Sequential updating via dynamic hierarchical models: A Bayesian approach to longitudinal data analysis

Most statistical analysis, theory and practice, is concerned with static models; models with a proposed set of parameters whose values are fixed across observational units. Static models implicitly assume that the quantified relationships remain the same across the design space of the data. While this is reasonable under many circumstances this can be a dangerous assumption when dealing with sequentially ordered data. The mere passage of time always brings fresh considerations and the interrelationships among parameters, or subsets of parameters, may need to be continually revised. ^ When data are gathered sequentially dynamic interim monitoring may be useful as new subject-specific parameters are introduced with each new observational unit. Sequential imputation via dynamic hierarchical models is an efficient strategy for handling missing data and analyzing longitudinal studies. Dynamic conditional independence models offers a flexible framework that exploits the Bayesian updating scheme for capturing the evolution of both the population and individual effects over time. While static models often describe aggregate information well they often do not reflect conflicts in the information at the individual level. Dynamic models prove advantageous over static models in capturing both individual and aggregate trends. Computations for such models can be carried out via the Gibbs sampler. An application using a small sample repeated measures normally distributed growth curve data is presented. ^

Estimating parameters in Markov models for longitudinal studies with missing data or surrogate outcomes

The discrete-time Markov chain is commonly used in describing changes of health states for chronic diseases in a longitudinal study. Statistical inferences on comparing treatment effects or on finding determinants of disease progression usually require estimation of transition probabilities. In many situations when the outcome data have some missing observations or the variable of interest (called a latent variable) can not be measured directly, the estimation of transition probabilities becomes more complicated. In the latter case, a surrogate variable that is easier to access and can gauge the characteristics of the latent one is usually used for data analysis. ^ This dissertation research proposes methods to analyze longitudinal data (1) that have categorical outcome with missing observations or (2) that use complete or incomplete surrogate observations to analyze the categorical latent outcome. For (1), different missing mechanisms were considered for empirical studies using methods that include EM algorithm, Monte Carlo EM and a procedure that is not a data augmentation method. For (2), the hidden Markov model with the forward-backward procedure was applied for parameter estimation. This method was also extended to cover the computation of standard errors. The proposed methods were demonstrated by the Schizophrenia example. The relevance of public health, the strength and limitations, and possible future research were also discussed. ^

Longitudinal categorical data analysis: A continuous -time Markov chain approach

In this dissertation, we propose a continuous-time Markov chain model to examine the longitudinal data that have three categories in the outcome variable. The advantage of this model is that it permits a different number of measurements for each subject and the duration between two consecutive time points of measurements can be irregular. Using the maximum likelihood principle, we can estimate the transition probability between two time points. By using the information provided by the independent variables, this model can also estimate the transition probability for each subject. The Monte Carlo simulation method will be used to investigate the goodness of model fitting compared with that obtained from other models. A public health example will be used to demonstrate the application of this method. ^

Multilevel analysis for a longitudinal clinical trial

This study applies the multilevel analysis technique to longitudinal data of a large clinical trial. The technique accounts for the correlation at different levels when modeling repeated blood pressure measurements taken throughout the trial. This modeling allows for closer inspection of the remaining correlation and non-homogeneity of variance in the data. Three methods of modeling the correlation were compared. ^

The effect of genotype-by-environment interaction on longitudinal triglyceride profiles in the Bogalusa Heart Study

Triglyceride levels are a component of plasma lipids that are thought to be an important risk factor for coronary heart disease and are influenced by genetic and environmental factors, such as single nucleotide polymorphisms (SNPs), alcohol intake, and smoking. This study used longitudinal data from the Bogalusa Heart Study, a biracial community-based survey of cardiovascular disease risk factors. A sample of 1191 individuals, 4 to 38 years of age, was measured multiple times from 1973 to 2000. The study sample consisted of 730 white and 461 African American participants. Individual growth models were developed in order to assess gene-environment interactions affecting plasma triglycerides over time. After testing for inclusion of significant covariates and interactions, final models, each accounting for the effects of a different SNP, were assessed for fit and normality. After adjustment for all other covariates and interactions, LIPC -514C/T was found to interact with age3, age2, and age and a non-significant interaction of CETP -971G/A genotype with smoking status was found (p = 0.0812). Ever-smokers had higher triglyceride levels than never smokers, but persons heterozygous at this locus, about half of both races, had higher triglyceride levels after smoking cessation compared to current smokers. Since tobacco products increase free fatty acids circulating in the bloodstream, smoking cessation programs have the potential to ultimately reduce triglyceride levels for many persons. However, due to the effect of smoking cessation on the triglyceride levels of CETP -971G/A heterozygotes, the need for smoking prevention programs is also demonstrated. Both smoking cessation and prevention programs would have a great public health impact on minimizing triglyceride levels and ultimately reducing heart disease. ^

Quality Data is Key to Improving Education

The Data Quality Campaign (DQC) has been focused since 2005 on advocating for states to build robust state longitudinal data systems (SLDS). While states have made great progress in their data infrastructure, and should continue to emphasize this work, t data systems alone will not improve outcomes. It is time for both DQC and states to focus on building capacity to use the information that these systems are producing at every level – from classrooms to state houses. To impact system performance and student achievement, the ingrained culture must be replaced with one that focuses on data use for continuous improvement. The effective use of data to inform decisions, provide transparency, improve the measurement of outcomes, and fuel continuous improvement will not come to fruition unless there is a system wide focus on building capacity around the collection, analysis, dissemination, and use of this data, including through research.

Breastfeeding the very preterm hospitalized infant: An ethnographic study

Purpose. To develop a greater understanding of the experience—including the thoughts, feelings, and actions—of mothers' initiation and maintenance of lactation within the context of the NICU following the birth of a very preterm infant. ^ Design. Mixed method with dominant focused ethnographic approach. Setting: A 76-bed neonatal intensive care unit in the largest children's hospital located in a large metropolitan city in southeast Texas. ^ Sample. Purposeful sampling resulted in 23 interviews with 14 subjects. ^ Methods. Mixed method design with a dominant qualitative approach combined with a quantitative component to further identify and expand upon the investigation of the population in question. Open-ended semi-structured interviews and fieldwork were used to explore the experience of breastfeeding in the context of the NICU for mothers of very preterm infants. Longitudinal data obtained from each subject included in-depth interviews, demographic and clinical information, milk expression patterns (including pumping frequency, duration, and milk volumes obtained), and scores obtained from the Edinburgh Postpartum Depression Scale (EPDS). ^ Findings. Thematic analysis revealed that mothers of very preterm infants experienced an interruption in the process of becoming a mother, a paradoxical experience related to aspects of their milk expression routines and patterns, and negotiating the NICU environment. Sub-themes of becoming a mother-interrupted included: attribution, separation, connection, and navigation. Additional sub-themes related to the paradoxical experience included: the pump sometimes acting as a wedge or link to the infant; diversionary thoughts/activities during pumping; and perceptions of milk flow/volume. The process of negotiation included the environment, adaptive/maladaptive strategies related to milk expression, motivating factors related to the provision of breast milk, and learning their infant's feeding cues/abilities. EPDS scores did not reveal congruent differences in those mothers scoring high compared to those scoring low. ^ Conclusions. Understanding the experiences of the mothers in this study allows for a better perspective of breastfeeding the very preterm infant in the context of the NICU. Findings from this study validate the difficult and incremental process of attaining maternal identity and the significant burden placed on these women with regards to the provision of breast milk and breastfeeding during their infant's hospitalization. ^

Determinants of CD4 cell count decline after treatment interruption

Patients who had started HAART (Highly Active Anti-Retroviral Treatment) under previous aggressive DHHS guidelines (1997) underwent a life-long continuous HAART that was associated with many short term as well as long term complications. Many interventions attempted to reduce those complications including intermittent treatment also called pulse therapy. Many studies were done to study the determinants of rate of fall in CD4 count after interruption as this data would help guide treatment interruptions. The data set used here was a part of a cohort study taking place at the Johns Hopkins AIDS service since January 1984, in which the data were collected both prospectively and retrospectively. The patients in this data set consisted of 47 patients receiving via pulse therapy with the aim of reducing the long-term complications. ^ The aim of this project was to study the impact of virologic and immunologic factors on the rate of CD4 loss after treatment interruption. The exposure variables under investigation included CD4 cell count and viral load at treatment initiation. The rates of change of CD4 cell count after treatment interruption was estimated from observed data using advanced longitudinal data analysis methods (i.e., linear mixed model). Using random effects accounted for repeated measures of CD4 per person after treatment interruption. The regression coefficient estimates from the model was then used to produce subject specific rates of CD4 change accounting for group trends in change. The exposure variables of interest were age, race, and gender, CD4 cell counts and HIV RNA levels at HAART initiation. ^ The rate of fall of CD4 count did not depend on CD4 cell count or viral load at initiation of treatment. Thus these factors may not be used to determine who can have a chance of successful treatment interruption. CD4 and viral load were again studied by t-tests and ANOVA test after grouping based on medians and quartiles to see any difference in means of rate of CD4 fall after interruption. There was no significant difference between the groups suggesting that there was no association between rate of fall of CD4 after treatment interruption and above mentioned exposure variables. ^

Parental Employment and Home Visiting Program Service Delivery

Home visiting programs, which provide in-home services to disadvantaged families with young children, rest on the assumption that poor parents can be reached at home. Increased levels of maternal employment raise questions about this assumption. In this study, longitudinal data collected for a home visiting program evaluation were analyzed to assess whether employment patterns of parents who receive home visiting services reflect employment patterns of other poor mothers between 1995 and 2000. The study also addresses the relationship between maternal employment and home visiting service intensity. To effectively reach home visiting participants, service providers may need to modify service delivery practices.

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. ^

Longitudinal dyadic data analysis of stroke survivors and their spousal caregivers

Approximately 795,000 new and recurrent strokes occur each year. Because of the resulting functional impairment, stroke survivors are often discharged into the care of a family caregiver, most often their spouse. This dissertation explored the effect that mutuality, a measure of the perceived positive aspects of the caregiving relationship, had on the stress and depression of 159 stroke survivors and their spousal caregivers over the first 12 months post discharge from inpatient rehabilitation. Specifically, cross-lagged regression was utilized to investigate the dyadic, longitudinal relationship between caregiver and stroke survivor mutuality and caregiver and stroke survivor stress over time. Longitudinal meditational analysis was employed to examine the mediating effect of mutuality on the dyads’ perception of family function and caregiver and stroke survivor depression over time.^ Caregivers’ mutuality was found to be associated with their own stress over time but not the stress of the stroke survivor. Caregivers who had higher mutuality scores over the 12 months of the study had lower perceived stress. Additionally, a partner effect of stress for the stroke survivor but not the caregiver was found, indicating that stroke survivors’ stress over time was associated with caregivers’ stress but caregivers’ stress over time was not significantly associated with the stress of the stroke survivor.^ This dissertation did not find mutuality to mediate the relationship between caregivers’ and stroke survivors’ perception of family function at baseline and their own or their partners’ depression at 12 months as hypothesized. However, caregivers who perceived healthier family functioning at baseline and stroke survivors who had higher perceived mutuality at 12 months had lower depression at one year post discharge from inpatient rehabilitation. Additionally, caregiver mutuality at 6 months, but not at baseline or 12 months, was found to be inversely related to caregiver depression at 12 months.^ These findings highlight the interpersonal nature of stress in the context of caregiving, especially among spousal relationships. Thus, health professionals should encourage caregivers and stroke survivors to focus on the positive aspects of the caregiving relationship in order to mitigate stress and depression. ^

An Innovative Family Preservation Program in an African American Community: Longitudinal Analysis

This paper presents a secondary analysis of data from a longitudinal evaluation of a community-based family preservation program in Portland, Oregon, designed for and by African Americans. Families served by the Family Enhancement Program (FEP) resemble chronically neglecting families in terms of numbers of children and length of contact with child protective services. Six- and twelve-month follow-ups for FEP clients were compared to data on families served by the Oregon State Office of Services to Children and Families (SOSCF). The author found that FEP families are more likely than SOSCFfamilies to show greater improvement between the pretest scores and the posttest scores for number of days in placement, number of placements, and number of founded maltreatment reports.

A longitudinal comparison of cardiovascular disease risk factors among children and adolescents in the U.S. and Japan: Project HeartBeat!

Blood cholesterol and blood pressure development in childhood and adolescence have important impact on the future adult level of cholesterol and blood pressure, and on increased risk of cardiovascular diseases. The U.S. has higher mortality rates of coronary heart diseases than Japan. A longitudinal comparison in children of risk factor development in the two countries provides more understanding about the causes of cardiovascular disease and its prevention. Such comparisons have not been reported in the past. ^ In Project HeartBeat!, 506 non-Hispanic white, 136 black and 369 Japanese children participated in the study in the U.S. and Japan from 1991 to 1995. A synthetic cohort of ages 8 to 18 years was composed by three cohorts with starting ages at 8, 11, and 14. A multilevel regression model was used for data analysis. ^ The study revealed that the Japanese children had significantly higher slopes of mean total cholesterol (TC) and high density lipoprotein (HDL) cholesterol levels than the U.S. children after adjusting for age and sex. The mean TC level of Japanese children was not significantly different from white and black children. The mean HDL level of Japanese children was significantly higher than white and black children after adjusting for age and sex. The ratio of HDL/TC in Japanese children was significantly higher than in U.S. whites, but not significantly different from the black children. The Japanese group had significantly lower mean diastolic blood pressure phase IV (DBP4) and phase V (DBP5) than the two U.S. groups. The Japanese group also showed significantly higher slopes in systolic blood pressure, DBP5 and DBP4 during the study period than both U.S. groups. The differences were independent from height and body mass index. ^ The study provided the first longitudinal comparison of blood cholesterol and blood pressure between the U.S. and Japanese children and adolescents. It revealed the dynamic process of these factors in the three ethnic groups. ^

The influence of social connectedness and self-esteem on participant retention in a bi-ethnic longitudinal study

In prospective studies it is essential that the study sample accurately represents the target population for meaningful inferences to be drawn. Understanding why some individuals do not participate, or fail to continue to participate, in longitudinal studies can provide an empirical basis for the development of effective recruitment and retention strategies to improve response rates. This study examined the influence of social connectedness and self-esteem on long-term retention of participants, using secondary data from the “San Antonio Longitudinal Study of Aging” (SALSA), a population-based study of Mexican Americans (MAs) and European Americans (EAs) aged over 65 years residing in San Antonio, Texas. We tested the effect of social connectedness, self-esteem and socioeconomic status on participant retention in both ethnic groups. In MAs only, we analyzed whether acculturation and assimilation moderated these associations and/or had a direct effect on participant retention. ^ Low income, low frequency of social contacts and length of recruitment interval were significant predictors of non-completer status. Participants with low levels of social contacts were almost twice as likely as those with high levels of social contacts to be non-completers, even after adjustment for age, sex, ethnic group, education, household income, and recruitment interval (OR = 1.95, 95% CI: 1.26–3.01, p = 0.003). Recruitment interval consistently and strongly predicted non-completer status in all the models tested. Depending on the model, for each year beyond baseline there was a 25–33% greater likelihood of non-completion. The only significant interaction, or moderating, effect observed was between social contacts and cultural values among MAs. Specifically, MAs with both low social contacts and low acculturation on cultural values (i.e., placed high value on preserving Mexican cultural origins) were three and half times more likely to be non-completers compared with MAs in other subgroups comprised of the combination of these variables, even after adjustment for covariates. ^ Long term studies with older and minority participants are challenging for participant retention. Strategies can be designed to enhance retention by paying special attention to participants with low social contacts and, in MAs, participants with both low social contacts and low acculturation on cultural values. Minimizing the time interval between baseline and follow-up recruitment, and maintaining frequent contact with participants during this interval should also be is integral to the study design.^

Growth and development of body fat distribution from skinfold measurements: Longitudinal principal components

Longitudinal principal components analyses on a combination of four subcutaneous skinfolds (biceps, triceps, subscapular and suprailiac) were performed using data from the London Longitudinal Growth Study. The main objectives were to discover at what age during growth sex differences in body fat distribution occur and to see if there is continuity in body fatness and body fat distribution from childhood into the adult status (18 years). The analyses were done for four age sectors (3mon-3yrs, 3yrs-8yrs, 8yrs-18yrs and 3yrs-18yrs). Longitudinal principal component one (LPC1) for each age interval in both sexes represents the population mean fat curve. Component two (LPC2) is a velocity of fatness component. Component three (LPC3) in the 3mon-3yrs age sector represents infant fat wave in both sexes. In the next two age sectors component three in males represents peaks and shifts in fat growth (change in velocity), while in females it represents body fat distribution. Component four (LPC4) in the same two age sectors is a reversal in the sexes of the patterns seen for component three, i.e., in males it is body fat distribution and in females velocity shifts. Components five and above represent more complicated patterns of change (multiple increases and decreases across the age interval). In both sexes there is strong tracking in fatness from middle childhood to adolescence. In males only there is also a low to moderate tracking of infant fat with middle to late childhood fat. These data are strongly supported in the literature. Several factors are known to predict adult fatness among the most important being previous levels of fatness (at earlier ages) and the age at rebound. In addition we found that the velocity of fat change in middle childhood was highly predictive of later fatness (r $\approx -$0.7), even more so than age at rebound (r $\approx -$0.5). In contrast to fatness (LPC1), body fat distribution (LPC3-LPC4) did not track well even though significant components of body fat distribution occur at each age. Tracking of body fat distribution was higher in females than males. Sex differences in body fat distribution are non existent. Some sex differences are evident with the peripheral-to-central ratios after age 14 years. ^