for estimation of the Youden index, and exemplify our methods by utilizing data from the National Health and Nutrition Examination Survey (NHANES) to evaluate the diagnostic ability of monocyte for predicting chlamydia.

Statistical Inference for Box-Cox based Receiver Operating Characteristic Curves

Receiver operating characteristic (ROC) curve analysis is widely used in evaluating the effectiveness of a diagnostic test/biomarker or classifier score. A parametric approach for statistical inference on ROC curves based on a Box-Cox transformation to normality has frequently been discussed in the literature. Many investigators have highlighted the difficulty of taking into account the variability of the estimated transformation parameter when carrying out such an analysis. This variability is often ignored and inferences are made by considering the estimated transformation parameter as fixed and known. In this paper, we will review the literature discussing the use of the Box-Cox transformation for ROC curves and the methodology for accounting for the estimation of the Box-Cox transformation parameter in the context of ROC analysis, and detail its application to a number of problems. We present a general framework for inference on any functional of interest, including common measures such as the AUC, the Youden index, and the sensitivity at a given specificity (and vice versa). We further developed a new R package (named 'rocbc') that carries out all discussed approaches and is available in CRAN.

Development and validation of HBV surveillance models using big data and machine learning

BACKGROUND

The construction of a robust healthcare information system is fundamental to enhancing countries' capabilities in the surveillance and control of hepatitis B virus (HBV). Making use of China's rapidly expanding primary healthcare system, this innovative approach using big data and machine learning (ML) could help towards the World Health Organization's (WHO) HBV infection elimination goals of reaching 90% diagnosis and treatment rates by 2030. We aimed to develop and validate HBV detection models using routine clinical data to improve the detection of HBV and support the development of effective interventions to mitigate the impact of this disease in China.

METHODS

Relevant data records extracted from the Family Medicine Clinic of the University of Hong Kong-Shenzhen Hospital's Hospital Information System were structuralized using state-of-the-art Natural Language Processing techniques. Several ML models have been used to develop HBV risk assessment models. The performance of the ML model was then interpreted using the Shapley value (SHAP) and validated using cohort data randomly divided at a ratio of 2:1 using a five-fold cross-validation framework.

RESULTS

The patterns of physical complaints of patients with and without HBV infection were identified by processing 158,988 clinic attendance records. After removing cases without any clinical parameters from the derivation sample (n = 105,992), 27,392 cases were analysed using six modelling methods. A simplified model for HBV using patients' physical complaints and parameters was developed with good discrimination (AUC = 0.78) and calibration (goodness of fit test p-value >0.05).

CONCLUSIONS

Suspected case detection models of HBV, showing potential for clinical deployment, have been developed to improve HBV surveillance in primary care setting in China. (Word count: 264).

Validation of the minimum dietary diversity for women as a predictor of micronutrient adequacy among lactating women in Ethiopia

Background

The Minimum Dietary Diversity for Women (MDD-W) indicator is used as a proxy indicator for assessing micronutrient adequacy among women of the reproductive age group. Variations were observed in studies, and there was also a lack of evidence regarding the performance of this proxy indicator in Ethiopia, a country with diverse dietary consumption practices. This study aimed to validate the performance of the MDD-W in predicting micronutrient intake adequacy among lactating women in Ethiopia.

Methods and materials

A community-based cross-sectional study was conducted among randomly selected 457 lactating women in Northwest Ethiopia from February 2 to 18, 2023. A multistage sampling technique was used to select 457 study participants. A single multiphasic interactive 24-h dietary recall was used to collect dietary intake data. Ten food groups were used to compute the Minimum Dietary Diversity for Women, and the Mean Adequacy Ratio was used to assess nutrient intake adequacy. Spearman's rank correlation test, Cohen's kappa statistics, and ROC curve analysis were conducted. The optimal cutoff points for Minimum Dietary Diversity for Women were determined by selecting the points that maximized the Youden index.

Results

MDD-W had poor positive correlation (ρ = 0.19, p < 0.001) and poor predictive ability (AUC = 0.62, 95% CI: 0.56, 0.67) (p < 0.001) with the Mean Adequacy Ratio in determining micronutrient intake adequacy. The sensitivity and specificity of the MDD-W in the ≥5 food groups standard cutoff were 25.2 and 82.3%, respectively. The optimal cutoff point for MDD-W to predict micronutrient intake adequacy was ≥3 food groups.

Conclusion

Minimum Dietary Diversity for Women had a poor correlation and poor predictive ability in predicting micronutrient intake adequacy. The variations noted in studies and differences from the Food and Agriculture Organization recommendations regarding the cutoff and level of performance of MDD-W in defining micronutrient adequacy warrant further investigation.

Technological Frontiers in Brain Cancer: A Systematic Review and Meta-Analysis of Hyperspectral Imaging in Computer-Aided Diagnosis Systems

Brain cancer is a substantial factor in the mortality associated with cancer, presenting difficulties in the timely identification of the disease. The precision of diagnoses is significantly dependent on the proficiency of radiologists and neurologists. Although there is potential for early detection with computer-aided diagnosis (CAD) algorithms, the majority of current research is hindered by its modest sample sizes. This meta-analysis aims to comprehensively assess the diagnostic test accuracy (DTA) of computer-aided design (CAD) models specifically designed for the detection of brain cancer utilizing hyperspectral (HSI) technology. We employ Quadas-2 criteria to choose seven papers and classify the proposed methodologies according to the artificial intelligence method, cancer type, and publication year. In order to evaluate heterogeneity and diagnostic performance, we utilize Deeks' funnel plot, the forest plot, and accuracy charts. The results of our research suggest that there is no notable variation among the investigations. The CAD techniques that have been examined exhibit a notable level of precision in the automated detection of brain cancer. However, the absence of external validation hinders their potential implementation in real-time clinical settings. This highlights the necessity for additional studies in order to authenticate the CAD models for wider clinical applicability.

Statistical inference for the two-sample problem under likelihood ratio ordering, with application to the ROC curve estimation

The receiver operating characteristic (ROC) curve is a powerful statistical tool and has been widely applied in medical research. In the ROC curve estimation, a commonly used assumption is that larger the biomarker value, greater severity the disease. In this article, we mathematically interpret "greater severity of the disease" as "larger probability of being diseased." This in turn is equivalent to assume the likelihood ratio ordering of the biomarker between the diseased and healthy individuals. With this assumption, we first propose a Bernstein polynomial method to model the distributions of both samples; we then estimate the distributions by the maximum empirical likelihood principle. The ROC curve estimate and the associated summary statistics are obtained subsequently. Theoretically, we establish the asymptotic consistency of our estimators. Via extensive numerical studies, we compare the performance of our method with competitive methods. The application of our method is illustrated by a real-data example.

Construction of joint confidence spaces for the optimal true class fraction triplet in the ROC space using alternative biomarker cutoffs

Hepatocellular carcinoma (HCC) is the most common primary cancer of the liver. Finding new biomarkers for its early detection is of high clinical importance. As with many other diseases, cancer has a progressive nature. In cancer biomarker studies, it is often the case that the true disease status of the recruited individuals exhibits more than two classes. The receiver operating characteristic (ROC) surface is a well-known statistical tool for assessing the biomarkers' discriminatory ability in trichotomous settings. The volume under the ROC surface (VUS) is an overall measure of the discriminatory ability of a marker. In practice, clinicians are often in need of cutoffs for decision-making purposes. A popular approach for computing such cutoffs is the Youden index and its recent three-class generalization. A drawback of such a method is that it treats the data in a pairwise fashion rather than consider all the data simultaneously. The use of the minimized Euclidean distance from the perfection corner to the ROC surface (also known as closest to perfection method) is an alternative to the Youden index that may be preferable in some settings. When such a method is employed, there is a need for inferences around the resulting true class rates/fractions that correspond to the optimal operating point. In this paper, we provide an inferential framework for the derivation of marginal confidence intervals (CIs) and joint confidence spaces (CSs) around the corresponding true class fractions, when dealing with trichotomous settings. We explore parametric and nonparametric approaches for the construction of such CIs and CSs. We evaluate our approaches through extensive simulations and apply them to a real data set that refers to HCC patients.

A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index Maximization

Combining multiple biomarkers to provide predictive models with a greater discriminatory ability is a discipline that has received attention in recent years. Choosing the probability threshold that corresponds to the highest combined marker accuracy is key in disease diagnosis. The Youden index is a statistical metric that provides an appropriate synthetic index for diagnostic accuracy and a good criterion for choosing a cut-off point to dichotomize a biomarker. In this study, we present a new stepwise algorithm for linearly combining continuous biomarkers to maximize the Youden index. To investigate the performance of our algorithm, we analyzed a wide range of simulated scenarios and compared its performance with that of five other linear combination methods in the literature (a stepwise approach introduced by Yin and Tian, the min-max approach, logistic regression, a parametric approach under multivariate normality and a non-parametric kernel smoothing approach). The obtained results show that our proposed stepwise approach showed similar results to other algorithms in normal simulated scenarios and outperforms all other algorithms in non-normal simulated scenarios. In scenarios of biomarkers with the same means and a different covariance matrix for the diseased and non-diseased population, the min-max approach outperforms the rest. The methods were also applied on two real datasets (to discriminate Duchenne muscular dystrophy and prostate cancer), whose results also showed a higher predictive ability in our algorithm in the prostate cancer database.

Joint inference about the AUC and Youden index for paired biomarkers

It is common to compare biomarkers' diagnostic or prognostic performance using some summary ROC measures such as the area under the ROC curve (AUC) or the Youden index. We propose to compare two paired biomarkers using both the AUC and the Youden index since the two indices describe different aspects of the ROC curve. This comparison can be made by estimating the joint confidence region (an elliptical area) of the differences of the paired AUCs and the Youden indices. Furthermore, for deciding if one marker is better than the other in terms of both the A U C and the Youden index (J), we can test H 0 : A U C a ≤ A U C b or J a ≤ J b against H a : A U C a > A U C b and J a > J b using the paired differences. The construction of such a joint hypothesis is an example of the multivariate order-restricted hypotheses. For such a hypothesis, we propose and compare three testing procedures: (1) the intersection-union test ( I U T ); (2) the conditional test; and (3) the joint test. The performance of the proposed inference methods was evaluated and compared through simulations. The simulation results demonstrate that the proposed joint confidence region maintains the desired confidence level, and all three tests maintain the type I error under the null. Furthermore, among the three proposed testing methods, the conditional test is the preferred approach with markedly larger power consistently than the other two competing methods.

Exact inference for disease prevalence based on a test with unknown specificity and sensitivity

To make informative public policy decisions in battling the ongoing COVID-19 pandemic, it is important to know the disease prevalence in a population. There are two intertwined difficulties in estimating this prevalence based on testing results from a group of subjects. First, the test is prone to measurement error with unknown sensitivity and specificity. Second, the prevalence tends to be low at the initial stage of the pandemic and we may not be able to determine if a positive test result is a false positive due to the imperfect test specificity. The statistical inference based on a large sample approximation or conventional bootstrap may not be valid in such cases. In this paper, we have proposed a set of confidence intervals, whose validity doesn't depend on the sample size in the unweighted setting. For the weighted setting, the proposed inference is equivalent to hybrid bootstrap methods, whose performance is also more robust than those based on asymptotic approximations. The methods are used to reanalyze data from a study investigating the antibody prevalence in Santa Clara County, California in addition to several other seroprevalence studies. Simulation studies have been conducted to examine the finite-sample performance of the proposed method.

Incorporating a New Summary Statistic into the Min–Max Approach: A Min–Max–Median, Min–Max–IQR Combination of Biomarkers for Maximising the Youden Index

Linearly combining multiple biomarkers is a common practice that can provide a better diagnostic performance. When the number of biomarkers is sufficiently high, a computational burden problem arises. Liu et al. proposed a distribution-free approach (min–max approach) that linearly combines the minimum and maximum values of the biomarkers, involving only a single coefficient search. However, the combination of minimum and maximum biomarkers alone may not be sufficient in terms of discrimination. In this paper, we propose a new approach that extends that of Liu et al. by incorporating a new summary statistic, specifically, the median or interquartile range (min–max–median and min–max–IQR approaches) in order to find the optimal combination that maximises the Youden index. Although this approach is more computationally intensive than the one proposed by Liu et al, it includes more information and the number of parameters to be estimated remains reasonable. We compare the performance of the proposed approaches (min–max–median and min–max–IQR) with the min–max approach and logistic regression. For this purpose, a wide range of different simulated data scenarios were explored. We also apply the approaches to two real datasets (Duchenne Muscular Dystrophy and Small for Gestational Age).

Joint confidence region estimation on predictive values

For evaluating diagnostic accuracy of inherently continuous diagnostic tests/biomarkers, sensitivity and specificity are well-known measures both of which depend on a diagnostic cut-off, which is usually estimated. Sensitivity (specificity) is the conditional probability of testing positive (negative) given the true disease status. However, a more relevant question is "what is the probability of having (not having) a disease if a test is positive (negative)?". Such post-test probabilities are denoted as positive predictive value (PPV) and negative predictive value (NPV). The PPV and NPV at the same estimated cut-off are correlated, hence it is desirable to make the joint inference on PPV and NPV to account for such correlation. Existing inference methods for PPV and NPV focus on the individual confidence intervals and they were developed under binomial distribution assuming binary instead of continuous test results. Several approaches are proposed to estimate the joint confidence region as well as the individual confidence intervals of PPV and NPV. Simulation results indicate the proposed approaches perform well with satisfactory coverage probabilities for normal and non-normal data and, additionally, outperform existing methods with improved coverage as well as narrower confidence intervals for PPV and NPV. The Alzheimer's Disease Neuroimaging Initiative (ADNI) data set is used to illustrate the proposed approaches and compare them with the existing methods.

The length of the receiver operating characteristic curve and the two cutoff Youden index within a robust framework for discovery, evaluation, and cutoff estimation in biomarker studies involving improper receiver operating characteristic curves

During the early stage of biomarker discovery, high throughput technologies allow for simultaneous input of thousands of biomarkers that attempt to discriminate between healthy and diseased subjects. In such cases, proper ranking of biomarkers is highly important. Common measures, such as the area under the receiver operating characteristic (ROC) curve (AUC), as well as affordable sensitivity and specificity levels, are often taken into consideration. Strictly speaking, such measures are appropriate under a stochastic ordering assumption, which implies, without loss of generality, that higher measurements are more indicative for the disease. Such an assumption is not always plausible and may lead to rejection of extremely useful biomarkers at this early discovery stage. We explore the length of a smooth ROC curve as a measure for biomarker ranking, which is not subject to directionality. We show that the length corresponds to a ϕ divergence, is identical to the corresponding length of the optimal (likelihood ratio) ROC curve, and is an appropriate measure for ranking biomarkers. We explore the relationship between the length measure and the AUC of the optimal ROC curve. We then provide a complete framework for the evaluation of a biomarker in terms of sensitivity and specificity through a proposed ROC analogue for use in improper settings. In the absence of any clinical insight regarding the appropriate cutoffs, we estimate the sensitivity and specificity under a two-cutoff extension of the Youden index and we further take into account the implied costs. We apply our approaches on two biomarker studies that relate to pancreatic and esophageal cancer.

Prognostic value of pretreatment circulating basophils in patients with glioblastoma

Accumulating evidence demonstrated that atopic diseases were inversely related to glioma susceptibility and associated with improved prognosis of patients with glioma. This study aimed to elucidate the impacts of basophils, one of the important effector cells in the pathobiology of atopic disease, on prognosis of patients with glioblastoma (GBM). A total of 268 patients were newly diagnosed with GBM and treated with operation at our institution from January 2010 to December 2017. The association between pre-operation circulating eosinophil, basophil, neutrophil, lymphocyte, monocyte count and GBM progression free survival (PFS) was investigated. Moreover, based on the results of multivariate analysis, a prognostic nomogram was established and evaluated. Kaplan-Meier method showed that basophils ≥0.015 × 10⁹/L (p = 0.015) and lymphocytes ≥1.555 × 10⁹/L (p = 0.005) were correlated with better PFS. Cox regression model showed that basophils ≥0.015 × 10⁹/L were an independent prognostic factor for PFS. Prognostic nomogram was established and the concordance index (C-index) for PFS prediction was 0.629. The calibration plots for the probability of 0.5-, 1- and 3-year PFS showed optimal consistency between the prediction by nomogram and actual observation. Increased pre-operation circulating basophils portend better PFS, which might be a useful and novel marker for the prognosis of GBM patients.

Joint hypothesis testing of the area under the receiver operating characteristic curve and the Youden index

In the receiver operating characteristic (ROC) analysis, the area under the ROC curve (AUC) serves as an overall measure of diagnostic accuracy. Another popular ROC index is the Youden index (J), which corresponds to the maximum sum of sensitivity and specificity minus one. Since the AUC and J describe different aspects of diagnostic performance, we propose to test if a biomarker beats the pre-specified targeting values of AUC₀ and J₀ simultaneously with H₀  : AUC ≤ AUC₀ or J ≤ J₀ against H_a  : AUC > AUC₀ and J > J₀ . This is a multivariate order restrictive hypothesis with a non-convex space in H_a , and traditional likelihood ratio-based tests cannot apply. The intersection-union test (IUT) and the joint test are proposed for such test. While the IUT test independently tests for the AUC and the Youden index, the joint test is constructed based on the joint confidence region. Findings from the simulation suggest both tests yield similar power estimates. We also illustrated the tests using a real data example and the results of both tests are consistent. In conclusion, testing jointly on AUC and J gives more reliable results than using a single index, and the IUT is easy to apply and have similar power as the joint test.

Optimal cut-off for obesity and markers of metabolic syndrome for Ethiopian adults

BACKGROUND

Metabolic syndrome (MetS) is defined as the presence of central obesity plus any two of the following markers: high triglycerides (> 150 mg/dl), low high density lipoprotein (HDL) cholesterol < 40 mg/dl in men and < 50 mg/dl in women, hypertension (blood pressure > 130/85 mmHg or use of antihypertensive medication), high fasting blood glucose (> 100 mg/dl or use of treatment for diabetes mellitus). Since recently, metabolic syndrome and obesity have become emerging problems of both low and middle income countries, although they have been the leading cause of morbidity and mortality in high income countries for the past decades. It has been indicated that the international anthropometric cut-off for detecting obesity is not appropriate for Ethiopians. This study developed optimal cut off values for anthropometric indicators of obesity and markers of metabolic syndrome for Ethiopian adults to enhance preventive interventions.

METHODS

A total of 704 employees of Jimma University were randomly selected using their payroll as a sampling frame. Data on socio-demographic, anthropometry, clinical and blood samples were collected from February to April 2015. Receiver Operating Characteristic Curve analyses were used to determine optimal anthropometric cut-off values for obesity and markers of the metabolic syndrome. WHO indicators of obesity based on body fat percent (> 25% for males and > 35% for females) were used as binary classifiers for developing anthropometric cut-offs. Optimal cut-off values were presented using sensitivity, specificity and area under the curve.

RESULTS

The optimal cut-off for obesity using body mass index was 22.2 k/m2 for males and 24.5 kg/m2 for females. Similarly, the optimal waist circumference cut-off for obesity was 83.7 cm for males and 78.0 cm for females. The cut-off values for detecting obesity using waist to hip ratio and waist to height ratio were: WHR (0.88) and WHtR (0.49) for males, while they were 0.82 and 0.50 for females, respectively. Anthropometric cut-off values for markers of metabolic syndrome were lower compared to the international values. For females, the optimal BMI cut-offs for metabolic syndrome markers ranged from 24.8 kg/m2 (triglycerides) to 26.8 kg/m2 (fasting blood sugar). For WC the optimal cut-off ranged from of 82.1 cm (triglyceride) to 96.0 cm(HDL); while for WHtR the optimal values varied from 0.47(HDL) to 0.56(fasting blood sugar). Likewise, the optimal cut-offs of WHR for markers of metabolic syndrome ranged from 0.78(fasting blood sugar) to 0.89(HDL and blood pressure). For males, the optimal BMI cut-offs for metabolic syndrome markers ranged from 21.0 kg/m2 (HDL) to 23.5 kg/m2 (blood pressure). For WC, the optimal cut-off ranged from 85.3 cm (triglyceride) to 96.0 cm(fasting blood sugar); while for WHtR the optimal values varied from 0.47(BP, FBS and HDL) to 0.53(Triglyceride). Similarly, the optimal cut-offs of WHR form markers of metabolic syndrome ranged from 0.86(blood pressure) to 0.95(fasting blood sugar).

CONCLUSION

The optimal anthropometric cut-offs for obesity and markers of metabolic syndrome in Ethiopian adults are lower than the international values. The findings imply that the international cut-off for WC, WHtR, WHR and BMI underestimate obesity and metabolic syndrome markers among Ethiopian adults, which should be considered in developing intervention strategies. It is recommended to use the new cut-offs for public health interventions to curb the increasing magnitude of obesity and associated metabolic syndrome and diet related non-communicable diseases in Ethiopia.

Confidence intervals for differences between volumes under receiver operating characteristic surfaces (VUS) and generalized Youden indices (GYIs)

This article explores both existing and new methods for the construction of confidence intervals for differences of indices of diagnostic accuracy of competing pairs of biomarkers in three-class classification problems and fills the methodological gaps for both parametric and non-parametric approaches in the receiver operating characteristic surface framework. The most widely used such indices are the volume under the receiver operating characteristic surface and the generalized Youden index. We describe implementation of all methods and offer insight regarding the appropriateness of their use through a large simulation study with different distributional and sample size scenarios. Methods are illustrated using data from the Alzheimer's Disease Neuroimaging Initiative study, where assessment of cognitive function naturally results in a three-class classification setting.

Postepizootic Persistence of Asymptomatic Mycoplasma conjunctivae Infection in Iberian Ibex

The susceptibility of the Iberian ibex (Capra pyrenaica) to Mycoplasma conjunctivae ocular infection and the changes in their interaction over time were studied in terms of clinical outcome, molecular detection, and IgG immune response in a captive population that underwent a severe infectious keratoconjunctivitis (IKC) outbreak. Mycoplasma conjunctivae was detected in the Iberian ibex, coinciding with the IKC outbreak. Its prevalence had a decreasing trend in 2013 that was consistent with the clinical resolution (August, 35.4%; September, 8.7%; November, 4.3%). Infections without clinical outcome were, however, still detected in the last handling in November. Sequencing and cluster analyses of the M. conjunctivae strains found 1 year later in the ibex population confirmed the persistence of the same strain lineage that caused the IKC outbreak but with a high prevalence (75.3%) of mostly asymptomatic infections and with lower DNA load of M. conjunctivae in the eyes (mean quantitative PCR [qPCR] cycle threshold [CT ], 36.1 versus 20.3 in severe IKC). Significant age-related differences of M. conjunctivae prevalence were observed only under IKC epizootic conditions. No substantial effect of systemic IgG on M. conjunctivae DNA in the eye was evidenced with a linear mixed-models selection, which indicated that systemic IgG does not necessarily drive the resolution of M. conjunctivae infection and does not explain the epidemiological changes observed. The results show how both epidemiological scenarios, i.e., severe IKC outbreak and mostly asymptomatic infections, can consecutively occur by entailing mycoplasma persistence.IMPORTANCEMycoplasma infections are reported in a wide range of epidemiological scenarios that involve severe disease to asymptomatic infections. This study allows a better understanding of the transition between two different Mycoplasma conjunctivae epidemiological scenarios described in wild host populations and highlights the ability of M. conjunctivae to adapt, persist, and establish diverse interactions with its hosts. The proportion of asymptomatic and clinical M. conjunctivae infections in a host population may not be regarded only in response to intrinsic host species traits (i.e., susceptibility) but also to a specific host-pathogen interaction, which in turn influences the infection dynamics. Both epidemic infectious keratoconjunctivitis and a high prevalence of asymptomatic M. conjunctivae infections may occur in the same host population, depending on the circulation of M. conjunctivae, its maintenance, and the progression of the host-pathogen interactions.

Evaluation of three enzyme-linked immunosorbent assays for sarcoptic mange diagnosis and assessment in the Iberian ibex, Capra pyrenaica

BACKGROUND

Sarcoptic mange is a contagious skin disease caused by the mite Sarcoptes scabiei, affecting different mammalian species worldwide including the Iberian ibex (Capra pyrenaica), in which mortalities over 90 % of the population have been reported. No efficient diagnostic methods are available for this disease, particularly when there are low mite numbers and mild or no clinical signs. In this study, three enzyme-linked immunosorbent assays (ELISA) developed for dog (ELISA A), Cantabrian chamois (Rupicapra pyrenaica parva) (ELISA B) and Alpine chamois (Rupicapra rupicapra) (ELISA C), were evaluated to detect specific antibodies (IgG) to sarcoptic mange in Iberian ibex sera.

METHODS

Serum samples from 131 Iberian ibexes (86 healthy and 45 scabietic) were collected from 2005 to 2012 in the Sierra Nevada Natural and National Parks (southern Spain). Based on visual inspection, ibexes were classified into one of three categories, namely healthy (without scabietic compatible lesions), mildly affected (skin lesions over less than 50 % of the body surface) and severely affected (skin lesions over more than 50 % of the body surface). The optimal cut-off point, specificity, sensitivity and the area under the curve (AUC) were calculated, and the agreement between tests was determined. Moreover, differences in the optical density (OD) related to scabies severity have been evaluated for the best test.

RESULTS

ELISA C showed better performance than the two other tests, reaching higher values of sensitivity (93.0 %) and specificity (93.5 %) against the visual estimation of the percentage of affected skin, chosen as the gold standard. Significantly higher concentrations of specific antibodies were observed with this test in the mildly and severely infested ibexes than in healthy ones.

CONCLUSIONS

Our results revealed that ELISA C was an optimal test to diagnose sarcoptic mange in the Iberian ibex. Further studies characterizing immune response during the course of the disease, including spontaneous or drug induced recovery, should follow in order to better understand sarcoptic mange in Iberian ibex populations.

Improved nonparametric estimation of the optimal diagnostic cut-off point associated with the Youden index under different sampling schemes

A diagnostic cut-off point of a biomarker measurement is needed for classifying a random subject to be either diseased or healthy. However, the cut-off point is usually unknown and needs to be estimated by some optimization criteria. One important criterion is the Youden index, which has been widely adopted in practice. The Youden index, which is defined as the maximum of (sensitivity + specificity -1), directly measures the largest total diagnostic accuracy a biomarker can achieve. Therefore, it is desirable to estimate the optimal cut-off point associated with the Youden index. Sometimes, taking the actual measurements of a biomarker is very difficult and expensive, while ranking them without the actual measurement can be relatively easy. In such cases, ranked set sampling can give more precise estimation than simple random sampling, as ranked set samples are more likely to span the full range of the population. In this study, kernel density estimation is utilized to numerically solve for an estimate of the optimal cut-off point. The asymptotic distributions of the kernel estimators based on two sampling schemes are derived analytically and we prove that the estimators based on ranked set sampling are relatively more efficient than that of simple random sampling and both estimators are asymptotically unbiased. Furthermore, the asymptotic confidence intervals are derived. Intensive simulations are carried out to compare the proposed method using ranked set sampling with simple random sampling, with the proposed method outperforming simple random sampling in all cases. A real data set is analyzed for illustrating the proposed method.

Construction of joint confidence regions for the optimal true class fractions of Receiver Operating Characteristic (ROC) surfaces and manifolds

The three-class approach is used for progressive disorders when clinicians and researchers want to diagnose or classify subjects as members of one of three ordered categories based on a continuous diagnostic marker. The decision thresholds or optimal cut-off points required for this classification are often chosen to maximize the generalized Youden index (Nakas et al., Stat Med 2013; 32: 995-1003). The effectiveness of these chosen cut-off points can be evaluated by estimating their corresponding true class fractions and their associated confidence regions. Recently, in the two-class case, parametric and non-parametric methods were investigated for the construction of confidence regions for the pair of the Youden-index-based optimal sensitivity and specificity fractions that can take into account the correlation introduced between sensitivity and specificity when the optimal cut-off point is estimated from the data (Bantis et al., Biomet 2014; 70: 212-223). A parametric approach based on the Box-Cox transformation to normality often works well while for markers having more complex distributions a non-parametric procedure using logspline density estimation can be used instead. The true class fractions that correspond to the optimal cut-off points estimated by the generalized Youden index are correlated similarly to the two-class case. In this article, we generalize these methods to the three- and to the general k-class case which involves the classification of subjects into three or more ordered categories, where ROC surface or ROC manifold methodology, respectively, is typically employed for the evaluation of the discriminatory capacity of a diagnostic marker. We obtain three- and multi-dimensional joint confidence regions for the optimal true class fractions. We illustrate this with an application to the Trail Making Test Part A that has been used to characterize cognitive impairment in patients with Parkinson's disease.