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This chapter addresses diagnostic studies, which evaluate the performance of clinical tests and tools used to detect disease. The concepts of sensitivity, specificity, positive predictive value, and negative predictive value are explained in detail, highlighting how these metrics guide clinicians in interpreting test results. The role of prevalence in influencing predictive values is emphasised, underlining the need to consider population context when applying diagnostic tools. Receiver operating characteristic (ROC) curves are introduced as a method to assess test performance across varying thresholds, enabling identification of optimal cut-off points. The chapter also explores likelihood ratios, which integrate sensitivity and specificity into a single measure to support diagnostic decision-making. Strengths of diagnostic studies include their direct clinical relevance and utility in evaluating new technologies or biomarkers. Limitations include potential spectrum bias, verification bias, and challenges in defining an appropriate gold standard. Examples from infectious disease testing and mental health screening illustrate the practical implications of study design and interpretation. The chapter concludes by positioning diagnostic research as critical for improving clinical decision-making, resource allocation, and patient outcomes. This chapter maps to syllabus sections 3.2.5–3.2.8, which cover diagnostic accuracy measures including sensitivity, specificity, predictive values, likelihood ratios, and ROC curves.
We investigated the validity of the International Classification of Diseases 10th revision (ICD-10) (H53.2) diagnostic code for diplopia in the National Ambulatory Care Reporting Systems (NACRS) using a single-centre retrospective chart review study. The “gold-standard” definition was a blinded review of the abstracted chart by a neurology resident physician. Of the included 783 patients, 79 (10.1%) had diplopia as per the gold standard, while 51 (6.5%) had diplopia listed in NACRS. The specificity of the ICD-10 code was 96.9% (95% confidence interval 95.6–98.2), and sensitivity was 36.7% (26.1–47.3). The ICD-10 code for diplopia can reliably identify patients with true diplopia seen in the emergency departments.
Malaria remains one of the critical public health threats, particularly in endemic sub-Saharan countries like Malawi. Although malaria prevalence has declined over the years, the disease continues to pose a notable public health burden, contributing to high levels of morbidity and mortality. This study mapped malaria risk in Nsanje District, southern Malawi. Environmental variables (temperature, rainfall, elevation, slope, and proximity to rivers) were used to model malaria hazard, while socio-economic factors (proximity to health facilities and roads, and population density) defined vulnerability. Land use and land cover derived from Sentinel-2 using the random trees classifier in ArcGIS Pro were used to delineate elements at risk. The analytical hierarchy process and weighted overlay analysis were applied to generate hazard, vulnerability, and risk maps. Additionally, sensitivity analysis was conducted to determine the most influential factors. Results show that temperature and rainfall contributed more within the model to malaria hazard, with 20.4% and 35.1% of the area classified as high- and very high-hazard zones, respectively. Vulnerability was mainly affected by proximity to health facilities and population density, while 43.1% of the district was categorized as high risk and 40.5% as moderate risk. Overall, malaria hazard contributed most to the total risk, followed by vulnerability. The findings of this study are essential for understanding the complex dynamics of malaria transmission, which are influenced by a combination of environmental, climatic, and socio-economic factors. The study recommends enhancing healthcare accessibility and developing early warning systems, including malaria risk maps, to support targeted prevention and control efforts. Future studies should integrate long-term climate projections and real-time, high-frequency environmental and epidemiological data to enhance malaria risk modelling.
Thin-walled truncated conical shells subjected to axial compression are extremely susceptible to buckling, with experimentally observed buckling loads often falling well below classical theoretical predictions. The ratio of the experimentally measured critical load to its theoretical counterpart is defined as the Knockdown Factor (KDF). Although design guidelines proposed by agencies such as NASA provide conservative estimates of KDFs to ensure safety, recent research has highlighted the need to revisit and refine these provisions due to their excessive conservatism. In this context, the present study compares robust machine learning (ML) models for predicting buckling loads, or equivalently KDFs, of truncated conical shells using Artificial Neural Network (ANN), Support Vector Regression (SVR), Random Forest Regression (RFR) and Histogram Gradient Boosting (HGB). These models are able to capture strong nonlinear and complex feature interactions which are inherent in buckling phenomena. A comprehensive database compiled from existing literature and complemented with a set of simulated data is employed for model training and testing. To lead a new direction in the line of data-driven KDF prediction, a novel hybrid ML framework integrating Gaussian Process Regression (GPR) with Extreme Gradient Boosting (XGB), referred to as (GPR + XGB), is proposed. Additionally, a sensitivity analysis is performed to identify the most influential features governing the KDF predictions of truncated conical shells. The proposed hybrid framework that leverages experimental data as well as simulated data to accurately predict buckling KDFs of truncated conical shells, achieve significantly improved accuracy over existing ML models and conservative design guidelines.
Diagnostic test accuracy studies assess a diagnostic test’s performance against a reference standard. In this review, we explore and compare statistical methods used in meta-analyses of diagnostic test accuracy studies. Specifically, we evaluate two frequentist methods – split component synthesis (SCS) and bivariate model (BM) – alongside two Bayesian approaches: Bayesian hierarchical summary receiver operating characteristic (BHSROC) and Bayesian bivariate model (BBM). We also include their latent class variants (LC-BHSROC and LC-BBM). Using a meta-analysis of various multiplex nucleic acid amplification tests (NAATs/PCRs) against Campylobacter spp. as a case study we illustrate the practical applications of these methods. The reference standard was culture, and due to differences in cut-off values and primers among the NAAT/PCR brands, substantial heterogeneity was anticipated. Our findings reveal that the BM and BBM methods tend to estimate higher sensitivities than the other approaches, even when the number of studies is substantial, and heterogeneity is moderate – as observed in this case study. In such scenario, the SCS method or the BHSROC model may offer more robust and reliable outcomes. While our review is based on a real-life meta-analysis rather than simulations, it offers practical insights into the strengths and limitations of these statistical approaches for diagnostic test accuracy studies.
Proponents of modal knowledge accounts (safety and sensitivity) concur that one crucial advantage of their accounts is that they solve the so-called lottery problem—the problem of explaining why “lottery beliefs” based merely on statistical evidence do not constitute knowledge. Contra this claim, I argue that epistemic judgments about lottery beliefs do not consistently track what occurs in a specified set of nonactual possibilities. Thus, modal knowledge accounts cannot properly explain beliefs based merely on statistical evidence. Finally, I argue that these beliefs can be better accommodated by a rival theory of modal accounts—namely, explanationism.
A meta-analysis of diagnostic test accuracy (DTA) studies typically synthesizes study-specific test sensitivity ($Se$) and specificity ($Sp$) to quantify the accuracy of an index test of interest. The bivariate linear mixed effects model with logit transformation of $Se$ and $Sp$ (BLMM-Logit) is commonly used to make statistical inferences, but may lead to misleading results due to the need for Haldane–Anscombe correction and an approximate estimation of variance within the study. Alternative models based on the arcsine square root and Freeman–Tukey double arcsine transformation have been proposed to address these issues; however, they still rely on approximate variance estimation, which is suitable only for large sample sizes. The bivariate generalized linear mixed effects model (BGLMM) is another option, but it faces convergence issues with small meta-analyses or sparse primary studies. To address these limitations, we proposed an exact within-study variance calculation method that does not require Haldane–Anscombe correction and is applicable regardless of the transformation used or the number of studies and participants. We evaluated this method against existing approaches using real-life and simulated DTA meta-analyses. The methods were comparable for large meta-analyses. However, BLMM-Logit demonstrated substantial negative bias in estimating variances between studies and consistently underestimated summary $Se$ and $Sp$ in all simulation scenarios. In contrast, the proposed exact methods (Exact-Logit, Exact-ASR, and Exact-FTDA) and BGLMM had minimal bias and better performance metrics, particularly for meta-analyses with sparse primary studies. Thus, the proposed exact methods should be preferred for DTA meta-analyses with small or sparse studies.
Bentazon, a photosystem II–inhibiting postemergence herbicide, has been used in corn (Zea mays L.), soybean, wheat (Triticum aestivum L.), and vegetables to manage common lambsquarters (Chenopodium album L.), although growers have reported reduced efficacy across the country. The aim of this study was to describe the sensitivity response of C. album to bentazon and identify whether reported escapes could be considered to be cases of herbicide resistance evolution. We evaluated C. album populations collected from lima and snap bean (Phaseolus vulgaris L.) fields across Delaware, Illinois, Minnesota, New York, and Oregon. Dose–response experiments with 25 populations were conducted to create a reference response to bentazon, using rates that ranged from 0 to 8,406 g ai ha−1. Injury ratings and biomass were assessed at 28 d after herbicide application, and the herbicide rates required to reduce growth by 50% (I50 or GR50) and 80% (I80 or GR80) were calculated. Results indicated C. album responses to bentazon varied within and across states. Across all populations studied, the GR50 for biomass reduction ranged from 159 to 816 g ha−1, and GR80 from 230 to 1,944 g ha−1 with populations from Oregon exhibiting the highest average GR50, followed by those from New York, the Northcentral states, and Delaware. Based on our criteria that the injury rating- or biomass-based resistance index (ratio between I50 or GR50 of the suspected resistant and a local selected susceptible population) had to be at least 2, and the I80 or GR80 should be greater than the labeled field rate, one population from New York (NY6) and one from Oregon (OR29) were considered to be resistant. This research underscores the wide variation in C. album response to bentazon across the United States and the importance of herbicide resistance diagnostic strategies that account for local population variation, and highlights the increasing challenge of C. album management in specialty crops.
The Global Leadership Initiative on Malnutrition (GLIM) provides a consensus-based diagnostic framework for malnutrition in hospitalised patients, which includes at least one phenotypic and one aetiologic criterion. In GLIM, appendicular skeletal muscle based on bioelectrical impedance analysis (ASMBIA) and calf circumference (CC) are two common techniques for muscle mass assessment, but their accuracy remains debated. Therefore, the present study evaluates the prevalence of malnutrition upon hospital admission applied by GLIM criteria and mainly compares the effectiveness of ASMBIA and CC. We screened a total of 605 patients from four hospitals in Indonesia (August–October 2024). Multivariate logistic regression analysed associations with clinical outcomes. Prevalence of malnutrition was 72·7 % using three phenotypes, 55·9 % with two phenotypes, 22·1 % via ASMBIA and 62·6 % using CC. Significant associations (P < 0·05) were found between malnutrition and weight loss, BMI, mid-upper arm circumference, handgrip strength, sarcopenia and fat-free mass index. For all criteria combinations, sensitivity was greater in CC (86·1 %), followed by two phenotypes (76·8 %), while the ASMBIA had the poorest sensitivity (30·5 %). All GLIM-based diagnostic methods correlated with malnutrition risk screening and nutrition status indicators. The GLIM criteria provide a standardised, clinically relevant approach for diagnosing malnutrition in hospitalised patients, with CC emerging as a highly sensitive assessment to examine muscle mass.
This paper focuses on six-degree-of-freedom (six-DOF) spatial cable-suspended parallel robots with eight cables (8-6 CSPRs) because the redundantly actuated CSPRs are relevant in many applications, such as large-scale assembly and handling tasks, and pick-and-place operations. One of the main concerns for the 8-6 CSPRs is the stability because employing cables with strong flexibility and unidirectional restraint operates the end-effector of the robot under external disturbances. As a consequence, this paper attempts to address two key issues related to the 8-6 CSPRs: the force-pose stability measure method and the stability sensitivity analysis method. First, a force-pose stability measure model taking into account the poses of the end-effector and the cable tensions of the 8-6 CSPR is presented, in which two cable tension influencing factors and two position influencing factors are developed, while an attitude influence function representing the influence of the attitudes of the end-effector on the stability of the robot is constructed. And furthermore, a new type of workspace related to the force-pose stability of the 8-6 CSPRs is defined and generated in this paper. Second, a force-pose stability sensitivity analysis method for the 8-6 CSPRs is developed with the gray relational analysis method, where the relationship between the force-pose stability of the robot and the 14 influencing factors (the end-effector’s poses and cable tensions) is investigated to reveal the sequence of the 14 influencing factors on the force-pose stability of the robot. Finally, the proposed force-pose stability measure method and stability sensitivity analysis method for the 8-6 CSPRs are verified through simulations.
The sensitivity principle in epistemology has faced numerous, considerable, and relentless challenges since it emerged in Nozick’s Philosophical Explanations (1981). In this paper, I develop a version of sensitivity, based on Dretske’s notion of conclusive reasons (1971), that responds to the complaint that sensitivity is either incompatible with or makes an unprincipled mess of higher-level knowledge. There are three key moves in formulating reasons-based Dretskean sensitivity (RDS). First, sensitivity is conceived in terms of reasons, rather than beliefs, that track the truth. Second, focus shifts from whether S would have those reasons in the relevant counterfactual worlds to whether those reasons would be the case. Third, closer attention is paid to the structure of reasons. Critics of Nozick point out that, typically, even when S knows that they do not have a false belief that p, if S were to have a false belief that p, S would nonetheless believe that they do not have a false belief that p, violating Nozickean sensitivity. I explain how this fact does not preclude higher-level knowledge according to RDS, even if the false belief that p were based on their actual method.
Multivariable techniques produce two major kinds of information: Information about how well the model (all the independent variables together) fit the data and information about the relationship of each of the independent variables to the outcome (with adjustment for all other independent variables in the analysis). Common measures of the strength of the relationship between an independent variable and the outcome are odds ratio, relative hazard, and relative risk. Adjusting for multiple comparisons is challenging; most important, is to decide ahead of time whether there will be adjustments of multiple comparisons. A common convention is to not adjust the primary outcome, but to adjust secondary outcomes for multiple comparisons.
For continuous self-maps of compact metric spaces, we explore the relationship among the shadowable points, sensitive points, and entropy points. Specifically, we show that (1) if the set of shadowable points is dense in the phase space, then any interior point of the set of sensitive points is an entropy point; and (2) if the topological entropy is zero, then the denseness of the set of shadowable points is equivalent to almost chain continuity. In addition, we present a counter-example to a question raised by Ye and Zhang regarding entropy points.
In this chapter, new computational models will focus on whether environmental health texts are suitable for parents rather than the general public. Logistic regression models will identify linguistic features that are important contributors to the prediction of the suitability of environmental health materials for parents and caregivers of young children, who are more likely to be affected by environmental health risks such as water pollution, excessive sun exposure, and radiation in natural and indoor environments.
Early pregnancy loss is a common but distressing occurrence. Caring thoughtfully for women and others experiencing pregnancy loss and being able to listen to and understand their concerns can make a real and positive difference. Communication is key: communicating with patients clearly and thoughtfully, and delivering unexpected or bad news sensitively is hugely important. Health professionals may need to talk with and support patients and partners as they make difficult decisions within a short period of time, so should feel confident in talking about procedures including the benefits and risks of treatment. Equally, it is important for health professionals dealing with difficult situations to know how and where to find support for themselves, and to be aware of the resources the Miscarriage Association provides to both patients and professionals.
This study aims to illustrate a process approach for the calculation of minimum dietary diversity (MDD) indicators for interpretation of dietary diversity (DD) scores and to validate the MDD indicator as a proxy for adequate micronutrient intake using an existing dataset for 2 to younger than 10-year-old South African children. The DD scores were derived from nine food groups, adjusted from the ten food groups for women of reproductive age by combining pulses, nuts and seeds. Three reference methods were used to inspect micronutrient adequacy, namely the mean adequacy ratio and the mean probability of adequacy (MPA) using a single 24-h recall, and the MPA derived from usual intake using more than one 24-hour recall in a sub-sample. Adequacy threshold levels and candidate MDD indicators were inspected and validated using several performance criteria. Results show that the mean and median DD scores were 3·6 and 3·1, respectively. The resulting MDD indicators varied between 3 and 4 out of nine food groups favouring the identification of children with adequate and inadequate intake, respectively, depending on the method used and the age group. Our results and those from others furthermore support a simplified method or ‘rule of thumb’ for the determination of an MDD indicator to establish the integer values below and above the median of the DD scores. We conclude that finding a valid MDD indicator can be done using different methodologies and that results underscore the potential of a simplified method for determining an MDD indicator.
Recently, it has been recognized that the commonly used linear structural equation model is inadequate to deal with some complicated substantive theory. A new nonlinear structural equation model with fixed covariates is proposed in this article. A procedure, which utilizes the powerful path sampling for computing the Bayes factor, is developed for model comparison. In the implementation, the required random observations are simulated via a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm. It is shown that the proposed procedure is efficient and flexible; and it produces Bayesian estimates of the parameters, latent variables, and their highest posterior density intervals as by-products. Empirical performances of the proposed procedure such as sensitivity to prior inputs are illustrated by a simulation study and a real example.
The estimation of model parameters in structural equation models with polytomous variables can be handled by several computationally efficient procedures. However, sensitivity or influence analysis of the model is not well studied. We demonstrate that the existing influence analysis methods for contingency tables or for normal theory structural equation models cannot be applied directly to structural equation models with polytomous variables; and we develop appropriate procedures based on the local influence approach of Cook (1986). The proposed procedures are computationally efficient, the necessary bits of the proposed diagnostic measures are readily available following an usual fit of the model. We consider the influence of an individual cell frequency with respect to three cases: when all parameters in an unstructured model are of interest, when the unstructured polychoric correlations are of interest, and when the structural parameters are of interest. We also consider the sensitivity of the parameters estimates. Two examples based on real data are presented for illustration.
Meta-analysis of diagnostic studies experience the common problem that different studies might not be comparable since they have been using a different cut-off value for the continuous or ordered categorical diagnostic test value defining different regions for which the diagnostic test is defined to be positive. Hence specificities and sensitivities arising from different studies might vary just because the underlying cut-off value had been different. To cope with the cut-off value problem interest is usually directed towards the receiver operating characteristic (ROC) curve which consists of pairs of sensitivities and false-positive rates (1-specificity). In the context of meta-analysis one pair represents one study and the associated diagram is called an SROC curve where the S stands for “summary”. In meta-analysis of diagnostic studies emphasis has traditionally been placed on modelling this SROC curve with the intention of providing a summary measure of the diagnostic accuracy by means of an estimate of the summary ROC curve. Here, we focus instead on finding sub-groups or components in the data representing different diagnostic accuracies. The paper will consider modelling SROC curves with the Lehmann family which is characterised by one parameter only. Each single study can be represented by a specific value of that parameter. Hence we focus on the distribution of these parameter estimates and suggest modelling a potential heterogeneous or cluster structure by a mixture of specifically parameterised normal densities. We point out that this mixture is completely nonparametric and the associated mixture likelihood is well-defined and globally bounded. We use the theory and algorithms of nonparametric mixture likelihood estimation to identify a potential cluster structure in the diagnostic accuracies of the collection of studies to be analysed. Several meta-analytic applications on diagnostic studies, including AUDIT and AUDIT-C for detection of unhealthy alcohol use, the mini-mental state examination for cognitive disorders, as well as diagnostic accuracy inspection data on metal fatigue of aircraft spare parts, are discussed to illustrate the methodology.