A novel method for evaluating an interaction effect of correlated continuous covariates in a linear model

Interaction effect is an important scientific interest for many areas of research. Common approach for investigating the interaction effect of two continuous covariates on a response variable is through a cross-product term in multiple linear regression. In epidemiological studies, the two-way analysis of variance (ANOVA) type of method has also been utilized to examine the interaction effect by replacing the continuous covariates with their discretized levels. However, the implications of model assumptions of either approach have not been examined and the statistical validation has only focused on the general method, not specifically for the interaction effect.^ In this dissertation, we investigated the validity of both approaches based on the mathematical assumptions for non-skewed data. We showed that linear regression may not be an appropriate model when the interaction effect exists because it implies a highly skewed distribution for the response variable. We also showed that the normality and constant variance assumptions required by ANOVA are not satisfied in the model where the continuous covariates are replaced with their discretized levels. Therefore, naïve application of ANOVA method may lead to an incorrect conclusion. ^ Given the problems identified above, we proposed a novel method modifying from the traditional ANOVA approach to rigorously evaluate the interaction effect. The analytical expression of the interaction effect was derived based on the conditional distribution of the response variable given the discretized continuous covariates. A testing procedure that combines the p-values from each level of the discretized covariates was developed to test the overall significance of the interaction effect. According to the simulation study, the proposed method is more powerful then the least squares regression and the ANOVA method in detecting the interaction effect when data comes from a trivariate normal distribution. The proposed method was applied to a dataset from the National Institute of Neurological Disorders and Stroke (NINDS) tissue plasminogen activator (t-PA) stroke trial, and baseline age-by-weight interaction effect was found significant in predicting the change from baseline in NIHSS at Month-3 among patients received t-PA therapy.^

A multiplicative model for standardizing vital rates without using external standards

Standardization is a common method for adjusting confounding factors when comparing two or more exposure category to assess excess risk. Arbitrary choice of standard population in standardization introduces selection bias due to healthy worker effect. Small sample in specific groups also poses problems in estimating relative risk and the statistical significance is problematic. As an alternative, statistical models were proposed to overcome such limitations and find adjusted rates. In this dissertation, a multiplicative model is considered to address the issues related to standardized index namely: Standardized Mortality Ratio (SMR) and Comparative Mortality Factor (CMF). The model provides an alternative to conventional standardized technique. Maximum likelihood estimates of parameters of the model are used to construct an index similar to the SMR for estimating relative risk of exposure groups under comparison. Parametric Bootstrap resampling method is used to evaluate the goodness of fit of the model, behavior of estimated parameters and variability in relative risk on generated sample. The model provides an alternative to both direct and indirect standardization method. ^

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.^

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.^

Bayesian estimation of multilevel item response model with missing data

This study proposed a novel statistical method that modeled the multiple outcomes and missing data process jointly using item response theory. This method follows the "intent-to-treat" principle in clinical trials and accounts for the correlation between outcomes and missing data process. This method may provide a good solution to chronic mental disorder study. ^ The simulation study demonstrated that if the true model is the proposed model with moderate or strong correlation, ignoring the within correlation may lead to overestimate of the treatment effect and result in more type I error than specified level. Even if the within correlation is small, the performance of proposed model is as good as naïve response model. Thus, the proposed model is robust for different correlation settings if the data is generated by the proposed model.^

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.^

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.

Robust effect sizes and their confidence intervals for group difference between trajectories in hierarchical linear growth model

Hierarchical linear growth model (HLGM), as a flexible and powerful analytic method, has played an increased important role in psychology, public health and medical sciences in recent decades. Mostly, researchers who conduct HLGM are interested in the treatment effect on individual trajectories, which can be indicated by the cross-level interaction effects. However, the statistical hypothesis test for the effect of cross-level interaction in HLGM only show us whether there is a significant group difference in the average rate of change, rate of acceleration or higher polynomial effect; it fails to convey information about the magnitude of the difference between the group trajectories at specific time point. Thus, reporting and interpreting effect sizes have been increased emphases in HLGM in recent years, due to the limitations and increased criticisms for statistical hypothesis testing. However, most researchers fail to report these model-implied effect sizes for group trajectories comparison and their corresponding confidence intervals in HLGM analysis, since lack of appropriate and standard functions to estimate effect sizes associated with the model-implied difference between grouping trajectories in HLGM, and also lack of computing packages in the popular statistical software to automatically calculate them. ^ The present project is the first to establish the appropriate computing functions to assess the standard difference between grouping trajectories in HLGM. We proposed the two functions to estimate effect sizes on model-based grouping trajectories difference at specific time, we also suggested the robust effect sizes to reduce the bias of estimated effect sizes. Then, we applied the proposed functions to estimate the population effect sizes (d ) and robust effect sizes (du) on the cross-level interaction in HLGM by using the three simulated datasets, and also we compared the three methods of constructing confidence intervals around d and du recommended the best one for application. At the end, we constructed 95% confidence intervals with the suitable method for the effect sizes what we obtained with the three simulated datasets. ^ The effect sizes between grouping trajectories for the three simulated longitudinal datasets indicated that even though the statistical hypothesis test shows no significant difference between grouping trajectories, effect sizes between these grouping trajectories can still be large at some time points. Therefore, effect sizes between grouping trajectories in HLGM analysis provide us additional and meaningful information to assess group effect on individual trajectories. In addition, we also compared the three methods to construct 95% confident intervals around corresponding effect sizes in this project, which handled with the uncertainty of effect sizes to population parameter. We suggested the noncentral t-distribution based method when the assumptions held, and the bootstrap bias-corrected and accelerated method when the assumptions are not met.^

Behavioral decision making and the levels of change: An application of the transtheoretical model to prenatal smoking in low -income women

Despite continued research and public health efforts to reduce smoking during pregnancy, prenatal cessation rates in the United States have decreased and the incidence of low birth weight has increased from 1985 to 1991. Lower socioeconomic status women who are at increased risk for poor pregnancy outcomes may be resistant to current intervention efforts during pregnancy. The purpose of this dissertation was to investigate the determinants of continued smoking and quitting among low-income pregnant women.^ Using data from cross-sectional surveys of 323 low-income pregnant smokers, the first study developed and tested measures of the pros and cons of smoking during pregnancy. The original decisional balance measure for smoking was compared with a new measure that added items thought to be more salient to the target population. Confirmatory factor analysis using structural equation modeling showed neither the original nor new measure fit the data adequately. Using behavioral science theory, content from interviews with the population, and statistical evidence, two 7-item scales representing the pros and cons were developed from a portion (n = 215) of the sample and successfully cross-validated on the remainder of the sample (n = 108). Logistic regression found only pros were significantly associated with continued smoking. In a discriminant function analysis, stage of change was significantly associated with pros and cons of smoking.^ The second study examined the structural relationships between psychosocial constructs representing some of the levels of and the pros and cons of smoking. The cross-sectional design mandates that statements made regarding prediction do not prove causation or directionality from the data or methods analysis. Structural equation modeling found the following: more stressors and family criticism were significantly more predictive of negative affect than social support; a bi-directional relationship was found between negative affect and current nicotine addiction; and negative affect, addiction, stressors, and family criticism were significant predictors of pros of smoking.^ The findings imply reversing the trend of decreasing smoking cessation during pregnancy may require supplementing current interventions for this population of pregnant smokers with programs addressing nicotine addiction, negative affect, and other psychosocial factors such as family functioning and stressors. ^

Improving care of women at risk of unsafe abortion: implementing a risk-reduction model at the Uruguayan-Brazilian border

OBJECTIVE: To describe the initial stages of the implementation of a risk-reduction model designed by Iniciativas Sanitarias to shield women from unsafe abortion in a traditional community on the Uruguay-Brazil border. METHODS: This mixed-design study was conducted first between 22 and 26 March 2010, and then between 2 and 7 May 2011, in Rivera, Uruguay, to gather information from women seen at health centers, healthcare providers, and local policy makers before the project started and midway through the project. RESULTS: At baseline most women and providers considered abortion justifiable only on narrow grounds, yet favored the implementation of a risk-reduction model that would include preabortion as well as postabortion counseling, the former providing information on different abortion methods and their risks. By the midterm assessment, the counseling service had assisted 87 women with unwanted pregnancies. Of the 52 who came for a postabortion visit, 50 had self-administered misoprostol, with no complications. Women were highly satisfied with the counseling. At baseline, misoprostol seemed to be available from both pharmacists and informal sellers. At midterm, it was still available from informal vendors but pharmacists said they did not provide misoprostol. The risk-reduction initiative heightened public attention to the abortion issue but the controversy it generated did not seriously impede its implementation. CONCLUSION: It is feasible to implement the proposed risk-reduction model in a traditional community such as Rivera, not only in Uruguay but in any country irrespective of its abortion laws.

ODP Site 162-980 age model and color reflectance record of sediments from ODP Leg 162 sites

Sediment spectral reflectance measurements were generated aboard the JOIDES Resolution during Ocean Drilling Program Leg 162 shipboard operations. The large size of the raw data set (over 1.3 gigabytes) and limited computer hard disk storage space precluded detailed analysis of the data at sea, although broad band averages were used as aids in developing splices and determining lithologic boundaries. This data report describes the methods used to collect these data and their shipboard and postcruise processing. These initial results provide the basis for further postcruise research.

Age model and Plio-Pleistocene benthic stable oxygen isotope ratios of ODP Site 184-1143 in the Sourh China Sea

Based on benthic foraminiferal delta18O from ODP Site 1143, a 5-Myr astronomical timescale for the West Pacific Plio-Pleistocene was established using an automatic orbital tuning method. The tuned Brunhes/Matuyama paleomagnetic polarity reversal age agrees well with the previously published age of 0.78 Ma. The tuned ages for several planktonic foraminifer bio-events also agree well with published dates, and new ages for some other bio-events in the South China Sea were also estimated. The benthic delta18O from Site 1143 is highly coherent with the Earth's orbit (ETP) both at the obliquity and precession bands for the last 5 Myr, and at the eccentricity band for the last 2 Myr. In general, the 41-kyr cycle was dominant through the Plio-Pleistocene although the 23-kyr cycle was also very strong. The 100-kyr cycle became dominant only during the last 1 Myr. A comparison of the benthic delta18O between the Atlantic (ODP 659) and the East and West Pacific (846 and 1143) reveals that the Atlantic-Pacific benthic oxygen isotope difference ratio (Delta delta18OAtl-Pac) displays an increasing trend in three time intervals: 3.6-2.7 Ma, 2.7-2.1 Ma and 1.5-0.25 Ma. Each of the intervals begins with a rapid negative shift in Delta delta18OAtl-Pac, followed by a long period with an increasing trend, corresponding to the growth of the Northern Hemisphere ice sheet. This means that all three intervals of ice sheet growth in the Northern Hemisphere were accompanied at the beginning by a rapid relative warming of deep water in the Atlantic as compared to that of the Pacific, followed by its gradual relative cooling. This general trend, superimposed on the frequent fluctuations with glacial cycles, should yield insights into the processes leading to the boreal glaciation. Cross-spectral analyses of the Delta delta18OAtl-Pac with the Earth's orbit suggests that after the initiation of Northern Hemisphere glaciation at about 2.5 Ma, obliquity rather than precession had become the dominant force controlling the vertical structure or thermohaline circulation in the paleo-ocean.

Age model, stable isotopes, major element proportions and endmember unmixing results from four western tropical Atlantic cores

We investigate changes in the delivery and oceanic transport of Amazon sediments related to terrestrial climate variations over the last 250 ka. We present high-resolution geochemical records from four marine sediment cores located between 5 and 12° N along the northern South American margin. The Amazon River is the sole source of terrigenous material for sites at 5 and 9° N, while the core at 12° N receives a mixture of Amazon and Orinoco detrital particles. Using an endmember unmixing model, we estimated the relative proportions of Amazon Andean material ("%-Andes", at 5 and 9° N) and of Amazon material ("%-Amazon", at 12° N) within the terrigenous fraction. The %-Andes and %-Amazon records exhibit significant precessional variations over the last 250 ka that are more pronounced during interglacials in comparison to glacial periods. High %-Andes values observed during periods of high austral summer insolation reflect the increased delivery of suspended sediments by Andean tributaries and enhanced Amazonian precipitation, in agreement with western Amazonian speleothem records. Increased Amazonian rainfall reflects the intensification of the South American monsoon in response to enhanced land-ocean thermal gradient and moisture convergence. However, low %-Amazon values obtained at 12° N during the same periods seem to contradict the increased delivery of Amazon sediments. We propose that reorganizations in surface ocean currents modulate the northwestward transport of Amazon material. In agreement with published records, the seasonal North Brazil Current retroflection is intensified (or prolonged in duration) during cold substages of the last 250 ka (which correspond to intervals of high DJF or low JJA insolation) and deflects eastward the Amazon sediment and freshwater plume.