Statistical issues on studies of mixed longitudinal design

Mixed longitudinal designs are important study designs for many areas of medical research. Mixed longitudinal studies have several advantages over cross-sectional or pure longitudinal studies, including shorter study completion time and ability to separate time and age effects, thus are an attractive choice. Statistical methodology used in general longitudinal studies has been rapidly developing within the last few decades. Common approaches for statistical modeling in studies with mixed longitudinal designs have been the linear mixed-effects model incorporating an age or time effect. The general linear mixed-effects model is considered an appropriate choice to analyze repeated measurements data in longitudinal studies. However, common use of linear mixed-effects model on mixed longitudinal studies often incorporates age as the only random-effect but fails to take into consideration the cohort effect in conducting statistical inferences on age-related trajectories of outcome measurements. We believe special attention should be paid to cohort effects when analyzing data in mixed longitudinal designs with multiple overlapping cohorts. Thus, this has become an important statistical issue to address. ^ This research aims to address statistical issues related to mixed longitudinal studies. The proposed study examined the existing statistical analysis methods for the mixed longitudinal designs and developed an alternative analytic method to incorporate effects from multiple overlapping cohorts as well as from different aged subjects. The proposed study used simulation to evaluate the performance of the proposed analytic method by comparing it with the commonly-used model. Finally, the study applied the proposed analytic method to the data collected by an existing study Project HeartBeat!, which had been evaluated using traditional analytic techniques. Project HeartBeat! is a longitudinal study of cardiovascular disease (CVD) risk factors in childhood and adolescence using a mixed longitudinal design. The proposed model was used to evaluate four blood lipids adjusting for age, gender, race/ethnicity, and endocrine hormones. The result of this dissertation suggest the proposed analytic model could be a more flexible and reliable choice than the traditional model in terms of fitting data to provide more accurate estimates in mixed longitudinal studies. Conceptually, the proposed model described in this study has useful features, including consideration of effects from multiple overlapping cohorts, and is an attractive approach for analyzing data in mixed longitudinal design studies.^

Attitudes of dental students to hand hygiene practices at a dental school

Objectives. The purpose of this study was to elucidate behavioral determinants (prevailing attitudes and beliefs) of hand hygiene practices among undergraduate dental students in a dental school. ^ Methods. Statistical modeling using the Integrative Behavioral Model (IBM) prediction was utilized to develop a questionnaire for evaluating behavioral perceptions of hand hygiene practices by dental school students. Self-report questionnaires were given to second, third and fourth year undergraduate dental students. Models representing two distinct hand hygiene practices, termed "elective in-dental school hand hygiene practice" and "inherent in-dental school hand hygiene practice" were tested using linear regression analysis. ^ Results. 58 responses were received (24.5%); the sample mean age was 26.6 years old and females comprised 51%. In our models, elective in-dental school hand hygiene practice and inherent in-dental school hand hygiene practice, explained 40% and 28%, respectively, of the variance in behavioral intention. Translation of community hand hygiene practice to the dental school setting is the predominant driver of elective hand hygiene practice. Intended elective in-school hand hygiene practice is further significantly predicted by students' self-efficacy. Students' attitudes, peer pressure of other dental students and clinic administrators, and role modeling had minimal effects. Inherent hand hygiene intent was strongly predicted by students' beliefs in the benefits of the activity and, to a lesser extent, role modeling. Inherent and elective community behaviors were insignificant. ^ Conclusions. This study provided significant insights into dental student's hand hygiene behavior and can form the basis for an effective behavioral intervention program designed to improve hand hygiene compliance.^

Evaluating statistical methods used to estimate the number of postsynaptic receptors.

Calcium levels in spines play a significant role in determining the sign and magnitude of synaptic plasticity. The magnitude of calcium influx into spines is highly dependent on influx through N-methyl D-aspartate (NMDA) receptors, and therefore depends on the number of postsynaptic NMDA receptors in each spine. We have calculated previously how the number of postsynaptic NMDA receptors determines the mean and variance of calcium transients in the postsynaptic density, and how this alters the shape of plasticity curves. However, the number of postsynaptic NMDA receptors in the postsynaptic density is not well known. Anatomical methods for estimating the number of NMDA receptors produce estimates that are very different than those produced by physiological techniques. The physiological techniques are based on the statistics of synaptic transmission and it is difficult to experimentally estimate their precision. In this paper we use stochastic simulations in order to test the validity of a physiological estimation technique based on failure analysis. We find that the method is likely to underestimate the number of postsynaptic NMDA receptors, explain the source of the error, and re-derive a more precise estimation technique. We also show that the original failure analysis as well as our improved formulas are not robust to small estimation errors in key parameters.

A full pedigree based method for the statistical assessment of genetic anticipation

Genetic anticipation is defined as a decrease in age of onset or increase in severity as the disorder is transmitted through subsequent generations. Anticipation has been noted in the literature for over a century. Recently, anticipation in several diseases including Huntington's Disease, Myotonic Dystrophy and Fragile X Syndrome were shown to be caused by expansion of triplet repeats. Anticipation effects have also been observed in numerous mental disorders (e.g. Schizophrenia, Bipolar Disorder), cancers (Li-Fraumeni Syndrome, Leukemia) and other complex diseases. ^ Several statistical methods have been applied to determine whether anticipation is a true phenomenon in a particular disorder, including standard statistical tests and newly developed affected parent/affected child pair methods. These methods have been shown to be inappropriate for assessing anticipation for a variety of reasons, including familial correlation and low power. Therefore, we have developed family-based likelihood modeling approaches to model the underlying transmission of the disease gene and penetrance function and hence detect anticipation. These methods can be applied in extended families, thus improving the power to detect anticipation compared with existing methods based only upon parents and children. The first method we have proposed is based on the regressive logistic hazard model. This approach models anticipation by a generational covariate. The second method allows alleles to mutate as they are transmitted from parents to offspring and is appropriate for modeling the known triplet repeat diseases in which the disease alleles can become more deleterious as they are transmitted across generations. ^ To evaluate the new methods, we performed extensive simulation studies for data simulated under different conditions to evaluate the effectiveness of the algorithms to detect genetic anticipation. Results from analysis by the first method yielded empirical power greater than 87% based on the 5% type I error critical value identified in each simulation depending on the method of data generation and current age criteria. Analysis by the second method was not possible due to the current formulation of the software. The application of this method to Huntington's Disease and Li-Fraumeni Syndrome data sets revealed evidence for a generation effect in both cases. ^

Bayesian joint modeling of longitudinal and survival data

The joint modeling of longitudinal and survival data is a new approach to many applications such as HIV, cancer vaccine trials and quality of life studies. There are recent developments of the methodologies with respect to each of the components of the joint model as well as statistical processes that link them together. Among these, second order polynomial random effect models and linear mixed effects models are the most commonly used for the longitudinal trajectory function. In this study, we first relax the parametric constraints for polynomial random effect models by using Dirichlet process priors, then three longitudinal markers rather than only one marker are considered in one joint model. Second, we use a linear mixed effect model for the longitudinal process in a joint model analyzing the three markers. In this research these methods were applied to the Primary Biliary Cirrhosis sequential data, which were collected from a clinical trial of primary biliary cirrhosis (PBC) of the liver. This trial was conducted between 1974 and 1984 at the Mayo Clinic. The effects of three longitudinal markers (1) Total Serum Bilirubin, (2) Serum Albumin and (3) Serum Glutamic-Oxaloacetic transaminase (SGOT) on patients' survival were investigated. Proportion of treatment effect will also be studied using the proposed joint modeling approaches. ^ Based on the results, we conclude that the proposed modeling approaches yield better fit to the data and give less biased parameter estimates for these trajectory functions than previous methods. Model fit is also improved after considering three longitudinal markers instead of one marker only. The results from analysis of proportion of treatment effects from these joint models indicate same conclusion as that from the final model of Fleming and Harrington (1991), which is Bilirubin and Albumin together has stronger impact in predicting patients' survival and as a surrogate endpoints for treatment. ^

Fluorophotometry is a sensitive method/technique to evaluate epithelial permeability in murine experimental dry eye

Purpose. Fluorophotometry is a well validated method for assessing corneal permeability in human subjects. However, with the growing importance of basic science animal research in ophthalmology, fluorophotometry’s use in animals must be further evaluated. The purpose of this study was to evaluate corneal epithelial permeability following desiccating stress using the modified Fluorotron Master™. ^ Methods. Corneal permeability was evaluated prior to and after subjecting 6-8 week old C57BL/6 mice to experimental dry eye (EDE) for 2 and 5 days (n=9/time point). Untreated mice served as controls. Ten microliters of 0.001% sodium fluorescein (NaF) were instilled topically into each mouse’s left eye to create an eye bath, and left to permeate for 3 minutes. The eye bath was followed by a generous wash with Buffered Saline Solution (BSS) and alignment with the Fluorotron Master™. Seven corneal scans using the Fluorotron Master were performed during 15 minutes (1 st post-wash scans), followed by a second wash using BSS and another set of five corneal scans (2nd post-wash scans) during the next 15 minutes. Corneal permeability was calculated using data calculated with the FM™ Mouse software. ^ Results. When comparing the difference between the Post wash #1 scans within the group and the Post wash #2 scans within the group using a repeated measurement design, there was a statistical difference in the corneal fluorescein permeability of the Post-wash #1 scans after 5 days (1160.21±108.26 vs. 1000.47±75.56 ng/mL, P<0.016 for UT-5 day comparison 8 [0.008]), but not after only 2 days of EDE compared to Untreated mice (1115.64±118.94 vs. 1000.47±75.56 ng/mL, P>0.016 for UT-2 day comparison [0.050]). There was no statistical difference between the 2 day and 5 day Post wash #1 scans (P=.299). The Post-wash #2 scans demonstrated that EDE caused a significant NaF retention at both 2 and 5 days of EDE compared to baseline, untreated controls (1017.92±116.25, 1015.40±120.68 vs. 528.22±127.85 ng/mL, P<0.05 [0.0001 for both]). There was no statistical difference between the 2 day and 5 day Post wash #2 scans (P=.503). The comparison between the Untreated post wash #1 with untreated post wash #2 scans using a Paired T-test showed a significant difference between the two sets of scans (P=0.000). There is also a significant difference between the 2 day comparison and the 5 day comparison (P values = 0.010 and 0.002, respectively). ^ Conclusion. Desiccating stress increases permeability of the corneal epithelium to NaF, and increases NaF retention in the corneal stroma. The Fluorotron Master is a useful and sensitive tool to evaluate corneal permeability in murine dry eye, and will be a useful tool to evaluate the effectiveness of dry eye treatments in animal-model drug trials.^

The information bottleneck method for genome-wide association studies

In population studies, most current methods focus on identifying one outcome-related SNP at a time by testing for differences of genotype frequencies between disease and healthy groups or among different population groups. However, testing a great number of SNPs simultaneously has a problem of multiple testing and will give false-positive results. Although, this problem can be effectively dealt with through several approaches such as Bonferroni correction, permutation testing and false discovery rates, patterns of the joint effects by several genes, each with weak effect, might not be able to be determined. With the availability of high-throughput genotyping technology, searching for multiple scattered SNPs over the whole genome and modeling their joint effect on the target variable has become possible. Exhaustive search of all SNP subsets is computationally infeasible for millions of SNPs in a genome-wide study. Several effective feature selection methods combined with classification functions have been proposed to search for an optimal SNP subset among big data sets where the number of feature SNPs far exceeds the number of observations. ^ In this study, we take two steps to achieve the goal. First we selected 1000 SNPs through an effective filter method and then we performed a feature selection wrapped around a classifier to identify an optimal SNP subset for predicting disease. And also we developed a novel classification method-sequential information bottleneck method wrapped inside different search algorithms to identify an optimal subset of SNPs for classifying the outcome variable. This new method was compared with the classical linear discriminant analysis in terms of classification performance. Finally, we performed chi-square test to look at the relationship between each SNP and disease from another point of view. ^ In general, our results show that filtering features using harmononic mean of sensitivity and specificity(HMSS) through linear discriminant analysis (LDA) is better than using LDA training accuracy or mutual information in our study. Our results also demonstrate that exhaustive search of a small subset with one SNP, two SNPs or 3 SNP subset based on best 100 composite 2-SNPs can find an optimal subset and further inclusion of more SNPs through heuristic algorithm doesn't always increase the performance of SNP subsets. Although sequential forward floating selection can be applied to prevent from the nesting effect of forward selection, it does not always out-perform the latter due to overfitting from observing more complex subset states. ^ Our results also indicate that HMSS as a criterion to evaluate the classification ability of a function can be used in imbalanced data without modifying the original dataset as against classification accuracy. Our four studies suggest that Sequential Information Bottleneck(sIB), a new unsupervised technique, can be adopted to predict the outcome and its ability to detect the target status is superior to the traditional LDA in the study. ^ From our results we can see that the best test probability-HMSS for predicting CVD, stroke,CAD and psoriasis through sIB is 0.59406, 0.641815, 0.645315 and 0.678658, respectively. In terms of group prediction accuracy, the highest test accuracy of sIB for diagnosing a normal status among controls can reach 0.708999, 0.863216, 0.639918 and 0.850275 respectively in the four studies if the test accuracy among cases is required to be not less than 0.4. On the other hand, the highest test accuracy of sIB for diagnosing a disease among cases can reach 0.748644, 0.789916, 0.705701 and 0.749436 respectively in the four studies if the test accuracy among controls is required to be at least 0.4. ^ A further genome-wide association study through Chi square test shows that there are no significant SNPs detected at the cut-off level 9.09451E-08 in the Framingham heart study of CVD. Study results in WTCCC can only detect two significant SNPs that are associated with CAD. In the genome-wide study of psoriasis most of top 20 SNP markers with impressive classification accuracy are also significantly associated with the disease through chi-square test at the cut-off value 1.11E-07. ^ Although our classification methods can achieve high accuracy in the study, complete descriptions of those classification results(95% confidence interval or statistical test of differences) require more cost-effective methods or efficient computing system, both of which can't be accomplished currently in our genome-wide study. We should also note that the purpose of this study is to identify subsets of SNPs with high prediction ability and those SNPs with good discriminant power are not necessary to be causal markers for the disease.^

A STUDY OF INFLUENZA AND OF STATISTICAL METHODS USED TO REPORT INFLUENZA

This paper defines and compares several models for describing excess influenza pneumonia mortality in Houston. First, the methodology used by the Center for Disease Control is examined and several variations of this methodology are studied. All of the models examined emphasize the difficulty of omitting epidemic weeks.^ In an attempt to find a better method of describing expected and epidemic mortality, time series methods are examined. Grouping in four-week periods, truncating the data series to adjust epidemic periods, and seasonally-adjusting the series y(,t), by:^ (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)^ is the best method examined. This new series w(,t) is stationary and a moving average model MA(1) gives a good fit for forecasting influenza and pneumonia mortality in Houston.^ Influenza morbidity, other causes of death, sex, race, age, climate variables, environmental factors, and school absenteeism are all examined in terms of their relationship to influenza and pneumonia mortality. Both influenza morbidity and ischemic heart disease mortality show a very high relationship that remains when seasonal trends are removed from the data. However, when jointly modeling the three series it is obvious that the simple time series MA(1) model of truncated, seasonally-adjusted four-week data gives a better forecast.^

TIME SERIES ANALYSIS AS INPUT FOR PREDICTIVE MODELING: PREDICTING CARDIAC ARREST IN A PEDIATRIC INTENSIVE CARE UNIT

The first manuscript, entitled "Time-Series Analysis as Input for Clinical Predictive Modeling: Modeling Cardiac Arrest in a Pediatric ICU" lays out the theoretical background for the project. There are several core concepts presented in this paper. First, traditional multivariate models (where each variable is represented by only one value) provide single point-in-time snapshots of patient status: they are incapable of characterizing deterioration. Since deterioration is consistently identified as a precursor to cardiac arrests, we maintain that the traditional multivariate paradigm is insufficient for predicting arrests. We identify time series analysis as a method capable of characterizing deterioration in an objective, mathematical fashion, and describe how to build a general foundation for predictive modeling using time series analysis results as latent variables. Building a solid foundation for any given modeling task involves addressing a number of issues during the design phase. These include selecting the proper candidate features on which to base the model, and selecting the most appropriate tool to measure them. We also identified several unique design issues that are introduced when time series data elements are added to the set of candidate features. One such issue is in defining the duration and resolution of time series elements required to sufficiently characterize the time series phenomena being considered as candidate features for the predictive model. Once the duration and resolution are established, there must also be explicit mathematical or statistical operations that produce the time series analysis result to be used as a latent candidate feature. In synthesizing the comprehensive framework for building a predictive model based on time series data elements, we identified at least four classes of data that can be used in the model design. The first two classes are shared with traditional multivariate models: multivariate data and clinical latent features. Multivariate data is represented by the standard one value per variable paradigm and is widely employed in a host of clinical models and tools. These are often represented by a number present in a given cell of a table. Clinical latent features derived, rather than directly measured, data elements that more accurately represent a particular clinical phenomenon than any of the directly measured data elements in isolation. The second two classes are unique to the time series data elements. The first of these is the raw data elements. These are represented by multiple values per variable, and constitute the measured observations that are typically available to end users when they review time series data. These are often represented as dots on a graph. The final class of data results from performing time series analysis. This class of data represents the fundamental concept on which our hypothesis is based. The specific statistical or mathematical operations are up to the modeler to determine, but we generally recommend that a variety of analyses be performed in order to maximize the likelihood that a representation of the time series data elements is produced that is able to distinguish between two or more classes of outcomes. The second manuscript, entitled "Building Clinical Prediction Models Using Time Series Data: Modeling Cardiac Arrest in a Pediatric ICU" provides a detailed description, start to finish, of the methods required to prepare the data, build, and validate a predictive model that uses the time series data elements determined in the first paper. One of the fundamental tenets of the second paper is that manual implementations of time series based models are unfeasible due to the relatively large number of data elements and the complexity of preprocessing that must occur before data can be presented to the model. Each of the seventeen steps is analyzed from the perspective of how it may be automated, when necessary. We identify the general objectives and available strategies of each of the steps, and we present our rationale for choosing a specific strategy for each step in the case of predicting cardiac arrest in a pediatric intensive care unit. Another issue brought to light by the second paper is that the individual steps required to use time series data for predictive modeling are more numerous and more complex than those used for modeling with traditional multivariate data. Even after complexities attributable to the design phase (addressed in our first paper) have been accounted for, the management and manipulation of the time series elements (the preprocessing steps in particular) are issues that are not present in a traditional multivariate modeling paradigm. In our methods, we present the issues that arise from the time series data elements: defining a reference time; imputing and reducing time series data in order to conform to a predefined structure that was specified during the design phase; and normalizing variable families rather than individual variable instances. The final manuscript, entitled: "Using Time-Series Analysis to Predict Cardiac Arrest in a Pediatric Intensive Care Unit" presents the results that were obtained by applying the theoretical construct and its associated methods (detailed in the first two papers) to the case of cardiac arrest prediction in a pediatric intensive care unit. Our results showed that utilizing the trend analysis from the time series data elements reduced the number of classification errors by 73%. The area under the Receiver Operating Characteristic curve increased from a baseline of 87% to 98% by including the trend analysis. In addition to the performance measures, we were also able to demonstrate that adding raw time series data elements without their associated trend analyses improved classification accuracy as compared to the baseline multivariate model, but diminished classification accuracy as compared to when just the trend analysis features were added (ie, without adding the raw time series data elements). We believe this phenomenon was largely attributable to overfitting, which is known to increase as the ratio of candidate features to class examples rises. Furthermore, although we employed several feature reduction strategies to counteract the overfitting problem, they failed to improve the performance beyond that which was achieved by exclusion of the raw time series elements. Finally, our data demonstrated that pulse oximetry and systolic blood pressure readings tend to start diminishing about 10-20 minutes before an arrest, whereas heart rates tend to diminish rapidly less than 5 minutes before an arrest.

Modeling Techniques for the High-Resolution Interpretation of Cryo-Electron Microscopy Reconstructions

Essential biological processes are governed by organized, dynamic interactions between multiple biomolecular systems. Complexes are thus formed to enable the biological function and get dissembled as the process is completed. Examples of such processes include the translation of the messenger RNA into protein by the ribosome, the folding of proteins by chaperonins or the entry of viruses in host cells. Understanding these fundamental processes by characterizing the molecular mechanisms that enable then, would allow the (better) design of therapies and drugs. Such molecular mechanisms may be revealed trough the structural elucidation of the biomolecular assemblies at the core of these processes. Various experimental techniques may be applied to investigate the molecular architecture of biomolecular assemblies. High-resolution techniques, such as X-ray crystallography, may solve the atomic structure of the system, but are typically constrained to biomolecules of reduced flexibility and dimensions. In particular, X-ray crystallography requires the sample to form a three dimensional (3D) crystal lattice which is technically di‑cult, if not impossible, to obtain, especially for large, dynamic systems. Often these techniques solve the structure of the different constituent components within the assembly, but encounter difficulties when investigating the entire system. On the other hand, imaging techniques, such as cryo-electron microscopy (cryo-EM), are able to depict large systems in near-native environment, without requiring the formation of crystals. The structures solved by cryo-EM cover a wide range of resolutions, from very low level of detail where only the overall shape of the system is visible, to high-resolution that approach, but not yet reach, atomic level of detail. In this dissertation, several modeling methods are introduced to either integrate cryo-EM datasets with structural data from X-ray crystallography, or to directly interpret the cryo-EM reconstruction. Such computational techniques were developed with the goal of creating an atomic model for the cryo-EM data. The low-resolution reconstructions lack the level of detail to permit a direct atomic interpretation, i.e. one cannot reliably locate the atoms or amino-acid residues within the structure obtained by cryo-EM. Thereby one needs to consider additional information, for example, structural data from other sources such as X-ray crystallography, in order to enable such a high-resolution interpretation. Modeling techniques are thus developed to integrate the structural data from the different biophysical sources, examples including the work described in the manuscript I and II of this dissertation. At intermediate and high-resolution, cryo-EM reconstructions depict consistent 3D folds such as tubular features which in general correspond to alpha-helices. Such features can be annotated and later on used to build the atomic model of the system, see manuscript III as alternative. Three manuscripts are presented as part of the PhD dissertation, each introducing a computational technique that facilitates the interpretation of cryo-EM reconstructions. The first manuscript is an application paper that describes a heuristics to generate the atomic model for the protein envelope of the Rift Valley fever virus. The second manuscript introduces the evolutionary tabu search strategies to enable the integration of multiple component atomic structures with the cryo-EM map of their assembly. Finally, the third manuscript develops further the latter technique and apply it to annotate consistent 3D patterns in intermediate-resolution cryo-EM reconstructions. The first manuscript, titled An assembly model for Rift Valley fever virus, was submitted for publication in the Journal of Molecular Biology. The cryo-EM structure of the Rift Valley fever virus was previously solved at 27Å-resolution by Dr. Freiberg and collaborators. Such reconstruction shows the overall shape of the virus envelope, yet the reduced level of detail prevents the direct atomic interpretation. High-resolution structures are not yet available for the entire virus nor for the two different component glycoproteins that form its envelope. However, homology models may be generated for these glycoproteins based on similar structures that are available at atomic resolutions. The manuscript presents the steps required to identify an atomic model of the entire virus envelope, based on the low-resolution cryo-EM map of the envelope and the homology models of the two glycoproteins. Starting with the results of the exhaustive search to place the two glycoproteins, the model is built iterative by running multiple multi-body refinements to hierarchically generate models for the different regions of the envelope. The generated atomic model is supported by prior knowledge regarding virus biology and contains valuable information about the molecular architecture of the system. It provides the basis for further investigations seeking to reveal different processes in which the virus is involved such as assembly or fusion. The second manuscript was recently published in the of Journal of Structural Biology (doi:10.1016/j.jsb.2009.12.028) under the title Evolutionary tabu search strategies for the simultaneous registration of multiple atomic structures in cryo-EM reconstructions. This manuscript introduces the evolutionary tabu search strategies applied to enable a multi-body registration. This technique is a hybrid approach that combines a genetic algorithm with a tabu search strategy to promote the proper exploration of the high-dimensional search space. Similar to the Rift Valley fever virus, it is common that the structure of a large multi-component assembly is available at low-resolution from cryo-EM, while high-resolution structures are solved for the different components but lack for the entire system. Evolutionary tabu search strategies enable the building of an atomic model for the entire system by considering simultaneously the different components. Such registration indirectly introduces spatial constrains as all components need to be placed within the assembly, enabling the proper docked in the low-resolution map of the entire assembly. Along with the method description, the manuscript covers the validation, presenting the benefit of the technique in both synthetic and experimental test cases. Such approach successfully docked multiple components up to resolutions of 40Å. The third manuscript is entitled Evolutionary Bidirectional Expansion for the Annotation of Alpha Helices in Electron Cryo-Microscopy Reconstructions and was submitted for publication in the Journal of Structural Biology. The modeling approach described in this manuscript applies the evolutionary tabu search strategies in combination with the bidirectional expansion to annotate secondary structure elements in intermediate resolution cryo-EM reconstructions. In particular, secondary structure elements such as alpha helices show consistent patterns in cryo-EM data, and are visible as rod-like patterns of high density. The evolutionary tabu search strategy is applied to identify the placement of the different alpha helices, while the bidirectional expansion characterizes their length and curvature. The manuscript presents the validation of the approach at resolutions ranging between 6 and 14Å, a level of detail where alpha helices are visible. Up to resolution of 12 Å, the method measures sensitivities between 70-100% as estimated in experimental test cases, i.e. 70-100% of the alpha-helices were correctly predicted in an automatic manner in the experimental data. The three manuscripts presented in this PhD dissertation cover different computation methods for the integration and interpretation of cryo-EM reconstructions. The methods were developed in the molecular modeling software Sculptor (http://sculptor.biomachina.org) and are available for the scientific community interested in the multi-resolution modeling of cryo-EM data. The work spans a wide range of resolution covering multi-body refinement and registration at low-resolution along with annotation of consistent patterns at high-resolution. Such methods are essential for the modeling of cryo-EM data, and may be applied in other fields where similar spatial problems are encountered, such as medical imaging.

THE NATURAL AND ORTHOGONAL INTERACTION (NOIA) MODELS FOR QUANTITATIVE TRAITS (QTs) AND COMPLEX DISEASES

My dissertation focuses on developing methods for gene-gene/environment interactions and imprinting effect detections for human complex diseases and quantitative traits. It includes three sections: (1) generalizing the Natural and Orthogonal interaction (NOIA) model for the coding technique originally developed for gene-gene (GxG) interaction and also to reduced models; (2) developing a novel statistical approach that allows for modeling gene-environment (GxE) interactions influencing disease risk, and (3) developing a statistical approach for modeling genetic variants displaying parent-of-origin effects (POEs), such as imprinting. In the past decade, genetic researchers have identified a large number of causal variants for human genetic diseases and traits by single-locus analysis, and interaction has now become a hot topic in the effort to search for the complex network between multiple genes or environmental exposures contributing to the outcome. Epistasis, also known as gene-gene interaction is the departure from additive genetic effects from several genes to a trait, which means that the same alleles of one gene could display different genetic effects under different genetic backgrounds. In this study, we propose to implement the NOIA model for association studies along with interaction for human complex traits and diseases. We compare the performance of the new statistical models we developed and the usual functional model by both simulation study and real data analysis. Both simulation and real data analysis revealed higher power of the NOIA GxG interaction model for detecting both main genetic effects and interaction effects. Through application on a melanoma dataset, we confirmed the previously identified significant regions for melanoma risk at 15q13.1, 16q24.3 and 9p21.3. We also identified potential interactions with these significant regions that contribute to melanoma risk. Based on the NOIA model, we developed a novel statistical approach that allows us to model effects from a genetic factor and binary environmental exposure that are jointly influencing disease risk. Both simulation and real data analyses revealed higher power of the NOIA model for detecting both main genetic effects and interaction effects for both quantitative and binary traits. We also found that estimates of the parameters from logistic regression for binary traits are no longer statistically uncorrelated under the alternative model when there is an association. Applying our novel approach to a lung cancer dataset, we confirmed four SNPs in 5p15 and 15q25 region to be significantly associated with lung cancer risk in Caucasians population: rs2736100, rs402710, rs16969968 and rs8034191. We also validated that rs16969968 and rs8034191 in 15q25 region are significantly interacting with smoking in Caucasian population. Our approach identified the potential interactions of SNP rs2256543 in 6p21 with smoking on contributing to lung cancer risk. Genetic imprinting is the most well-known cause for parent-of-origin effect (POE) whereby a gene is differentially expressed depending on the parental origin of the same alleles. Genetic imprinting affects several human disorders, including diabetes, breast cancer, alcoholism, and obesity. This phenomenon has been shown to be important for normal embryonic development in mammals. Traditional association approaches ignore this important genetic phenomenon. In this study, we propose a NOIA framework for a single locus association study that estimates both main allelic effects and POEs. We develop statistical (Stat-POE) and functional (Func-POE) models, and demonstrate conditions for orthogonality of the Stat-POE model. We conducted simulations for both quantitative and qualitative traits to evaluate the performance of the statistical and functional models with different levels of POEs. Our results showed that the newly proposed Stat-POE model, which ensures orthogonality of variance components if Hardy-Weinberg Equilibrium (HWE) or equal minor and major allele frequencies is satisfied, had greater power for detecting the main allelic additive effect than a Func-POE model, which codes according to allelic substitutions, for both quantitative and qualitative traits. The power for detecting the POE was the same for the Stat-POE and Func-POE models under HWE for quantitative traits.

BAYESIAN STATISTICAL METHODS IN GENE-ENVIRONMENT AND GENE-GENE INTERACTION STUDIES

Complex diseases such as cancer result from multiple genetic changes and environmental exposures. Due to the rapid development of genotyping and sequencing technologies, we are now able to more accurately assess causal effects of many genetic and environmental factors. Genome-wide association studies have been able to localize many causal genetic variants predisposing to certain diseases. However, these studies only explain a small portion of variations in the heritability of diseases. More advanced statistical models are urgently needed to identify and characterize some additional genetic and environmental factors and their interactions, which will enable us to better understand the causes of complex diseases. In the past decade, thanks to the increasing computational capabilities and novel statistical developments, Bayesian methods have been widely applied in the genetics/genomics researches and demonstrating superiority over some regular approaches in certain research areas. Gene-environment and gene-gene interaction studies are among the areas where Bayesian methods may fully exert its functionalities and advantages. This dissertation focuses on developing new Bayesian statistical methods for data analysis with complex gene-environment and gene-gene interactions, as well as extending some existing methods for gene-environment interactions to other related areas. It includes three sections: (1) Deriving the Bayesian variable selection framework for the hierarchical gene-environment and gene-gene interactions; (2) Developing the Bayesian Natural and Orthogonal Interaction (NOIA) models for gene-environment interactions; and (3) extending the applications of two Bayesian statistical methods which were developed for gene-environment interaction studies, to other related types of studies such as adaptive borrowing historical data. We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions (epistasis) and gene by environment interactions in the same model. It is well known that, in many practical situations, there exists a natural hierarchical structure between the main effects and interactions in the linear model. Here we propose a model that incorporates this hierarchical structure into the Bayesian mixture model, such that the irrelevant interaction effects can be removed more efficiently, resulting in more robust, parsimonious and powerful models. We evaluate both of the 'strong hierarchical' and 'weak hierarchical' models, which specify that both or one of the main effects between interacting factors must be present for the interactions to be included in the model. The extensive simulation results show that the proposed strong and weak hierarchical mixture models control the proportion of false positive discoveries and yield a powerful approach to identify the predisposing main effects and interactions in the studies with complex gene-environment and gene-gene interactions. We also compare these two models with the 'independent' model that does not impose this hierarchical constraint and observe their superior performances in most of the considered situations. The proposed models are implemented in the real data analysis of gene and environment interactions in the cases of lung cancer and cutaneous melanoma case-control studies. The Bayesian statistical models enjoy the properties of being allowed to incorporate useful prior information in the modeling process. Moreover, the Bayesian mixture model outperforms the multivariate logistic model in terms of the performances on the parameter estimation and variable selection in most cases. Our proposed models hold the hierarchical constraints, that further improve the Bayesian mixture model by reducing the proportion of false positive findings among the identified interactions and successfully identifying the reported associations. This is practically appealing for the study of investigating the causal factors from a moderate number of candidate genetic and environmental factors along with a relatively large number of interactions. The natural and orthogonal interaction (NOIA) models of genetic effects have previously been developed to provide an analysis framework, by which the estimates of effects for a quantitative trait are statistically orthogonal regardless of the existence of Hardy-Weinberg Equilibrium (HWE) within loci. Ma et al. (2012) recently developed a NOIA model for the gene-environment interaction studies and have shown the advantages of using the model for detecting the true main effects and interactions, compared with the usual functional model. In this project, we propose a novel Bayesian statistical model that combines the Bayesian hierarchical mixture model with the NOIA statistical model and the usual functional model. The proposed Bayesian NOIA model demonstrates more power at detecting the non-null effects with higher marginal posterior probabilities. Also, we review two Bayesian statistical models (Bayesian empirical shrinkage-type estimator and Bayesian model averaging), which were developed for the gene-environment interaction studies. Inspired by these Bayesian models, we develop two novel statistical methods that are able to handle the related problems such as borrowing data from historical studies. The proposed methods are analogous to the methods for the gene-environment interactions on behalf of the success on balancing the statistical efficiency and bias in a unified model. By extensive simulation studies, we compare the operating characteristics of the proposed models with the existing models including the hierarchical meta-analysis model. The results show that the proposed approaches adaptively borrow the historical data in a data-driven way. These novel models may have a broad range of statistical applications in both of genetic/genomic and clinical studies.