Regression with autocorrelated data: A study of time trend of global infant mortality rate

The infant mortality rate (IMR) is considered to be one of the most important indices of a country's well-being. Countries around the world and other health organizations like the World Health Organization are dedicating their resources, knowledge and energy to reduce the infant mortality rates. The well-known Millennium Development Goal 4 (MDG 4), whose aim is to archive a two thirds reduction of the under-five mortality rate between 1990 and 2015, is an example of the commitment. ^ In this study our goal is to model the trends of IMR between the 1950s to 2010s for selected countries. We would like to know how the IMR is changing overtime and how it differs across countries. ^ IMR data collected over time forms a time series. The repeated observations of IMR time series are not statistically independent. So in modeling the trend of IMR, it is necessary to account for these correlations. We proposed to use the generalized least squares method in general linear models setting to deal with the variance-covariance structure in our model. In order to estimate the variance-covariance matrix, we referred to the time-series models, especially the autoregressive and moving average models. Furthermore, we will compared results from general linear model with correlation structure to that from ordinary least squares method without taking into account the correlation structure to check how significantly the estimates change.^

Analysis of life expectancy using linear and nonlinear models

Life expectancy has consistently increased over the last 150 years due to improvements in nutrition, medicine, and public health. Several studies found that in many developed countries, life expectancy continued to rise following a nearly linear trend, which was contrary to a common belief that the rate of improvement in life expectancy would decelerate and was fit with an S-shaped curve. Using samples of countries that exhibited a wide range of economic development levels, we explored the change in life expectancy over time by employing both nonlinear and linear models. We then observed if there were any significant differences in estimates between linear models, assuming an auto-correlated error structure. When data did not have a sigmoidal shape, nonlinear growth models sometimes failed to provide meaningful parameter estimates. The existence of an inflection point and asymptotes in the growth models made them inflexible with life expectancy data. In linear models, there was no significant difference in the life expectancy growth rate and future estimates between ordinary least squares (OLS) and generalized least squares (GLS). However, the generalized least squares model was more robust because the data involved time-series variables and residuals were positively correlated. ^

Bayesian adaptive designs in early phase clinical trials

There are two practical challenges in the phase I clinical trial conduct: lack of transparency to physicians, and the late onset toxicity. In my dissertation, Bayesian approaches are used to address these two problems in clinical trial designs. The proposed simple optimal designs cast the dose finding problem as a decision making process for dose escalation and deescalation. The proposed designs minimize the incorrect decision error rate to find the maximum tolerated dose (MTD). For the late onset toxicity problem, a Bayesian adaptive dose-finding design for drug combination is proposed. The dose-toxicity relationship is modeled using the Finney model. The unobserved delayed toxicity outcomes are treated as missing data and Bayesian data augment is employed to handle the resulting missing data. Extensive simulation studies have been conducted to examine the operating characteristics of the proposed designs and demonstrated the designs' good performances in various practical scenarios.^

On Bayesian seamless phase I-II designs

Early phase clinical trial designs have long been the focus of interest for clinicians and statisticians working in oncology field. There are several standard phse I and phase II designs that have been widely-implemented in medical practice. For phase I design, the most commonly used methods are 3+3 and CRM. A newly-developed Bayesian model-based mTPI design has now been used by an increasing number of hospitals and pharmaceutical companies. The advantages and disadvantages of these three top phase I designs have been discussed in my work here and their performances were compared using simulated data. It was shown that mTPI design exhibited superior performance in most scenarios in comparison with 3+3 and CRM designs. ^ The next major part of my work is proposing an innovative seamless phase I/II design that allows clinicians to conduct phase I and phase II clinical trials simultaneously. Bayesian framework was implemented throughout the whole design. The phase I portion of the design adopts mTPI method, with the addition of futility rule which monitors the efficacy performance of the tested drugs. Dose graduation rules were proposed in this design to allow doses move forward from phase I portion of the study to phase II portion without interrupting the ongoing phase I dose-finding schema. Once a dose graduated to phase II, adaptive randomization was used to randomly allocated patients into different treatment arms, with the intention of more patients being assigned to receive more promising dose(s). Again simulations were performed to compare the performance of this innovative phase I/II design with a recently published phase I/II design, together with the conventional phase I and phase II designs. The simulation results indicated that the seamless phase I/II design outperform the other two competing methods in most scenarios, with superior trial power and the fact that it requires smaller sample size. It also significantly reduces the overall study time. ^ Similar to other early phase clinical trial designs, the proposed seamless phase I/II design requires that the efficacy and safety outcomes being able to be observed in a short time frame. This limitation can be overcome by using validated surrogate marker for the efficacy and safety endpoints.^

Mixture modeling for joint analysis of survival, discrete, and continuous data

Mixture modeling is commonly used to model categorical latent variables that represent subpopulations in which population membership is unknown but can be inferred from the data. In relatively recent years, the potential of finite mixture models has been applied in time-to-event data. However, the commonly used survival mixture model assumes that the effects of the covariates involved in failure times differ across latent classes, but the covariate distribution is homogeneous. The aim of this dissertation is to develop a method to examine time-to-event data in the presence of unobserved heterogeneity under a framework of mixture modeling. A joint model is developed to incorporate the latent survival trajectory along with the observed information for the joint analysis of a time-to-event variable, its discrete and continuous covariates, and a latent class variable. It is assumed that the effects of covariates on survival times and the distribution of covariates vary across different latent classes. The unobservable survival trajectories are identified through estimating the probability that a subject belongs to a particular class based on observed information. We applied this method to a Hodgkin lymphoma study with long-term follow-up and observed four distinct latent classes in terms of long-term survival and distributions of prognostic factors. Our results from simulation studies and from the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. This flexible inference method provides more accurate estimation and accommodates unobservable heterogeneity among individuals while taking involved interactions between covariates into consideration.^

Gene-gene interaction and gene-pathway analysis of genome-wide association for schizophrenia

Schizophrenia (SZ) is a complex disorder with high heritability and variable phenotypes that has limited success in finding causal genes associated with the disease development. Pathway-based analysis is an effective approach in investigating the molecular mechanism of susceptible genes associated with complex diseases. The etiology of complex diseases could be a network of genetic factors and within the genes, interaction may occur. In this work we argue that some genes might be of small effect that by itself are neither sufficient nor necessary to cause the disease however, their effect may induce slight changes to the gene expression or affect the protein function, therefore, analyzing the gene-gene interaction mechanism within the disease pathway would play crucial role in dissecting the genetic architecture of complex diseases, making the pathway-based analysis a complementary approach to GWAS technique. ^ In this study, we implemented three novel linkage disequilibrium based statistics, the linear combination, the quadratic, and the decorrelation test statistics, to investigate the interaction between linked and unlinked genes in two independent case-control GWAS datasets for SZ including participants of European (EA) and African (AA) ancestries. The EA population included 1,173 cases and 1,378 controls with 729,454 genotyped SNPs, while the AA population included 219 cases and 288 controls with 845,814 genotyped SNPs. We identified 17,186 interacting gene-sets at significant level in EA dataset, and 12,691 gene-sets in AA dataset using the gene-gene interaction method. We also identified 18,846 genes in EA dataset and 19,431 genes in AA dataset that were in the disease pathways. However, few genes were reported of significant association to SZ. ^ Our research determined the pathways characteristics for schizophrenia through the gene-gene interaction and gene-pathway based approaches. Our findings suggest insightful inferences of our methods in studying the molecular mechanisms of common complex diseases.^

A comparison of adherence with minocycline treatment in Parkinson's disease and rheumatoid arthritis clinical trials

Background: Little is known about the effects on patient adherence when the same study drug is administered in the same dose in two populations with two different diseases in two different clinical trials. The Minocycline in Rheumatoid Arthritis (MIRA) trial and the NIH Exploratory Trials in Parkinson's disease (NET-PD) Futility Study I provide a unique opportunity to do the above and to compare methods measuring adherence. This study may increase understanding of the influence of disease and adverse events on patient adherence and will provide insights to investigators selecting adherence assessment methods in clinical trials of minocycline and other drugs in future.^ Methods: Minocycline adherence by pill count and the effect of adverse events was compared in the MIRA and NET-PD FS1 trials using multivariable linear regression. Within the MIRA trial, agreement between assay and pill count was compared. The association of adverse events with assay adherence was examined using multivariable logistic regression.^ Results: Adherence derived from pill count in the MIRA and NET-PD FS1 trials did not differ significantly. Adverse events potentially related to minocycline did not appear useful to predict minocycline adherence. In the MIRA trial, adherence measured by pill count appears higher than adherence measured by assay. Agreement between pill count and assay was poor (kappa statistic = 0.25).^ Limitations: Trial and disease are completely confounded and hence the independent effect of disease on adherence to minocycline treatment cannot be studied.^ Conclusion: Simple pill count may be preferred over assay in the minocycline clinical trials to measure adherence. Assays may be less sensitive in a clinical setting where appointments are not scheduled in relation to medication administration time, given assays depend on many pharmacokinetic and instrument-related factors. However, pill count can be manipulated by the patient. Another study suggested that self-report method is more sensitive than pill count method in differentiating adherence from non-adherence. An effect of medication-related adverse events on adherence could not be detected.^

INTEGRATIVE BIOMARKER IDENTIFICATION AND CLASSIFICATION USING HIGH THROUGHPUT ASSAYS

It is well accepted that tumorigenesis is a multi-step procedure involving aberrant functioning of genes regulating cell proliferation, differentiation, apoptosis, genome stability, angiogenesis and motility. To obtain a full understanding of tumorigenesis, it is necessary to collect information on all aspects of cell activity. Recent advances in high throughput technologies allow biologists to generate massive amounts of data, more than might have been imagined decades ago. These advances have made it possible to launch comprehensive projects such as (TCGA) and (ICGC) which systematically characterize the molecular fingerprints of cancer cells using gene expression, methylation, copy number, microRNA and SNP microarrays as well as next generation sequencing assays interrogating somatic mutation, insertion, deletion, translocation and structural rearrangements. Given the massive amount of data, a major challenge is to integrate information from multiple sources and formulate testable hypotheses. This thesis focuses on developing methodologies for integrative analyses of genomic assays profiled on the same set of samples. We have developed several novel methods for integrative biomarker identification and cancer classification. We introduce a regression-based approach to identify biomarkers predictive to therapy response or survival by integrating multiple assays including gene expression, methylation and copy number data through penalized regression. To identify key cancer-specific genes accounting for multiple mechanisms of regulation, we have developed the integIRTy software that provides robust and reliable inferences about gene alteration by automatically adjusting for sample heterogeneity as well as technical artifacts using Item Response Theory. To cope with the increasing need for accurate cancer diagnosis and individualized therapy, we have developed a robust and powerful algorithm called SIBER to systematically identify bimodally expressed genes using next generation RNAseq data. We have shown that prediction models built from these bimodal genes have the same accuracy as models built from all genes. Further, prediction models with dichotomized gene expression measurements based on their bimodal shapes still perform well. The effectiveness of outcome prediction using discretized signals paves the road for more accurate and interpretable cancer classification by integrating signals from multiple sources.

DEVELOPMENT OF NOVEL METHODS TO MINIMIZE THE IMPACT OF SEQUENCING ERRORS IN THE NEXT-GENERATION SEQUENCING DATA ANALYSIS

Next-generation sequencing (NGS) technology has become a prominent tool in biological and biomedical research. However, NGS data analysis, such as de novo assembly, mapping and variants detection is far from maturity, and the high sequencing error-rate is one of the major problems. . To minimize the impact of sequencing errors, we developed a highly robust and efficient method, MTM, to correct the errors in NGS reads. We demonstrated the effectiveness of MTM on both single-cell data with highly non-uniform coverage and normal data with uniformly high coverage, reflecting that MTM’s performance does not rely on the coverage of the sequencing reads. MTM was also compared with Hammer and Quake, the best methods for correcting non-uniform and uniform data respectively. For non-uniform data, MTM outperformed both Hammer and Quake. For uniform data, MTM showed better performance than Quake and comparable results to Hammer. By making better error correction with MTM, the quality of downstream analysis, such as mapping and SNP detection, was improved. SNP calling is a major application of NGS technologies. However, the existence of sequencing errors complicates this process, especially for the low coverage (

Identification of genes associated with quantitative traits involved in cardiovascular disease and lipoprotein metabolism

Cardiovascular disease (CVD) is a threat to public health. It has been reported to be the leading cause of death in United States. The invention of next generation sequencing (NGS) technology has revolutionized the biomedical research. To investigate NGS data of CVD related quantitative traits would contribute to address the unknown etiology and disease mechanism of CVD. NHLBI's Exome Sequencing Project (ESP) contains CVD related phenotypes and their associated NGS exomes sequence data. Initially, a subset of next generation sequencing data consisting of 13 CVD-related quantitative traits was investigated. Only 6 traits, systolic blood pressure (SBP), diastolic blood pressure (DBP), height, platelet counts, waist circumference, and weight, were analyzed by functional linear model (FLM) and 7 currently existing methods. FLM outperformed all currently existing methods by identifying the highest number of significant genes and had identified 96, 139, 756, 1162, 1106, and 298 genes associated with SBP, DBP, Height, Platelet, Waist, and Weight respectively. ^

Nonlinear dimension reduction in pathway-based genome-wide association analysis

Pathway based genome wide association study evolves from pathway analysis for microarray gene expression and is under rapid development as a complementary for single-SNP based genome wide association study. However, it faces new challenges, such as the summarization of SNP statistics to pathway statistics. The current study applies the ridge regularized Kernel Sliced Inverse Regression (KSIR) to achieve dimension reduction and compared this method to the other two widely used methods, the minimal-p-value (minP) approach of assigning the best test statistics of all SNPs in each pathway as the statistics of the pathway and the principal component analysis (PCA) method of utilizing PCA to calculate the principal components of each pathway. Comparison of the three methods using simulated datasets consisting of 500 cases, 500 controls and100 SNPs demonstrated that KSIR method outperformed the other two methods in terms of causal pathway ranking and the statistical power. PCA method showed similar performance as the minP method. KSIR method also showed a better performance over the other two methods in analyzing a real dataset, the WTCCC Ulcerative Colitis dataset consisting of 1762 cases, 3773 controls as the discovery cohort and 591 cases, 1639 controls as the replication cohort. Several immune and non-immune pathways relevant to ulcerative colitis were identified by these methods. Results from the current study provided a reference for further methodology development and identified novel pathways that may be of importance to the development of ulcerative colitis.^

New methods for quantification and analysis of quantitative real-time polymerase chain reaction data

Quantitative real-time polymerase chain reaction (qPCR) is a sensitive gene quantitation method that has been widely used in the biological and biomedical fields. The currently used methods for PCR data analysis, including the threshold cycle (CT) method, linear and non-linear model fitting methods, all require subtracting background fluorescence. However, the removal of background fluorescence is usually inaccurate, and therefore can distort results. Here, we propose a new method, the taking-difference linear regression method, to overcome this limitation. Briefly, for each two consecutive PCR cycles, we subtracted the fluorescence in the former cycle from that in the later cycle, transforming the n cycle raw data into n-1 cycle data. Then linear regression was applied to the natural logarithm of the transformed data. Finally, amplification efficiencies and the initial DNA molecular numbers were calculated for each PCR run. To evaluate this new method, we compared it in terms of accuracy and precision with the original linear regression method with three background corrections, being the mean of cycles 1-3, the mean of cycles 3-7, and the minimum. Three criteria, including threshold identification, max R2, and max slope, were employed to search for target data points. Considering that PCR data are time series data, we also applied linear mixed models. Collectively, when the threshold identification criterion was applied and when the linear mixed model was adopted, the taking-difference linear regression method was superior as it gave an accurate estimation of initial DNA amount and a reasonable estimation of PCR amplification efficiencies. When the criteria of max R2 and max slope were used, the original linear regression method gave an accurate estimation of initial DNA amount. Overall, the taking-difference linear regression method avoids the error in subtracting an unknown background and thus it is theoretically more accurate and reliable. This method is easy to perform and the taking-difference strategy can be extended to all current methods for qPCR data analysis.^

Network-based analysis of genome-wide scans of natural selection

The genomic era brought by recent advances in the next-generation sequencing technology makes the genome-wide scans of natural selection a reality. Currently, almost all the statistical tests and analytical methods for identifying genes under selection was performed on the individual gene basis. Although these methods have the power of identifying gene subject to strong selection, they have limited power in discovering genes targeted by moderate or weak selection forces, which are crucial for understanding the molecular mechanisms of complex phenotypes and diseases. Recent availability and rapid completeness of many gene network and protein-protein interaction databases accompanying the genomic era open the avenues of exploring the possibility of enhancing the power of discovering genes under natural selection. The aim of the thesis is to explore and develop normal mixture model based methods for leveraging gene network information to enhance the power of natural selection target gene discovery. The results show that the developed statistical method, which combines the posterior log odds of the standard normal mixture model and the Guilt-By-Association score of the gene network in a naïve Bayes framework, has the power to discover moderate/weak selection gene which bridges the genes under strong selection and it helps our understanding the biology under complex diseases and related natural selection phenotypes.^

Application of the general linear model to assess the effect of missing data on bone marrow mononuclear cell therapy with infusion timing and follow-up MRI

With most clinical trials, missing data presents a statistical problem in evaluating a treatment's efficacy. There are many methods commonly used to assess missing data; however, these methods leave room for bias to enter the study. This thesis was a secondary analysis on data taken from TIME, a phase 2 randomized clinical trial conducted to evaluate the safety and effect of the administration timing of bone marrow mononuclear cells (BMMNC) for subjects with acute myocardial infarction (AMI).^ We evaluated the effect of missing data by comparing the variance inflation factor (VIF) of the effect of therapy between all subjects and only subjects with complete data. Through the general linear model, an unbiased solution was made for the VIF of the treatment's efficacy using the weighted least squares method to incorporate missing data. Two groups were identified from the TIME data: 1) all subjects and 2) subjects with complete data (baseline and follow-up measurements). After the general solution was found for the VIF, it was migrated Excel 2010 to evaluate data from TIME. The resulting numerical value from the two groups was compared to assess the effect of missing data.^ The VIF values from the TIME study were considerably less in the group with missing data. By design, we varied the correlation factor in order to evaluate the VIFs of both groups. As the correlation factor increased, the VIF values increased at a faster rate in the group with only complete data. Furthermore, while varying the correlation factor, the number of subjects with missing data was also varied to see how missing data affects the VIF. When subjects with only baseline data was increased, we saw a significant rate increase in VIF values in the group with only complete data while the group with missing data saw a steady and consistent increase in the VIF. The same was seen when we varied the group with follow-up only data. This essentially showed that the VIFs steadily increased when missing data is not ignored. When missing data is ignored as with our comparison group, the VIF values sharply increase as correlation increases.^

Data quality in trauma transfusion studies and the impact of missing data on predicting massive transfusion

Maximizing data quality may be especially difficult in trauma-related clinical research. Strategies are needed to improve data quality and assess the impact of data quality on clinical predictive models. This study had two objectives. The first was to compare missing data between two multi-center trauma transfusion studies: a retrospective study (RS) using medical chart data with minimal data quality review and the PRospective Observational Multi-center Major Trauma Transfusion (PROMMTT) study with standardized quality assurance. The second objective was to assess the impact of missing data on clinical prediction algorithms by evaluating blood transfusion prediction models using PROMMTT data. RS (2005-06) and PROMMTT (2009-10) investigated trauma patients receiving ≥ 1 unit of red blood cells (RBC) from ten Level I trauma centers. Missing data were compared for 33 variables collected in both studies using mixed effects logistic regression (including random intercepts for study site). Massive transfusion (MT) patients received ≥ 10 RBC units within 24h of admission. Correct classification percentages for three MT prediction models were evaluated using complete case analysis and multiple imputation based on the multivariate normal distribution. A sensitivity analysis for missing data was conducted to estimate the upper and lower bounds of correct classification using assumptions about missing data under best and worst case scenarios. Most variables (17/33=52%) had <1% missing data in RS and PROMMTT. Of the remaining variables, 50% demonstrated less missingness in PROMMTT, 25% had less missingness in RS, and 25% were similar between studies. Missing percentages for MT prediction variables in PROMMTT ranged from 2.2% (heart rate) to 45% (respiratory rate). For variables missing >1%, study site was associated with missingness (all p≤0.021). Survival time predicted missingness for 50% of RS and 60% of PROMMTT variables. MT models complete case proportions ranged from 41% to 88%. Complete case analysis and multiple imputation demonstrated similar correct classification results. Sensitivity analysis upper-lower bound ranges for the three MT models were 59-63%, 36-46%, and 46-58%. Prospective collection of ten-fold more variables with data quality assurance reduced overall missing data. Study site and patient survival were associated with missingness, suggesting that data were not missing completely at random, and complete case analysis may lead to biased results. Evaluating clinical prediction model accuracy may be misleading in the presence of missing data, especially with many predictor variables. The proposed sensitivity analysis estimating correct classification under upper (best case scenario)/lower (worst case scenario) bounds may be more informative than multiple imputation, which provided results similar to complete case analysis.^