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.^

Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

A model for use by local public health departments to evaluate pandemic influenza plans

The events of the 1990's and early 2000's demonstrated the need for effective planning and response to natural and man-made disasters. One of those potential natural disasters is pandemic flu. Once defined, the CDC stated that program, or plan, effectiveness is improved through the process of program evaluation. (Centers for Disease Control and Prevention, 1999) Program evaluation should be accomplished not only periodically, but in the course of routine administration of the program. (Centers for Disease Control and Prevention, 1999) Accomplishing this task for a "rare, but significant event" is challenging. (Herbold, John R., PhD., 2008) To address this challenge, the RAND Corporation (under contract to the CDC) developed the "Facilitated Look-Backs" approach that was tested and validated at the state level. (Aledort et al., 2006).^ Nevertheless, no comprehensive and generally applicable pandemic influenza program evaluation tool or model is readily found for use at the local public health department level. This project developed such a model based on the "Facilitated Look-Backs" approach developed by RAND Corporation. (Aledort et al., 2006) Modifications to the RAND model included stakeholder additions, inclusion of all six CDC program evaluation steps, and suggestions for incorporating pandemic flu response plans in seasonal flu management implementation. Feedback on the model was then obtained from three LPHD's—one rural, one suburban, and one urban. These recommendations were incorporated into the final model. Feedback from the sites also supported the assumption that this model promotes the effective and efficient evaluation of both pandemic flu and seasonal flu response by reducing redundant evaluations of pandemic flu plans, seasonal flu plans, and funding requirement accountability. Site feedback also demonstrated that the model is comprehensive and flexible, so it can be adapted and applied to different LPHD needs and settings. It also stimulates evaluation of the major issues associated with pandemic flu planning. ^ The next phase in evaluating this model should be to apply it in a program evaluation of one or more LPHD's seasonal flu response that incorporates pandemic flu response plans.^

DISCHARGE PLANNING: A PROCESS MODEL

As the requirements for health care hospitalization have become more demanding, so has the discharge planning process become a more important part of the health services system. A thorough understanding of hospital discharge planning can, then, contribute to our understanding of the health services system. This study involved the development of a process model of discharge planning from hospitals. Model building involved the identification of factors used by discharge planners to develop aftercare plans, and the specification of the roles of these factors in the development of the discharge plan. The factors in the model were concatenated in 16 discrete decision sequences, each of which produced an aftercare plan.^ The sample for this study comprised 407 inpatients admitted to the M. D. Anderson Hospital and Tumor Institution at Houston, Texas, who were discharged to any site within Texas during a 15 day period. Allogeneic bone marrow donors were excluded from the sample. The factors considered in the development of discharge plans were recorded by discharge planners and were used to develop the model. Data analysis consisted of sorting the discharge plans using the plan development factors until for some combination and sequence of factors all patients were discharged to a single site. The arrangement of factors that led to that aftercare plan became a decision sequence in the model.^ The model constructs the same discharge plans as those developed by hospital staff for every patient in the study. Tests of the validity of the model should be extended to other patients at the MDAH, to other cancer hospitals, and to other inpatient services. Revisions of the model based on these tests should be of value in the management of discharge planning services and in the design and development of comprehensive community health services.^

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.^

Risk and protective factors associated with depression among racial and ethnic mothers of adolescents

The central paradigm linking disadvantaged social status and mental health has been the social stress model (Horwitz, 1999), the assumption being that individuals residing in lower social status groups are subjected to greater levels of stress not experienced by individuals from higher status groups. A further assumption is that such individuals have fewer resources to cope with stress, in turn leading to higher levels of psychological disorder, including depression (Pearlin, 1989). Despite these key assumptions, there is a dearth of literature comparing the social patterning of stress exposure (Hatch & Dohrenwend, 2007; Meyer, Schwartz, & Frost, 2008; Kessler, Mickelson, & Williams, 1999; Turner & Avison, 2003; Turner & Lloyd, 1999; Turner, Wheaton, & Lloyd, 1995), and the distribution and contribution of protective factors, posited to play a role in the low rates of depression found among African- and Latino-Americans (Alegria et al., 2007; Breslau, Aguilar-Gaxiola, Kendler, Su, Williams, & Kessler, 2006; Breslau, Borges, Hagar, Tancredi, Gilman, 2009; Gavin, Walton, Chae, Alegria, Jackson, & Takeuchi, 2010; Williams, & Neighbors, 2006). Thus, this study sought to describe both the distribution and contribution of risk and protective factors in relation to depression among a sample of African-, European-, and Latina-American mothers of adolescents, including testing a hypothesized mechanism through which social support, an important protective factor specific to women and depression, operates. ^ Despite the finding that the levels of depression were not statistically different across all three groups of women, surprising results were found in describing the distribution of both risk and protective factors, in that results reported among all women who were mothers when analyzed masked differences within each ethnic group when SES was assessed, a point made explicit by Williams (2002) regarding racial and ethnic variations in women's health. In the final analysis, while perceived social support was found to partially mediate the effect of social isolation on depression, among African-Americans, the direct effect of social isolation and depression was lower among this group of women, as was the indirect effect of social isolation and perceived social support when compared to European- and Latina-American mothers. Or, put differently, higher levels of social isolation were not found to be as associated with more depression or lower social support among African-American mothers when compared to their European- and Latina-American counterparts. ^ Women in American society occupy a number of roles, i.e., that of being female, married or single, mother, homemaker or employee. In addition, to these roles, ethnicity and SES also come into play, such that the intersection of all these roles and the social contexts that they occupy are equally important and must be taken into consideration when making predictions drawn from the social stress model. Based on these findings, it appears that the assumptions of the social stress model need to be revisited to include the variety of roles that intersect among individuals from differing social groups. More specifically, among women who are mothers and occupy a myriad of other roles, i.e., that of being female, married or single, African- or Latina-American, mother, homemaker or employee, the intersection of all the roles and the social contexts that women occupy are equally important and must be taken into consideration when looking at both the types and distribution of stressors across women. Predictions based on simple, mutually exclusive categories of social groups may lead to erroneous assumptions and misleading results.^