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.

SURVIVAL PREDICTION FOR BRAIN TUMOR PATIENTS USING GENE EXPRESSION DATA

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. In order to evaluate this hypothesis, the general goal of this research is to build models for survival prediction of glioma patients using DNA molecular profiles (U133 Affymetrix gene expression microarrays) along with clinical information. First, a predictive Random Forest model is built for binary outcomes (i.e. short vs. long-term survival) and a small subset of genes whose expression values can be used to predict survival time is selected. Following, a new statistical methodology is developed for predicting time-to-death outcomes using Bayesian ensemble trees. Due to a large heterogeneity observed within prognostic classes obtained by the Random Forest model, prediction can be improved by relating time-to-death with gene expression profile directly. We propose a Bayesian ensemble model for survival prediction which is appropriate for high-dimensional data such as gene expression data. Our approach is based on the ensemble "sum-of-trees" model which is flexible to incorporate additive and interaction effects between genes. We specify a fully Bayesian hierarchical approach and illustrate our methodology for the CPH, Weibull, and AFT survival models. We overcome the lack of conjugacy using a latent variable formulation to model the covariate effects which decreases computation time for model fitting. Also, our proposed models provides a model-free way to select important predictive prognostic markers based on controlling false discovery rates. We compare the performance of our methods with baseline reference survival methods and apply our methodology to an unpublished data set of brain tumor survival times and gene expression data, selecting genes potentially related to the development of the disease under study. A closing discussion compares results obtained by Random Forest and Bayesian ensemble methods under the biological/clinical perspectives and highlights the statistical advantages and disadvantages of the new methodology in the context of DNA microarray data analysis.

BAYESIAN PHASE I DOSE FINDING IN CANCER TRIALS

This dissertation explores phase I dose-finding designs in cancer trials from three perspectives: the alternative Bayesian dose-escalation rules, a design based on a time-to-dose-limiting toxicity (DLT) model, and a design based on a discrete-time multi-state (DTMS) model. We list alternative Bayesian dose-escalation rules and perform a simulation study for the intra-rule and inter-rule comparisons based on two statistical models to identify the most appropriate rule under certain scenarios. We provide evidence that all the Bayesian rules outperform the traditional ``3+3'' design in the allocation of patients and selection of the maximum tolerated dose. The design based on a time-to-DLT model uses patients' DLT information over multiple treatment cycles in estimating the probability of DLT at the end of treatment cycle 1. Dose-escalation decisions are made whenever a cycle-1 DLT occurs, or two months after the previous check point. Compared to the design based on a logistic regression model, the new design shows more safety benefits for trials in which more late-onset toxicities are expected. As a trade-off, the new design requires more patients on average. The design based on a discrete-time multi-state (DTMS) model has three important attributes: (1) Toxicities are categorized over a distribution of severity levels, (2) Early toxicity may inform dose escalation, and (3) No suspension is required between accrual cohorts. The proposed model accounts for the difference in the importance of the toxicity severity levels and for transitions between toxicity levels. We compare the operating characteristics of the proposed design with those from a similar design based on a fully-evaluated model that directly models the maximum observed toxicity level within the patients' entire assessment window. We describe settings in which, under comparable power, the proposed design shortens the trial. The proposed design offers more benefit compared to the alternative design as patient accrual becomes slower.

Gene by BMI Interactions Influencing C-Reactive Protein Levels in European-Americans

C-Reactive Protein (CRP) is a biomarker indicating tissue damage, inflammation, and infection. High-sensitivity CRP (hsCRP) is an emerging biomarker often used to estimate an individual’s risk for future coronary heart disease (CHD). hsCRP levels falling below 1.00 mg/l indicate a low risk for developing CHD, levels ranging between 1.00 mg/l and 3.00 mg/l indicate an elevated risk, and levels exceeding 3.00 mg/l indicate high risk. Multiple Genome-Wide Association Studies (GWAS) have identified a number of genetic polymorphisms which influence CRP levels. SNPs implicated in such studies have been found in or near genes of interest including: CRP, APOE, APOC, IL-6, HNF1A, LEPR, and GCKR. A strong positive correlation has also been found to exist between CRP levels and BMI, a known risk factor for CHD and a state of chronic inflammation. We conducted a series of analyses designed to identify loci which interact with BMI to influence CRP levels in a subsample of European-Americans in the ARIC cohort. In a stratified GWA analysis, 15 genetic regions were identified as having significantly (p-value < 2.00*10-3) distinct effects on hsCRP levels between the two obesity strata: lean (18.50 kg/m2 < BMI < 24.99 kg/m2) and obese (BMI ≥ 30.00 kg/m2). A GWA analysis performed on all individuals combined (i.e. not a priori stratified for obesity status) with the inclusion of an additional parameter for BMI by gene interaction, identified 11 regions which interact with BMI to influence hsCRP levels. Two regions containing the genes GJA5 and GJA8 (on chromosome 1) and FBXO11 (on chromosome 2) were identified in both methods of analysis suggesting that these genes possibly interact with BMI to influence hsCRP levels. We speculate that atrial fibrillation (AF), age-related cataracts and the TGF-β pathway may be the biological processes influenced by the interaction of GJA5, GJA8 and FBXO11, respectively, with BMI to cause changes in hsCRP levels. Future studies should focus on the influence of gene x bmi interaction on AF, age-related cataracts and TGF-β.

PREDICTION OF DNA METHYLATION BASED ON GENOMIC ARCHITECTURE AND APPLICATIONS OF POSITIONAL WEIGHT MATRICES

Gene silencing due to epigenetic mechanisms shows evidence of significant contributions to cancer development. We hypothesis that the genetic architecture based on retrotransposon elements surrounding the transcription start site, plays an important role in the suppression and promotion of DNA methylation. In our investigation we found a high rate of SINE and LINEs retrotransposon elements near the transcription start site of unmethylated genes when compared to methylated genes. The presence of these elements were positively associated with promoter methylation, contrary to logical expectations, due to the malicious effects of retrotransposon elements which insert themselves randomly into the genome causing possible loss of gene function. In our genome wide analysis of human genes, results suggested that 22% of the genes in cancer were predicted to be methylation-prone; in cancer these genes are generally down-regulated and function in the development process. In summary, our investigation validated our hypothesis and showed that these widespread genomic elements in cancer are highly associated with promoter DNA methylation and may further participate in influencing epigenetic regulation.

Development of a Bayesian Joint Logistic Model to Better Study the Association between Haplotypes and Disease

In 2011, there will be an estimated 1,596,670 new cancer cases and 571,950 cancer-related deaths in the US. With the ever-increasing applications of cancer genetics in epidemiology, there is great potential to identify genetic risk factors that would help identify individuals with increased genetic susceptibility to cancer, which could be used to develop interventions or targeted therapies that could hopefully reduce cancer risk and mortality. In this dissertation, I propose to develop a new statistical method to evaluate the role of haplotypes in cancer susceptibility and development. This model will be flexible enough to handle not only haplotypes of any size, but also a variety of covariates. I will then apply this method to three cancer-related data sets (Hodgkin Disease, Glioma, and Lung Cancer). I hypothesize that there is substantial improvement in the estimation of association between haplotypes and disease, with the use of a Bayesian mathematical method to infer haplotypes that uses prior information from known genetics sources. Analysis based on haplotypes using information from publically available genetic sources generally show increased odds ratios and smaller p-values in both the Hodgkin, Glioma, and Lung data sets. For instance, the Bayesian Joint Logistic Model (BJLM) inferred haplotype TC had a substantially higher estimated effect size (OR=12.16, 95% CI = 2.47-90.1 vs. 9.24, 95% CI = 1.81-47.2) and more significant p-value (0.00044 vs. 0.008) for Hodgkin Disease compared to a traditional logistic regression approach. Also, the effect sizes of haplotypes modeled with recessive genetic effects were higher (and had more significant p-values) when analyzed with the BJLM. Full genetic models with haplotype information developed with the BJLM resulted in significantly higher discriminatory power and a significantly higher Net Reclassification Index compared to those developed with haplo.stats for lung cancer. Future analysis for this work could be to incorporate the 1000 Genomes project, which offers a larger selection of SNPs can be incorporated into the information from known genetic sources as well. Other future analysis include testing non-binary outcomes, like the levels of biomarkers that are present in lung cancer (NNK), and extending this analysis to full GWAS studies.

Origins and evolution of VNTR loci: The apolipoprotein B 3$\sp\prime$ VNTR

I studied the apolipoprotein (apo) B 3$\sp\prime$ variable number tandem repeat (VNTR) and did computer simulations of the stepwise mutation model to address four questions: (1) How did the apo B VNTR originate? (2) What is the mutational mechanism of repeat number change at the apo B VNTR? (3) To what extent are population and molecular level events responsible for the determination of the contemporary apo B allele frequency distribution? (4) Can VNTR allele frequency distributions be explained by a simple and conservative mutation-drift model? I used three general approaches to address these questions: (1) I characterized the apo B VNTR region in non-human primate species; (2) I constructed haplotypes of polymorphic markers flanking the apo B VNTR in a sample of individuals from Lorrain, France and studied the associations between the flanking-marker haplotypes and apo B VNTR size; (3) I did computer simulations of the one-step stepwise mutation model and compared the results to real data in terms of four allele frequency distribution characteristics.^ The results of this work have allowed me to conclude that the apo B VNTR originated after an initial duplication of a sequence which is still present as a single copy sequence in New World monkey species. I conclude that this locus did not originate by the transposition of an array of repeats from somewhere else in the genome. It is unlikely that recombination is the primary mutational mechanism. Furthermore, the clustered nature of these associations implicates a stepwise mutational mechanism. From the high frequencies of certain haplotype-allele size combinations, it is evident that population level events have also been important in the determination of the apo B VNTR allele frequency distribution. Results from computer simulations of the one-step stepwise mutation model have allowed me to conclude that bimodal and multimodal allele frequency distributions are not unexpected at loci evolving via stepwise mutation mechanisms. Short tandem repeat loci fit the stepwise mutation model best, followed by microsatellite loci. I therefore conclude that there are differences in the mutational mechanisms of VNTR loci as classed by repeat unit size. (Abstract shortened by UMI.) ^

Population genetics of VNTR loci and their applications in evolutionary studies

Variable number of tandem repeats (VNTR) are genetic loci at which short sequence motifs are found repeated different numbers of times among chromosomes. To explore the potential utility of VNTR loci in evolutionary studies, I have conducted a series of studies to address the following questions: (1) What are the population genetic properties of these loci? (2) What are the mutational mechanisms of repeat number change at these loci? (3) Can DNA profiles be used to measure the relatedness between a pair of individuals? (4) Can DNA fingerprint be used to measure the relatedness between populations in evolutionary studies? (5) Can microsatellite and short tandem repeat (STR) loci which mutate stepwisely be used in evolutionary analyses?^ A large number of VNTR loci typed in many populations were studied by means of statistical methods developed recently. The results of this work indicate that there is no significant departure from Hardy-Weinberg expectation (HWE) at VNTR loci in most of the human populations examined, and the departure from HWE in some VNTR loci are not solely caused by the presence of population sub-structure.^ A statistical procedure is developed to investigate the mutational mechanisms of VNTR loci by studying the allele frequency distributions of these loci. Comparisons of frequency distribution data on several hundreds VNTR loci with the predictions of two mutation models demonstrated that there are differences among VNTR loci grouped by repeat unit sizes.^ By extending the ITO method, I derived the distribution of the number of shared bands between individuals with any kinship relationship. A maximum likelihood estimation procedure is proposed to estimate the relatedness between individuals from the observed number of shared bands between them.^ It was believed that classical measures of genetic distance are not applicable to analysis of DNA fingerprints which reveal many minisatellite loci simultaneously in the genome, because the information regarding underlying alleles and loci is not available. I proposed a new measure of genetic distance based on band sharing between individuals that is applicable to DNA fingerprint data.^ To address the concern that microsatellite and STR loci may not be useful for evolutionary studies because of the convergent nature of their mutation mechanisms, by a theoretical study as well as by computer simulation, I conclude that the possible bias caused by the convergent mutations can be corrected, and a novel measure of genetic distance that makes the correction is suggested. In summary, I conclude that hypervariable VNTR loci are useful in evolutionary studies of closely related populations or species, especially in the study of human evolution and the history of geographic dispersal of Homo sapiens. (Abstract shortened by UMI.) ^

Amyotrophic lateral sclerosis and Parkinsonism-dementia complex of Guam: Descriptive epidemiology, secular trends, and birth cohort effects on incidence, 1950--1989

This study describes the patterns of occurrence of amyotrophic lateral sclerosis (ALS) and parkinsonism-dementia complex (PDC) of Guam during 1950-1989. Both ALS and PDC occur with high frequency among the indigenous Chamorro population, first recognized in the early 1950's. Reports in the early 1980's indicated that both ALS and PDC were disappearing, due to a purported reduction in exposure to harmful environmental factors as a result of the dramatic changes in lifestyle that took place after World War II. However, this study provides compelling evidence that ALS and PDC have not disappeared on Guam and that rates for both are higher during 1980-1989 than previously reported.^ The patterns of occurrence for both ALS and PDC overlap in most respects: (1) incidence and mortality are decreasing; (2) median age at onset is increasing; (3) males are at increased risk for developing disease; (4) risk is higher for those residing in the south compared to the non-south; and (5) age-specific incidence is decreasing over time except in the oldest age groups.^ Age-specific incidence of ALS and PDC, separately and together, is generally higher for cohorts born before 1920 than for those born after 1920. A significant birth cohort effect on the incidence of PDC for the 1906-1915 birth cohort was found, but not for ALS and for ALS and PDC together. Whether or not a cohort effect, period effect, or both are associated with incidence of ALS and PDC cannot be determined from the data currently available and will require additional follow-up of individuals born after 1920.^ The epidemiological data amassed over this 40-year period provide evidence that supports an environmental exposure model for disease occurrence as opposed to a simple genetic or infectious disease model. Whether neurodegenerative disease in this population occurs as a consequence of a single exposure or is explained by a multifactorial model such as a genetic predisposition with some environmental interaction is yet to be determined. However, descriptive studies such as this can provide clues concerning timing and location of potential adverse exposures but cannot determine etiology, underscoring the urgent need for analytic studies of ALS and PDC to further investigate existing etiologic hypotheses and to test new hypotheses. ^

Structural equation modeling of the medical outcome study: Short Form 36 (SF-36)

The factorial validity of the SF-36 was evaluated using confirmatory factor analysis (CFA) methods, structural equation modeling (SEM), and multigroup structural equation modeling (MSEM). First, the measurement and structural model of the hypothesized SF-36 was explicated. Second, the model was tested for the validity of a second-order factorial structure, upon evidence of model misfit, determined the best-fitting model, and tested the validity of the best-fitting model on a second random sample from the same population. Third, the best-fitting model was tested for invariance of the factorial structure across race, age, and educational subgroups using MSEM.^ The findings support the second-order factorial structure of the SF-36 as proposed by Ware and Sherbourne (1992). However, the results suggest that: (a) Mental Health and Physical Health covary; (b) general mental health cross-loads onto Physical Health; (c) general health perception loads onto Mental Health instead of Physical Health; (d) many of the error terms are correlated; and (e) the physical function scale is not reliable across these two samples. This hierarchical factor pattern was replicated across both samples of health care workers, suggesting that the post hoc model fitting was not data specific. Subgroup analysis suggests that the physical function scale is not reliable across the "age" or "education" subgroups and that the general mental health scale path from Mental Health is not reliable across the "white/nonwhite" or "education" subgroups.^ The importance of this study is in the use of SEM and MSEM in evaluating sample data from the use of the SF-36. These methods are uniquely suited to the analysis of latent variable structures and are widely used in other fields. The use of latent variable models for self reported outcome measures has become widespread, and should now be applied to medical outcomes research. Invariance testing is superior to mean scores or summary scores when evaluating differences between groups. From a practical, as well as, psychometric perspective, it seems imperative that construct validity research related to the SF-36 establish whether this same hierarchical structure and invariance holds for other populations.^ This project is presented as three articles to be submitted for publication. ^

Statistical characterization and development of summary measures of non-normal distributions of nuclear morphometry data from prostate cancer cells for use as prognostic indicators

Nuclear morphometry (NM) uses image analysis to measure features of the cell nucleus which are classified as: bulk properties, shape or form, and DNA distribution. Studies have used these measurements as diagnostic and prognostic indicators of disease with inconclusive results. The distributional properties of these variables have not been systematically investigated although much of the medical data exhibit nonnormal distributions. Measurements are done on several hundred cells per patient so summary measurements reflecting the underlying distribution are needed.^ Distributional characteristics of 34 NM variables from prostate cancer cells were investigated using graphical and analytical techniques. Cells per sample ranged from 52 to 458. A small sample of patients with benign prostatic hyperplasia (BPH), representing non-cancer cells, was used for general comparison with the cancer cells.^ Data transformations such as log, square root and 1/x did not yield normality as measured by the Shapiro-Wilks test for normality. A modulus transformation, used for distributions having abnormal kurtosis values, also did not produce normality.^ Kernel density histograms of the 34 variables exhibited non-normality and 18 variables also exhibited bimodality. A bimodality coefficient was calculated and 3 variables: DNA concentration, shape and elongation, showed the strongest evidence of bimodality and were studied further.^ Two analytical approaches were used to obtain a summary measure for each variable for each patient: cluster analysis to determine significant clusters and a mixture model analysis using a two component model having a Gaussian distribution with equal variances. The mixture component parameters were used to bootstrap the log likelihood ratio to determine the significant number of components, 1 or 2. These summary measures were used as predictors of disease severity in several proportional odds logistic regression models. The disease severity scale had 5 levels and was constructed of 3 components: extracapsulary penetration (ECP), lymph node involvement (LN+) and seminal vesicle involvement (SV+) which represent surrogate measures of prognosis. The summary measures were not strong predictors of disease severity. There was some indication from the mixture model results that there were changes in mean levels and proportions of the components in the lower severity levels. ^

A comparison of Markov and generalized linear models of hospital mortality

This paper reports a comparison of three modeling strategies for the analysis of hospital mortality in a sample of general medicine inpatients in a Department of Veterans Affairs medical center. Logistic regression, a Markov chain model, and longitudinal logistic regression were evaluated on predictive performance as measured by the c-index and on accuracy of expected numbers of deaths compared to observed. The logistic regression used patient information collected at admission; the Markov model was comprised of two absorbing states for discharge and death and three transient states reflecting increasing severity of illness as measured by laboratory data collected during the hospital stay; longitudinal regression employed Generalized Estimating Equations (GEE) to model covariance structure for the repeated binary outcome. Results showed that the logistic regression predicted hospital mortality as well as the alternative methods but was limited in scope of application. The Markov chain provides insights into how day to day changes of illness severity lead to discharge or death. The longitudinal logistic regression showed that increasing illness trajectory is associated with hospital mortality. The conclusion is reached that for standard applications in modeling hospital mortality, logistic regression is adequate, but for new challenges facing health services research today, alternative methods are equally predictive, practical, and can provide new insights. ^

Design and implementation of a multicriteria medical decision support system for diagnosis and treatment

Health care providers face the problem of trying to make decisions with inadequate information and also with an overload of (often contradictory) information. Physicians often choose treatment long before they know which disease is present. Indeed, uncertainty is intrinsic to the practice of medicine. Decision analysis can help physicians structure and work through a medical decision problem, and can provide reassurance that decisions are rational and consistent with the beliefs and preferences of other physicians and patients. ^ The primary purpose of this research project is to develop the theory, methods, techniques and tools necessary for designing and implementing a system to support solving medical decision problems. A case study involving “abdominal pain” serves as a prototype for implementing the system. The research, however, focuses on a generic class of problems and aims at covering theoretical as well as practical aspects of the system developed. ^ The main contributions of this research are: (1) bridging the gap between the statistical approach and the knowledge-based (expert) approach to medical decision making; (2) linking a collection of methods, techniques and tools together to allow for the design of a medical decision support system, based on a framework that involves the Analytic Network Process (ANP), the generalization of the Analytic Hierarchy Process (AHP) to dependence and feedback, for problems involving diagnosis and treatment; (3) enhancing the representation and manipulation of uncertainty in the ANP framework by incorporating group consensus weights; and (4) developing a computer program to assist in the implementation of the system. ^

Evaluation of the accuracy of multilevel analysis parameter estimates for intra-cluster correlation in correlated binary data

Many studies in biostatistics deal with binary data. Some of these studies involve correlated observations, which can complicate the analysis of the resulting data. Studies of this kind typically arise when a high degree of commonality exists between test subjects. If there exists a natural hierarchy in the data, multilevel analysis is an appropriate tool for the analysis. Two examples are the measurements on identical twins, or the study of symmetrical organs or appendages such as in the case of ophthalmic studies. Although this type of matching appears ideal for the purposes of comparison, analysis of the resulting data while ignoring the effect of intra-cluster correlation has been shown to produce biased results.^ This paper will explore the use of multilevel modeling of simulated binary data with predetermined levels of correlation. Data will be generated using the Beta-Binomial method with varying degrees of correlation between the lower level observations. The data will be analyzed using the multilevel software package MlwiN (Woodhouse, et al, 1995). Comparisons between the specified intra-cluster correlation of these data and the estimated correlations, using multilevel analysis, will be used to examine the accuracy of this technique in analyzing this type of data. ^

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. ^