With new tests being developed and marketed, the comparison of the diagnostic accuracy of two continuous-scale diagnostic tests are of great importance. Comparing the partial areas under the receiver operating characteristic curves (pAUC) is an effective method to evaluate the accuracy of two diagnostic tests. In this thesis, we study the semi-parametric inference for the difference between two pAUCs. A normal approximation for the distribution of the difference between two pAUCs has been derived. The empirical likelihood ratio for the difference between two pAUCs is defined and its asymptotic distribution is shown to be a scaled chi-quare distribution. Bootstrap and empirical likelihood based inferential methods for the difference are proposed. We construct five confidence intervals for the difference between two pAUCs. Simulation studies are conducted to compare the finite sample performance of these intervals. We also use a real example as an application of our recommended intervals.

The outcome of a production process might not only deviate from a theoretical maximum due to inefficiency, but also because of non-controllable influences. This raises the issue of reliability of Data Envelopment Analysis in noisy environments. I propose to assume an i.i.d. data generating process with bounded noise component, so that the following approach is feasible: Use DEA to estimate a pseudo frontier first (nonparametric shape estimation). Next apply a ML-technique to the DEA-estimated efficiencies, to estimate the scalar value by which this pseudo-frontier must be shifted downward to get the true production frontier (location estimation). I prove, that this approach yields consistent estimates of the true frontier. (author's abstract) / Series: Department of Economics Working Paper Series

Profile monitoring is a relatively new approach in quality control best used when the process data follow a profile (or curve). The majority of previous studies in profile monitoring focused on the parametric modeling of either linear or nonlinear profiles under the assumption of the correct model specification. Our work considers those cases where the parametric model for the family of profiles is unknown or, at least uncertain. Consequently, we consider monitoring Poisson profiles via three methods, a nonparametric (NP) method using penalized splines, a nonparametric (NP) method using wavelets and a semi parametric (SP) procedure that combines both parametric and NP profile fits. Our simulation results show that SP method is robust to the common problem of model misspecification of the user's proposed parametric model. We also showed that Haar wavelets are a better choice than the penalized splines in situations where a sudden jump happens or the jump is edgy. In addition, we showed that the penalized splines are better than wavelets when the shape of the profiles are smooth. The proposed novel techniques have been applied to a real data set and compare with some state-of-the arts.

An efficient way of analyzing survival clinical data such as cancer data is a great concern to health experts. In this study, we investigate and propose an efficient way of handling survival clinical data. Simulation studies were conducted to compare performances of various forms of survival model techniques using an R package ``survsim". Models performance was conducted with varying sample sizes as small ($n5000$). For small and mild samples, the performance of the semi-parametric outperform or approximate the performance of the parametric model. However, for large samples, the parametric model outperforms the semi-parametric model. We compared the effectiveness and reliability of our proposed techniques using a real clinical data of mild sample size. Finally, systematic steps on how to model and explain the proposed techniques on real survival clinical data was provided.

Survival Analysis in the context of Political Science is frequently used to study the duration of agreements, political party influence, wars, senator term lengths, etc. This paper surveys a collection of methods implemented on a modified version of the Power-Sharing Event Dataset (which documents civil war peace agreement durations in the Post-Cold War era) in order to identify the research questions that are optimally addressed by each method. A primary comparison will be made between a Cox Proportional Hazards Model using some advanced capabilities in the glmnet package, a Survival Random Forest Model, and a Survival SVM. En route to this comparison, issues including Cox Model variable selection using the LASSO, identification of clusters using Hierarchal Clustering, and discretizing the response for Classification Analysis will be discussed. The results of the analysis will be used to justify the need and accessibility of the Survival Random Forest algorithm as an additional tool for survival analysis.

Indiana University-Purdue University Indianapolis (IUPUI) / A semi-parametric approach incorporates parametric and nonparametric functions in the model and is very useful in situations when a fully parametric model is inadequate. The objective of this dissertation is to extend statistical methodology employing the semi-parametric modeling approach to analyze data in health science research areas. This dissertation has three parts. The first part discusses the modeling of the dose-response relationship with correlated data by introducing overall drug effects in addition to the deviation of each subject-specific curve from the population average. Here, a penalized spline regression method that allows modeling of the smooth dose-response relationship is applied to data in studies monitoring malaria drug resistance through the ex-vivo assays.The second part of the dissertation extends the SiZer map, which is an exploratory and a powerful visualization tool, to detect underlying significant features (increase, decrease, or no change) of the curve at various smoothing levels. Here, Penalized Spline Significant Zero Crossings of Derivatives (PS-SiZer), using a penalized spline regression, is introduced to investigate significant features in correlated data arising from longitudinal settings. The third part of the dissertation applies the proposed PS-SiZer methodology to analyze HIV data. The durability of significant weight change over a period is explored from the PS-SiZer visualization. PS-SiZer is a graphical tool for exploring structures in curves by mapping areas where rate of change is significantly increasing, decreasing, or does not change. PS-SiZer maps provide information about the significant rate of weigh change that occurs in two ART regimens at various level of smoothing. A penalized spline regression model at an optimum smoothing level is applied to obtain an estimated first-time point where weight no longer increases for different treatment regimens.

Indiana University-Purdue University Indianapolis (IUPUI) / Background: Tobacco use is associated with an increased risk of developing Alzheimer's disease (AD). 14% of the incidence of AD is associated with various types of tobacco exposure. Additional real-world evidence is warranted to reveal the association between tobacco use and AD in age/gender-specific subpopulations. Method: In this thesis, the relationships between diagnoses related to tobacco use and diagnoses of AD in gender- and age-specific subgroups were investigated, using health information exchange data. The non-parametric Kaplan-Meier method was used to estimate the incidence of AD. Furthermore, the log-rank test was used to compare incidence between individuals with and without tobacco related diagnoses. In addition, we used semi-parametric Cox models to examine the association between tobacco related diagnoses and diagnoses of AD, while adjusting covariates. Results: Tobacco related diagnosis was associated with increased risk of developing AD comparing to no tobacco related diagnosis among individuals aged 60-74 years (female hazard ratio [HR] =1.26, 95% confidence interval [CI]: 1.07 – 1.48, p-value = 0.005; and male HR =1.33, 95% CI: 1.10 - 1.62, p-value =0.004). Tobacco related diagnosis was associated with decreased risk of developing AD comparing to no tobacco related diagnosis among individuals aged 75-100 years (female HR =0.79, 95% CI: 0.70 - 0.89, p-value =0.001; and male HR =0.90, 95% CI: 0.82 - 0.99, p-value =0.023). Conclusion: Individuals with tobacco related diagnoses were associated with an increased risk of developing AD in older adults aged 60-75 years. Among older adults aged 75-100 years, individuals with tobacco related diagnoses were associated with a decreased risk of developing AD.

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<p>Due to the advancements in computing power and the availability of high-frequency data, the analyses of the high frequency stock data and market microstructure has become more and more important in econometrics. In the high frequency data setting, volatility is a very important indicator on the movement of stock prices and measure of risk. It is a key input in pricing of assets, portfolio reallocation, and risk management. In this thesis, we use the Heterogeneous Autoregressive model of realized volatility, combined with Bayesian inference as well as Markov chain Monte Carlo method’s to estimate the innovation density of the daily realized volatility. A Dirichlet process is used as the prior in a countably infinite mixture model. The semi-parametric model provides a robust alternative to the models used in the literature. I find evidence of thick tails in the density of innovations to log-realized volatility.</p> / Master of Science (MSc)