Nonparametric Estimation of the Bivariate Recurrence Time Distribution

This paper considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In literature, statistical methods have been developed to estimate the joint distribution of bivariate recurrence times based on data of the first pair of censored bivariate recurrence times. These methods are efficient in the current model because recurrence times of higher orders are not used. Asymptotic properties of the estimators are established. Numerical studies demonstrate the estimator performs well with practical sample sizes. We apply the proposed method to a Denmark psychiatric case register data set for illustration of the methods and theory.

Evaluating northern hardwood management using retrospective analysis and diameter distributions

Northern hardwood management was assessed throughout the state of Michigan using data collected on recently harvested stands in 2010 and 2011. Methods of forensic estimation of diameter at breast height were compared and an ideal, localized equation form was selected for use in reconstructing pre-harvest stand structures. Comparisons showed differences in predictive ability among available equation forms which led to substantial financial differences when used to estimate the value of removed timber. Management on all stands was then compared among state, private, and corporate landowners. Comparisons of harvest intensities against a liberal interpretation of a well-established management guideline showed that approximately one third of harvests were conducted in a manner which may imply that the guideline was followed. One third showed higher levels of removals than recommended, and one third of harvests were less intensive than recommended. Multiple management guidelines and postulated objectives were then synthesized into a novel system of harvest taxonomy, against which all harvests were compared. This further comparison showed approximately the same proportions of harvests, while distinguishing sanitation cuts and the future productive potential of harvests cut more intensely than suggested by guidelines. Stand structures are commonly represented using diameter distributions. Parametric and nonparametric techniques for describing diameter distributions were employed on pre-harvest and post-harvest data. A common polynomial regression procedure was found to be highly sensitive to the method of histogram construction which provides the data points for the regression. The discriminative ability of kernel density estimation was substantially different from that of the polynomial regression technique.

A BAYESIAN APPROACH TO DOSE-RESPONSE ASSESSMENT AND DRUG-DRUG INTERACTION ANALYSIS: APPLICATION TO IN VITRO STUDIES

The considerable search for synergistic agents in cancer research is motivated by the therapeutic benefits achieved by combining anti-cancer agents. Synergistic agents make it possible to reduce dosage while maintaining or enhancing a desired effect. Other favorable outcomes of synergistic agents include reduction in toxicity and minimizing or delaying drug resistance. Dose-response assessment and drug-drug interaction analysis play an important part in the drug discovery process, however analysis are often poorly done. This dissertation is an effort to notably improve dose-response assessment and drug-drug interaction analysis. The most commonly used method in published analysis is the Median-Effect Principle/Combination Index method (Chou and Talalay, 1984). The Median-Effect Principle/Combination Index method leads to inefficiency by ignoring important sources of variation inherent in dose-response data and discarding data points that do not fit the Median-Effect Principle. Previous work has shown that the conventional method yields a high rate of false positives (Boik, Boik, Newman, 2008; Hennessey, Rosner, Bast, Chen, 2010) and, in some cases, low power to detect synergy. There is a great need for improving the current methodology. We developed a Bayesian framework for dose-response modeling and drug-drug interaction analysis. First, we developed a hierarchical meta-regression dose-response model that accounts for various sources of variation and uncertainty and allows one to incorporate knowledge from prior studies into the current analysis, thus offering a more efficient and reliable inference. Second, in the case that parametric dose-response models do not fit the data, we developed a practical and flexible nonparametric regression method for meta-analysis of independently repeated dose-response experiments. Third, and lastly, we developed a method, based on Loewe additivity that allows one to quantitatively assess interaction between two agents combined at a fixed dose ratio. The proposed method makes a comprehensive and honest account of uncertainty within drug interaction assessment. Extensive simulation studies show that the novel methodology improves the screening process of effective/synergistic agents and reduces the incidence of type I error. We consider an ovarian cancer cell line study that investigates the combined effect of DNA methylation inhibitors and histone deacetylation inhibitors in human ovarian cancer cell lines. The hypothesis is that the combination of DNA methylation inhibitors and histone deacetylation inhibitors will enhance antiproliferative activity in human ovarian cancer cell lines compared to treatment with each inhibitor alone. By applying the proposed Bayesian methodology, in vitro synergy was declared for DNA methylation inhibitor, 5-AZA-2'-deoxycytidine combined with one histone deacetylation inhibitor, suberoylanilide hydroxamic acid or trichostatin A in the cell lines HEY and SKOV3. This suggests potential new epigenetic therapies in cell growth inhibition of ovarian cancer cells.

A nonparametric method of comparing the partial areas under two correlated receiver operating characteristic curves

A non-parametric method was developed and tested to compare the partial areas under two correlated Receiver Operating Characteristic curves. Based on the theory of generalized U-statistics the mathematical formulas have been derived for computing ROC area, and the variance and covariance between the portions of two ROC curves. A practical SAS application also has been developed to facilitate the calculations. The accuracy of the non-parametric method was evaluated by comparing it to other methods. By applying our method to the data from a published ROC analysis of CT image, our results are very close to theirs. A hypothetical example was used to demonstrate the effects of two crossed ROC curves. The two ROC areas are the same. However each portion of the area between two ROC curves were found to be significantly different by the partial ROC curve analysis. For computation of ROC curves with large scales, such as a logistic regression model, we applied our method to the breast cancer study with Medicare claims data. It yielded the same ROC area computation as the SAS Logistic procedure. Our method also provides an alternative to the global summary of ROC area comparison by directly comparing the true-positive rates for two regression models and by determining the range of false-positive values where the models differ. ^

Liberalization, Ownership, and Efficiency in Indian Banking: A Nonparametric Approach

This paper empirically estimates and analyzes various efficiency scores of Indian banks during 1997-2003 using data envelopment analysis (DEA). During the 1990s India's financial sector underwent a process of gradual liberalization aimed at strengthening and improving the operational efficiency of the financial system. It is observed, none the less, that Indian banks are still not much differentiated in terms of input or output oriented technical efficiency and cost efficiency. However, they differ sharply in respect of revenue and profit efficiencies. The results provide interesting insight into the empirical correlates of efficiency scores of Indian banks. Bank size, ownership, and the fact of its being listed on the stock exchange are some of the factors that are found to have positive impact on the average profit efficiency and to some extent revenue efficiency scores are. Finally, we observe that the median efficiency scores of Indian banks in general and of bigger banks in particular have improved considerably during the post-reform period.

Reputation and Efficiency: A Nonparametric Assessment of America's Top-Rated MBA Programs

Widely publicized reports of fresh MBAs getting multiple job offers with six-figure annual salaries leave a long-lasting general impression about the high quality of selected business schools. While such spectacular achievement in job placement rightly deserves recognition, one should not lose sight of the resources expended in order to accomplish this result. In this study, we employ a measure of Pareto-Koopmans global efficiency to evaluate the efficiency levels of the MBA programs in Business Week's top-rated list. We compute input- and output-oriented radial and non-radial efficiency measures for comparison. Among three tier groups, the schools from a higher tier group on average are more efficient than those from lower tiers, although variations in efficiency levels do occur within the same tier, which exist over different measures of efficiency.

Application of stellar photometry to the analysis of microarray images

Improvements in the analysis of microarray images are critical for accurately quantifying gene expression levels. The acquisition of accurate spot intensities directly influences the results and interpretation of statistical analyses. This dissertation discusses the implementation of a novel approach to the analysis of cDNA microarray images. We use a stellar photometric model, the Moffat function, to quantify microarray spots from nylon microarray images. The inherent flexibility of the Moffat shape model makes it ideal for quantifying microarray spots. We apply our novel approach to a Wilms' tumor microarray study and compare our results with a fixed-circle segmentation approach for spot quantification. Our results suggest that different spot feature extraction methods can have an impact on the ability of statistical methods to identify differentially expressed genes. We also used the Moffat function to simulate a series of microarray images under various experimental conditions. These simulations were used to validate the performance of various statistical methods for identifying differentially expressed genes. Our simulation results indicate that tests taking into account the dependency between mean spot intensity and variance estimation, such as the smoothened t-test, can better identify differentially expressed genes, especially when the number of replicates and mean fold change are low. The analysis of the simulations also showed that overall, a rank sum test (Mann-Whitney) performed well at identifying differentially expressed genes. Previous work has suggested the strengths of nonparametric approaches for identifying differentially expressed genes. We also show that multivariate approaches, such as hierarchical and k-means cluster analysis along with principal components analysis, are only effective at classifying samples when replicate numbers and mean fold change are high. Finally, we show how our stellar shape model approach can be extended to the analysis of 2D-gel images by adapting the Moffat function to take into account the elliptical nature of spots in such images. Our results indicate that stellar shape models offer a previously unexplored approach for the quantification of 2D-gel spots. ^

Uncertainty analysis of cost effectiveness in a tailored intervention to promote screening for colorectal cancer

Background. Screening for colorectal cancer (CRC) is considered cost effective but screening compliance in the US remains low. There have been very few studies on economic analyses of screening promotion strategies for colorectal cancer. The main aim of the current study is to conduct a cost effectiveness analysis (CEA) and examine the uncertainty involved in the results of the CEA of a tailored intervention to promote screening for CRC among patients of a multispeciality clinic in Houston, TX. ^ Methods. The two intervention arms received a PC based tailored program and web based educational information to promote CRC screening. The incremental cost of implementing a tailored PC based program was compared to the website based education and the status quo of no intervention for each unit of effect after 12 months of delivering the intervention. Uncertainty analysis in the point estimates of cost and effect was conducted using nonparametric bootstrapping. ^ Results. The cost of implementing a web based educational intervention was $36.00 per person and the cost of the tailored PC based interactive intervention was $43.00 per person. The additional cost per person screened for the web-based strategy was $2374 and the effect of the tailored intervention was negative. ^

Secondary data analysis of lead screening compliance in high-risk children

Introduction. Despite the ban of lead-containing gasoline and paint, childhood lead poisoning remains a public health issue. Furthermore, a Medicaid-eligible child is 8 times more likely to have an elevated blood lead level (EBLL) than a non-Medicaid child, which is the primary reason for the early detection lead screening mandate for ages 12 and 24 months among the Medicaid population. Based on field observations, there was evidence that suggested a screening compliance issue. Objective. The purpose of this study was to analyze blood lead screening compliance in previously lead poisoned Medicaid children and test for an association between timely lead screening and timely childhood immunizations. The mean months between follow-up tests were also examined for a significant difference between the non-compliant and compliant lead screened children. Methods. Access to the surveillance data of all childhood lead poisoned cases in Bexar County was granted by the San Antonio Metropolitan Health District. A database was constructed and analyzed using descriptive statistics, logistic regression methods and non-parametric tests. Lead screening at 12 months of age was analyzed separately from lead screening at 24 months. The small portion of the population who were also related were included in one analysis and removed from a second analysis to check for significance. Gender, ethnicity, age of home, and having a sibling with an EBLL were ruled out as confounders for the association tests but ethnicity and age of home were adjusted in the nonparametric tests. Results. There was a strong significant association between lead screening compliance at 12 months and childhood immunization compliance, with or without including related children (p<0.00). However, there was no significant association between the two variables at the age of 24 months. Furthermore, there was no significant difference between the median of the mean months of follow-up blood tests among the non-compliant and compliant lead screened population for at the 12 month screening group but there was a significant difference at the 24 month screening group (p<0.01). Discussion. Descriptive statistics showed that 61% and 56% of the previously lead poisoned Medicaid population did not receive their 12 and 24 month mandated lead screening on time, respectively. This suggests that their elevated blood lead level may have been diagnosed earlier in their childhood. Furthermore, a child who is compliant with their lead screening at 12 months of age is 2.36 times more likely to also receive their childhood immunizations on time compared to a child who was not compliant with their 12 month screening. Even though there was no statistical significant association found for the 24 month group, the public health significance of a screening compliance issue is no less important. The Texas Medicaid program needs to enforce lead screening compliance because it is evident that there has been no monitoring system in place. Further recommendations include a need for an increased focus on parental education and the importance of taking their children for wellness exams on time.^

Results of bulk sediment X-ray diffraction analysis and quantification of mineral phases based on the RockJock and on the QUAX quantitative analysis

We have performed quantitative X-ray diffraction (qXRD) analysis of 157 grab or core-top samples from the western Nordic Seas between (WNS) ~57°-75°N and 5° to 45° W. The RockJock Vs6 analysis includes non-clay (20) and clay (10) mineral species in the <2 mm size fraction that sum to 100 weight %. The data matrix was reduced to 9 and 6 variables respectively by excluding minerals with low weight% and by grouping into larger groups, such as the alkali and plagioclase feldspars. Because of its potential dual origins calcite was placed outside of the sum. We initially hypothesized that a combination of regional bedrock outcrops and transport associated with drift-ice, meltwater plumes, and bottom currents would result in 6 clusters defined by "similar" mineral compositions. The hypothesis was tested by use of a fuzzy k-mean clustering algorithm and key minerals were identified by step-wise Discriminant Function Analysis. Key minerals in defining the clusters include quartz, pyroxene, muscovite, and amphibole. With 5 clusters, 87.5% of the observations are correctly classified. The geographic distributions of the five k-mean clusters compares reasonably well with the original hypothesis. The close spatial relationship between bedrock geology and discrete cluster membership stresses the importance of this variable at both the WNS-scale and at a more local scale in NE Greenland.

Nonparametric Message Passing Methods for Cooperative Localization and Tracking

The objective of this thesis is the development of cooperative localization and tracking algorithms using nonparametric message passing techniques. In contrast to the most well-known techniques, the goal is to estimate the posterior probability density function (PDF) of the position of each sensor. This problem can be solved using Bayesian approach, but it is intractable in general case. Nevertheless, the particle-based approximation (via nonparametric representation), and an appropriate factorization of the joint PDFs (using message passing methods), make Bayesian approach acceptable for inference in sensor networks. The well-known method for this problem, nonparametric belief propagation (NBP), can lead to inaccurate beliefs and possible non-convergence in loopy networks. Therefore, we propose four novel algorithms which alleviate these problems: nonparametric generalized belief propagation (NGBP) based on junction tree (NGBP-JT), NGBP based on pseudo-junction tree (NGBP-PJT), NBP based on spanning trees (NBP-ST), and uniformly-reweighted NBP (URW-NBP). We also extend NBP for cooperative localization in mobile networks. In contrast to the previous methods, we use an optional smoothing, provide a novel communication protocol, and increase the efficiency of the sampling techniques. Moreover, we propose novel algorithms for distributed tracking, in which the goal is to track the passive object which cannot locate itself. In particular, we develop distributed particle filtering (DPF) based on three asynchronous belief consensus (BC) algorithms: standard belief consensus (SBC), broadcast gossip (BG), and belief propagation (BP). Finally, the last part of this thesis includes the experimental analysis of some of the proposed algorithms, in which we found that the results based on real measurements are very similar with the results based on theoretical models.