The relationships between health, the scientific approach in medicine and concepts of epidemiology underlie theoretical and cultural attitudes of the nature of behavior and health risks. Medical tests that diagnose risk factors are thought to be predictive of disease. Physicians employ these tests to more accurately assess the health of their patients and convince their charges to change their behaviors. Communication of newly described risk factors is challenging for both physicians and patients as each party negotiates modifications of behavior and perceptions of reality.

Master of Science / Department of Diagnostic Medicine/Pathobiology / Melinda J. Wilkerson / Tick-borne bacteria, Ehrlichia canis, Anaplasma platys, and Ehrlichia chaffeensis are significant zoonotic pathogens of dogs and humans worldwide. In tropical regions such as Grenada, West Indies, dogs represent a major reservoir for E. canis and A. platys, and they are often co-infected. The purpose of this study was to develop a serologic, multiplex bead-based assay to detect species-specific exposures to E. canis, A. platys, and E. chaffeensis in dogs for purposes of surveillance and public health. Peptides from specific outer membrane proteins of P30 for E. canis, OMP1X of A. platys, and P28-19/P28-14 of E. chaffeensis were coupled to magnetic beads and assays were optimized using the multiplex Luminex xMAP® platform. In experimentally infected dogs, the multiplex assay successfully detected antibodies for E. canis and E. chaffeensis, but not A. platys. In the Grenadian population (n=104), the multiplex assay and the in-house ELISA, the SNAP® 4Dx®, detected A. platys antibodies as well as Ehrlichia spp.. Multiplex assay results were found to have “good” and “very good” agreement with the ELISA and IFA for E. canis antibody-positive dogs (K value of 0.73 and 0.84 respectively), while ELISA and IFA had “very good” agreement with each other (K value of 0.85). A. platys multiplex results had only “poor” agreement with ELISA and IFA (K value of -0.02 and 0.01, respectively), while the ELISA and IFA tests had “moderate” agreement with each other (K value of 0.5). These tests showed the prevalence of exposure to E. canis to be comparable with previous studies (38% in 2014), but a doubling of exposure to A. platys determined by IFA and 4Dx® from 9% in 2006, to 20% in 2014. Bayesian modeling (performed on E. canis data only) suggested conditional independence between the IFA, 4Dx®, and MAG tests using consensus priors calculated from literature, and that the bead-assay had comparable sensitivity and specificity to the IFA and ELISA tests. In conclusion, the multiplex peptide assay performed well in detecting the seropositive status of dogs to E. canis and had good agreement with commercial assays; however, more work needs to be done to assess performance in populations of dogs with exposures to multiple species of Ehrlichia. Further, the reasons for low seroreactivity to A. platys need to be further investigated.

Diagnostic testing is essential to distinguish non-diseased individuals from diseased individuals. The sensitivity and specificity are two important indices for the diagnostic accuracy of continuous-scale diagnostic tests. If we want to compare the effectiveness of two tests, it is of interest to construct a confidence interval for the difference of the two sensitivities at a fixed level of specificity. In this thesis, we propose two empirical likelihood based confidence intervals (HBELI and HBELII) for the difference of two sensitivities at a predetermined specificity level. Simulation studies show that when correlation between the two test results exists, HBELI and HBELII intervals perform better than the existing bootstrap based BCa, BTI and BTII intervals due to shorter interval lengths. However, when there is no correlation, BCa, BTI and BTII intervals outperform HBELI and HBELII intervals due to better coverage probability in most simulation settings.

In diagnostic test studies, one crucial task is to evaluate the diagnostic accuracy of a test. Currently, most studies focus on the Receiver Operating Characteristics Curve and the Area Under the Curve. On the other hand, the Youden index, widely applied in practice, is another comprehensive measurement for the performance of a diagnostic test. For a continuous-scale test classifying diseased and non-diseased groups, finding the Youden index of the test is equivalent to maximize the sum of sensitivity and specificity for all the possible values of the cut-point. This dissertation concentrates on statistical inferences for the Youden index. First, an auxiliary tool for the Youden index, called the diagnostic curve, is defined and used to evaluate the diagnostic test. Second, in the paired-design study to assess the diagnostic accuracy of two biomarkers, the difference in paired Youden indices frequently acts as an evaluation standard. We propose an exact confidence interval for the difference in paired Youden indices based on generalized pivotal quantities. A maximum likelihood estimate-based interval and a bootstrap-based interval are also included in the study. Third, for certain diseases, an intermediate level exists between diseased and non-diseased status. With such concern, we define the Youden index for three ordinal groups, propose the empirical estimate of the Youden index, study the asymptotic properties of the empirical Youden index estimate, and construct parametric and nonparametric confidence intervals for the Youden index. Finally, since covariates often affect the accuracy of a diagnostic test, therefore, we propose estimates for the Youden index with a covariate adjustment under heteroscedastic regression models for the test results. Asymptotic properties of the covariate-adjusted Youden index estimators are investigated under normal error and non-normal error assumptions.

Diagnostic testing is essential to distinguish non-diseased individuals from diseased individuals. More accurate tests lead to improved treatment and thus reduce medical mistakes. The sensitivity and specificity are two important measurements for the diagnostic accuracy of a diagnostic test. When the test results are continuous, it is of interest to construct a confidence interval for the sensitivity at a fixed level of specificity for the test. In this thesis, we propose three empirical likelihood intervals for the sensitivity. Simulation studies are conducted to compare the empirical likelihood based confidence intervals with the existing normal approximation based confidence interval. Our studies show that the new intervals had better coverage probability than the normal approximation based interval in most simulation settings.

Diagnostic tests are central in the field of modern medicine. One of the main factors for interpreting a diagnostic test is the discriminatory accuracy. For a continuous-scale diagnostic test, the area under the receiver operating characteristic (ROC) curve, AUC, is a useful one-number summary index for the diagnostic accuracy of the test. When only a particular region of the ROC curve would be of interest, the partial AUC (pAUC) is a more appropriate index for the diagnostic accuracy. In this thesis, we develop seven confidence intervals for the pAUC under the semi-parametric models for the diseased and non-diseased populations by using the normal approximation, bootstrap and empirical likelihood methods. In addition, we conduct simulation studies to compare the finite sample performance of the proposed confidence intervals for the pAUC. A real example is also used to illustrate the application of the recommended intervals.

Society is characterized by an increasing number of various competitive factors. Especially within the school system, there are countless moments where, consciously or not, individuals with extremely divers conditions are being compared to the goals that the school system foresees for the grades in question. Why do pupils have to do the same type of test again and again? Especially in mathematics, where many students experience difficulties or struggle with anxiety an uncertainty, this can be an obstacle to their development. Swedish pupils pass the ninth grade by writing a tiring number of national tests and after a short summer break, start high school by undergoing a marathon of diagnostic tests. Assuming no pupil continues learning during the summer holiday, the results of those diagnoses will show the same level of knowledge as the national test did before. This essay investigates how transition after ninth grade to high school can take place in a more efficient way. Questions addressed are whether there is anything more that the diagnosis should reveal and if the results of it form a basis for any kind of individually tailored measures? Could not the results of the national test serve to reveal this information instead? For this purpose, tree high school teachers in mathematics are being interviewed. The essay concludes that the information that is passed on, tends to be generally poor and the level of detail not fine enough to be of use for the receiving teacher. The teachers state that the diagnostic test and the national test provide grounds for the same type of decisions. However, whilst national tests provide more assured results in quality, diagnostic tests tend to be self-constructed and unrevised.

A diagnostic test identifies patients according to their disease status. Different meta-analytic models for diagnostic test accuracy studies have been developed to synthesize the sensitivity and specificity of the test. Because of the likely correlation between the sensitivity and specificity of a test, modeling the two parameters using a bivariate model is desirable. Historically, the logit transformation has been used to model sensitivity and specificity pairs from multiple studies as a bivariate normal. In this thesis, we propose two transformations, the arcsine square root and the Freeman-Tukey double arcsine transformation, in the context of a bivariate random-effects model to meta-analyze diagnostic test accuracy studies. We evaluated the performance of the three transformations (the commonly used logit and the proposed transformations) using an extensive simulation study in terms of bias, root mean square error and coverage probability. We illustrate the methods using three real data sets. The simulation study results showed that, for smaller sample size and higher values of sensitivity and specificity, the proposed transformations are less biased, have smaller root mean square error and better coverage probability than the standard logit transformation regardless of the number of studies. On the other hand, for large sample sizes, the usual logit transformation is less biased and has better coverage probability regardless of the true values of sensitivity, specificity and number of studies. However, when the sample size is large, the logit transformation has better root mean square error for moderate and large number of studies. The point estimates of the two parameters, sensitivity & specificity, from the methods using the three real data sets follow patterns similar to those reported by our simulation. / Thesis / Master of Science (MSc)

The Receiver Operating Characteristic (ROC) curve is the plot of Sensitivity vs. 1- Specificity of a quantitative diagnostic test, for a wide range of cut-off points c. The empirical ROC curve is probably the most used nonparametric estimator of the ROC curve. The asymptotic properties of this estimator were first developed by Hsieh and Turnbull (1996) based on strong approximations for quantile processes. Jensen et al. (2000) provided a general method to obtain regional confidence bands for the empirical ROC curve, based on its asymptotic distribution. Since most biomarkers do not have high enough sensitivity and specificity to qualify for good diagnostic test, a combination of biomarkers may result in a better diagnostic test than each one taken alone. Su and Liu (1993) proved that, if the panel of biomarkers is multivariate normally distributed for both diseased and non-diseased populations, then the linear combination, using Fisher's linear discriminant coefficients, maximizes the area under the ROC curve of the newly formed diagnostic test, called the generalized ROC curve. In this dissertation, we will derive the asymptotic properties of the generalized empirical ROC curve, the nonparametric estimator of the generalized ROC curve, by using the empirical processes theory as in van der Vaart (1998). The pivotal result used in finding the asymptotic behavior of the proposed nonparametric is the result on random functions which incorporate estimators as developed by van der Vaart (1998). By using this powerful lemma we will be able to decompose an equivalent process into a sum of two other processes, usually called the brownian bridge and the drift term, via Donsker classes of functions. Using a uniform convergence rate result given by Pollard (1984), we derive the limiting process of the drift term. Due to the independence of the random samples, the asymptotic distribution of the generalized empirical ROC process will be the sum of the asymptotic distributions of the decomposed processes. For completeness, we will first re-derive the asymptotic properties of the empirical ROC curve in the univariate case, using the same technique described before. The methodology is used to combine biomarkers in order to discriminate lung cancer patients from normals.

Dans le diagnostic médical, la surface ROC est l'outil statistique utilisée pour évaluer la précision d'un test diagnostic dans la discrimination de trois états d'une maladie, et le volume sous la surface ROC est l'indice utilisé pour la quantification de la performance du test. Dans certaines situations, différents facteurs peuvent affecter les résultats du test et ainsi les mesures de précision. Dans le cas des études longitudinales, le statut du patient peut changer au cours du temps. Dans ce manuscrit, nous avons développé des méthodes statistiques permettant d'évaluer les capacités discriminatoires des outils diagnostics et pronostics. Nous avons d'abord proposé une méthode semi-paramétrique pour estimer la surface ROC sous des modèles de rapport de densité. La construction de la méthode proposée est basée sur le modèle logit à catégories adjacentes et l'approche de vraisemblance empirique. Nous avons décrit la méthode bootstrap pour l'inférence des estimateurs obtenus. Ensuite, nous avons présenté une méthode d'estimation des surfaces ROC appelée famille de Lehmann des surfaces ROC. Cette méthode est basée sur la famille d'alternatives de Lehmann ou modèle à hasards proportionnels. Elle a l'avantage de prendre en compte les covariables qui peuvent affecter la précision d'un test diagnostic. En outre, nous avons développé une surface ROC covariable-spécifique basée sur la règle de Bayes. Pour cela, nous avons proposé un estimateur semi-paramétrique pour les surfaces ROC covariable-spécifique via des procédures de régression logistique polytomique et un modèle semi-paramétrique de localisation. Enfin, dans le cas où le statut du patient peut évoluer à travers différents stades d'une maladie, une méthode des surfaces ROC dépendant du temps a été développée. L'estimateur obtenu utilise l'approche "Inverse Probability of Censoring Weighting" (IPCW). Des simulations et des exemples sont fournis afin d'illustrer la performance des estimateurs proposés. / In diagnostic medical, the receiver operating characteristic (ROC) surface is the statistical tool used to assess the accuracy of a diagnostic test in discriminating three disease states, and the volume under the ROC surface is the used index for the quantification of the performance of the test. In some situations, various factors can affect the test results and subsequently the accuracy measures. In the case of longitudinal studies, the patient's status may change over time. In this manuscript, we developed statistical methods to assess the discriminatory capabilities of diagnostic and pronostic tools. We first proposed a semiparametric method for estimating ROC surface under density ratio models. The construction of the proposed method is based on the adjacent-category logit model and the empirical likelihood approach. We described the bootstrap method for inference of the obtained estimators. Next, we presented a method for estimating ROC surfaces called Lehmann family ROC surfaces. This method is based on the family of Lehmann alternatives or proportional hazards model. It has the advantage of taking into account covariates that may affect the accuracy of a diagnostic test. Moreover, we have developed a covariate-specific ROC surface based on the Bayes rule. For that, we proposed semiparametric estimator for covariate-specific ROC surfaces via polytomous logistic regression procedures and a semiparametric location model. Finally, in the case where patient's status may evolve through different stages of disease a method of time-dependent ROC surfaces was developed. The proposed estimator uses the "Inverse Probability of Censoring Weighting" (IPCW) approach. Simulations and examples are provided to illustrate the performance of the proposed estimators.