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. ^

In vivo longitudinal studies of spinal cord injury and vascular endothelial growth factor treatment

Approximately 12,000 new cases of spinal cord injury (SCI) are added each year to the estimated 259,000 Americans living with SCI. The majority of these patients return to society, their lives forever changed by permanent loss of sensory and motor function. While there are no FDA approved drugs for the treatment of SCI or a universally accepted standard therapy, the current though controversial treatment includes the delivery of high dosages of the corticosteroid methyliprednisolone sodium succinate, surgical interventions to stabilize the spinal column, and physical rehabilitation. It is therefore critically important to fully understand the pathology of injury and determine novel courses and rationally-based therapies for SCI. ^ Vascular endothelial growth factor (VEGF) is an attractive target for treating central nervous system (CNS) injury and disease because it has been shown to influence angiogenesis and neuroprotection. Preliminary studies have indicated that increased vasculature may be associated with functional recovery; therefore exogenous delivery of a pro-angiogenic growth factor such as VEGF may improve neurobehavioral outcome. In addition, VEGF may provide protection from secondary injury and result in increased survival and axonal sprouting. ^ In these studies, SCI rats received acute intraspinal injections of VEGF, the antibody to VEGF, or vehicle control. The effect of these various agents was investigated using longitudinalmulti-modal magnetic resonance imaging (MRI), neuro- and sensory behavioral assays, and end point immunohistochemistry. We found that rats that received VEGF after SCI had increased tissue sparing and improved white matter integrity at the earlier time points as shown by advanced magnetic resonance imaging (MRI) techniques. However, these favorable effects of VEGF were not maintained, suggesting that additional treatments with VEGF at multiple time points may be more beneficial, Histological examinations revealed that VEGF treatment may result in increased oligodendrogenesis and therefore may eventually lead to remyelination and improved functional outcome. ^ On the neurobehavioral studies, treatments with VEGF and Anti-VEGF did not significantly affect performance on tests of open-field locomotion, grid walk, inclined plane, or rearing. However, VEGF treatment resulted in significantly increased incidence of chronic neuropathic pain. This phenomenon could possibly be attributed to the fact that VEGF treatment may promote axonal sprouting and also results in tissue sparing, thereby providing a substrate for the growth of new axons. New connections made by these sprouting axons may involve components of pathways involved in the transmission of pain and therefore result in increased pain in those animals. ^

Design of mixed-longitudinal studies

Cross-sectional designs, longitudinal designs in which a single cohort is followed over time, and mixed-longitudinal designs in which several cohorts are followed for a shorter period are compared by their precision, potential for bias due to age, time and cohort effects, and feasibility. Mixed longitudinal studies have two advantages over longitudinal studies: isolation of time and age effects and shorter completion time. Though the advantages of mixed-longitudinal studies are clear, choosing an optimal design is difficult, especially given the number of possible combinations of the number of cohorts and number of overlapping intervals between cohorts. The purpose of this paper is to determine the optimal design for detecting differences in group growth rates.^ The type of mixed-longitudinal study appropriate for modeling both individual and group growth rates is called a "multiple-longitudinal" design. A multiple-longitudinal study typically requires uniform or simultaneous entry of subjects, who are each observed till the end of the study.^ While recommendations for designing pure-longitudinal studies have been made by Schlesselman (1973b), Lefant (1990) and Helms (1991), design recommendations for multiple-longitudinal studies have never been published. It is shown that by using power analyses to determine the minimum number of occasions per cohort and minimum number of overlapping occasions between cohorts, in conjunction with a cost model, an optimal multiple-longitudinal design can be determined. An example of systolic blood pressure values for cohorts of males and cohorts of females, ages 8 to 18 years, is given. ^

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.^

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. ^

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.^

IMPROVING QUANTITATIVE TREATMENT RESPONSE MONITORING WITH DEFORMABLE IMAGE REGISTRATION

Quantitative imaging with 18F-FDG PET/CT has the potential to provide an in vivo assessment of response to radiotherapy (RT). However, comparing tissue tracer uptake in longitudinal studies is often confounded by variations in patient setup and potential treatment induced gross anatomic changes. These variations make true response monitoring for the same anatomic volume a challenge, not only for tumors, but also for normal organs-at-risk (OAR). The central hypothesis of this study is that more accurate image registration will lead to improved quantitation of tissue response to RT with 18F-FDG PET/CT. Employing an in-house developed “demons” based deformable image registration algorithm, pre-RT tumor and parotid gland volumes can be more accurately mapped to serial functional images. To test the hypothesis, specific aim 1 was designed to analyze whether deformably mapping tumor volumes rather than aligning to bony structures leads to superior tumor response assessment. We found that deformable mapping of the most metabolically avid regions improved response prediction (P<0.05). The positive predictive power for residual disease was 63% compared to 50% for contrast enhanced post-RT CT. Specific aim 2 was designed to use parotid gland standardized uptake value (SUV) as an objective imaging biomarker for salivary toxicity. We found that relative change in parotid gland SUV correlated strongly with salivary toxicity as defined by the RTOG/EORTC late effects analytic scale (Spearman’s ρ = -0.96, P<0.01). Finally, the goal of specific aim 3 was to create a phenomenological dose-SUV response model for the human parotid glands. Utilizing only baseline metabolic function and the planned dose distribution, predicting parotid SUV change or salivary toxicity, based upon specific aim 2, became possible. We found that the predicted and observed parotid SUV relative changes were significantly correlated (Spearman’s ρ = 0.94, P<0.01). The application of deformable image registration to quantitative treatment response monitoring with 18F-FDG PET/CT could have a profound impact on patient management. Accurate and early identification of residual disease may allow for more timely intervention, while the ability to quantify and predict toxicity of normal OAR might permit individualized refinement of radiation treatment plan designs.

Heart rate variability in response to pain stimulus in VLBW infants followed longitudinally during NICU stay.

The objective of this longitudinal study, conducted in a neonatal intensive care unit, was to characterize the response to pain of high-risk very low birth weight infants (<1,500 g) from 23 to 38 weeks post-menstrual age (PMA) by measuring heart rate variability (HRV). Heart period data were recorded before, during, and after a heel lanced or wrist venipunctured blood draw for routine clinical evaluation. Pain response to the blood draw procedure and age-related changes of HRV in low-frequency and high-frequency bands were modeled with linear mixed-effects models. HRV in both bands decreased during pain, followed by a recovery to near-baseline levels. Venipuncture and mechanical ventilation were factors that attenuated the HRV response to pain. HRV at the baseline increased with post-menstrual age but the growth rate of high-frequency power was reduced in mechanically ventilated infants. There was some evidence that low-frequency HRV response to pain improved with advancing PMA.

The use of second-generation antipsychotics and the changes in physical growth in children and adolescents with perinatally acquired HIV.

Second-generation antipsychotics (SGAs) are increasingly prescribed to treat psychiatric symptoms in pediatric patients infected with HIV. We examined the relationship between prescribed SGAs and physical growth in a cohort of youth with perinatally acquired HIV-1 infection. Pediatric AIDS Clinical Trials Group (PACTG), Protocol 219C (P219C), a multicenter, longitudinal observational study of children and adolescents perinatally exposed to HIV, was conducted from September 2000 until May 2007. The analysis included P219C participants who were perinatally HIV-infected, 3-18 years old, prescribed first SGA for at least 1 month, and had available baseline data prior to starting first SGA. Each participant prescribed an SGA was matched (based on gender, age, Tanner stage, baseline body mass index [BMI] z score) with 1-3 controls without antipsychotic prescriptions. The main outcomes were short-term (approximately 6 months) and long-term (approximately 2 years) changes in BMI z scores from baseline. There were 236 participants in the short-term and 198 in the long-term analysis. In linear regression models, youth with SGA prescriptions had increased BMI z scores relative to youth without antipsychotic prescriptions, for all SGAs (short-term increase = 0.192, p = 0.003; long-term increase = 0.350, p < 0.001), and for risperidone alone (short-term = 0.239, p = 0.002; long-term = 0.360, p = 0.001). Participants receiving both protease inhibitors (PIs) and SGAs showed especially large increases. These findings suggest that growth should be carefully monitored in youth with perinatally acquired HIV who are prescribed SGAs. Future research should investigate the interaction between PIs and SGAs in children and adolescents with perinatally acquired HIV infection.

Impact of medications prescribed for treatment of attention-deficit hyperactivity disorder on physical growth in children and adolescents with HIV.

OBJECTIVE: To examine the relationships between physical growth and medications prescribed for symptoms of attention-deficit hyperactivity disorder in children with HIV. METHODS: Analysis of data from children with perinatally acquired HIV (N = 2251; age 3-19 years), with and without prescriptions for stimulant and nonstimulant medications used to treat attention-deficit hyperactivity disorder, in a long-term observational study. Height and weight measurements were transformed to z scores and compared across medication groups. Changes in z scores during a 2-year interval were compared using multiple linear regression models adjusting for selected covariates. RESULTS: Participants with (n = 215) and without (n = 2036) prescriptions were shorter than expected based on US age and gender norms (p < .001). Children without prescriptions weighed less at baseline than children in the general population (p < .001) but gained height and weight at a faster rate (p < .001). Children prescribed stimulants were similar to population norms in baseline weight; their height and weight growth velocities were comparable with the general population and children without prescriptions (for weight, p = .511 and .100, respectively). Children prescribed nonstimulants had the lowest baseline height but were similar to population norms in baseline weight. Their height and weight growth velocities were comparable with the general population but significantly slower than children without prescriptions (p = .01 and .02, respectively). CONCLUSION: The use of stimulants to treat symptoms of attention-deficit hyperactivity disorder does not significantly exacerbate the potential for growth delay in children with HIV and may afford opportunities for interventions that promote physical growth. Prospective studies are needed to confirm these findings.

Perfusion in rat brain at 7 T with arterial spin labeling using FAIR-TrueFISP and QUIPSS.

Measurement of perfusion in longitudinal studies allows for the assessment of tissue integrity and the detection of subtle pathologies. In this work, the feasibility of measuring brain perfusion in rats with high spatial resolution using arterial spin labeling is reported. A flow-sensitive alternating recovery sequence, coupled with a balanced gradient fast imaging with steady-state precession readout section was used to minimize ghosting and geometric distortions, while achieving high signal-to-noise ratio. The quantitative imaging of perfusion using a single subtraction method was implemented to address the effects of variable transit delays between the labeling of spins and their arrival at the imaging slice. Studies in six rats at 7 T showed good perfusion contrast with minimal geometric distortion. The measured blood flow values of 152.5+/-6.3 ml/100 g per minute in gray matter and 72.3+/-14.0 ml/100 g per minute in white matter are in good agreement with previously reported values based on autoradiography, considered to be the gold standard.

Family Preservation Research: Where We've Been, Where We Should Be Going

Although the literature has provided many critiques of research done on family preservation programs, these critiques have usually been limited to the studies ' assumptions, approach, or methodology. Because of the nature of these critiques, suggestions for future research in this field of practice have been scattered throughout the literature and have not benefitted from a wider historical perspective. This paper examines the historical evolution of family preservation studies in child welfare and suggests future directions for research in the field. Among the suggestions the authors posit are (1) research questions should be framed by what we know about improvements in the lives of families and children served by family preservation programs; (2) future explorations should include areas that have received relatively little attention in current research, including the impact of organizational conditions on service fidelity and worker performance; (3) newer treatment models, particularly those that provide both intensive services during a crisis period and less intensive services for maintenance, should be tested; (4) data collection points in longitudinal studies should be guided by theory, and measures should change over time to reflect the theoretically expected changes in families; (5) complex measures of placement prevention and other measures that capture changes in family functioning, child well-being, and child safety, should be utilized to obtain a full picture of program effects; and (6) multiple informants should be used to provide data about program effectiveness. In addition, the authors will argue that the field should carefully consider the amount of change that should be expected from the service models delivered.

Family Preservation Services to At-Risk Families: A Macro Case Study

Although the literature has provided many critiques of research done on family preservation programs, these critiques have usually been limited to the studies ' assumptions, approach, or methodology. Because of the nature of these critiques, suggestions for future research in this field of practice have been scattered throughout the literature and have not benefited from a wider historical perspective. This paper examines the historical evolution of family preservation studies in child welfare and suggests future directions for research in the field. Among the suggestions the authors posit are (1) research questions should be framed by what we know about improvements in the lives of families and children served by family preservation programs; (2) future explorations should include areas that have received relatively little attention in current research, including the impact of organizational conditions on service fidelity and worker performance; (3) newer treatment models, particularly those that provide both intensive services during a crisis period and less intensive services for maintenance, should be tested; (4) data collection points in longitudinal studies should be guided by theory, and measures should change over time to reflect the theoretically expected changes in families; (5) complex measures of placement prevention and other measures that capture changes in family functioning, child well-being, and child safety, should be utilized to obtain a full picture of program effects; and (6) multiple informants should be used to provide data about program effectiveness. In addition, the authors will argue that the field should carefully consider the amount of change that should be expected from the service models delivered.

Evaluation of androgenicity, abdominal adiposity, blood pressure and types of ovulatory patterns in a sample of women with menstrual irregularities

Objective: To determine the prevalence of and the relationships between the degree and source of hyperandrogenemia, ovulatory patterns and cardiovascular disease risk indicators (blood pressure, indices or amount of obesity and fat distribution) in women with menstrual irregularities seen at endocrinologists' clinic. Design: A cross-sectional study design. Participants: A sample of 159 women with menstrual irregularities, aged 15-44, seen at endocrinologists' clinic. Main Outcome Measures: androgen levels, body mass index (BMI), waist-hip ratio (WHR), systolic and diastolic blood pressure (SBP & DBP), source of androgens, ovulatory activity. Results: The prevalence of hyperandrogenemia was 54.7% in this study sample. As expected, women with acne or hirsutism had an odds ratio 12.5 (95%CI = 5.2-25.5) times and 36 (95%CI = 12.9-99.5) times more likely to have hyperandrogenemia than those without acne or hirsutism. The main findings of this study were the following: Hyperandrogenemic women were more likely to have oligomenorrheic cycles (OR = 3.8, 95%CI = 1.5-9.9), anovulatory cycles (OR = 6.6, 95%CI = 2.8-15.4), general obesity (BMI $\ge$ 27) (OR = 6.8, 95%CI = 2.2-27.2) and central obesity (WHR $\ge$ 127) (OR = 14.5, 95%CI = 6.1-38.7) than euandrogenemic women. Hyperandrogenemic women with non-suppressible androgens had a higher mean BMI (29.3 $\pm$ 8.9) than those with suppressible androgens (27.9 $\pm$ 7.9); the converse was true for abdominal adiposity (WHR). Hyperandrogenemic women had a 2.4 odds ratio (95%CI = 1.0-6.2) for an elevated SBP and a 2.7 odds ratio (95%CI = 0.8-8.8) for elevated DBP. When age differences were accounted for, this relationship was strengthened and further strengthened when sources of androgens were controlled. When the differences in BMI were controlled, the odds ratio for elevated SBP in hyperandrogenemic women increased to 8.8 (95%CI = 1.1-69.9). When the age, the source of androgens, the amount of obesity and the type of obesity were controlled, hyperandrogenemic women had 13.5 (95%CI = 1.1-158.9) odds ratio for elevated SBP. Conclusions: In this study population, the presence of menstrual irregularities are highly predictive for the presence of elevated androgens. Women with elevated androgens have a high risk for obesity, more specifically for central obesity. The androgenemic status is an independent predictor of blood pressure elevation. It is probable that in the general population, the presence of menstrual irregularities are predictive of hyperandrogenemia. There is a great need for a population study of the prevalence of hyperandrogenemia and for longitudinal studies in hyperandrogenemic women (adrenarche to menopause) to investigate the evolution of these relationships. ^

Changes in blood lipids and their associations with changes in measures of height, weight and body mass index from age 8 to 18 years: Project Heartbeat!

A variety of studies indicate that the process of athrosclerosis begins in childhood. There was limited information on the association of the changes in anthropometric variables to blood lipids in school age children and adolescents. Previous longitudinal studies of children typically with insufficient frequency of observation could not provide sound inference on the dynamics of change in blood lipids. The aims of this analysis are (1) to document the sex- and ethnic-specific trajectory and velocity curves of blood lipids (TC, LDL-C, HDL-C and TG); (2) to evaluate the relationship of changes in anthropometric variables, such as height, weight and BMI, to blood lipids from age 8 to 18 years. ^ Project HeartBeat! is a longitudinal study designed to examine the patterns of serial change in major cardiovascular risk factors. Cohort of three different age levels, 8, 11 and 14 years at baseline, with a total of 678 participants were enrolled. Each member of these cohorts was examined three times per year for up to four years. ^ Sex- and ethnic-specific trajectory and velocity curves of blood lipids; demonstrated the complex and polyphasic changes in TC, LDL-C, HDL-C and TG longitudinally. The trajectory curves of TC, LDL-C and HDL-C with age showed curvilinear patterns of change. The velocity change in TC, HDL-C and LDL-C showed U-shaped curves for non-Blacks, and nearly linear lines in velocity of TG for both Blacks and non-Blacks. ^ The relationship of changes in anthropometric variables to blood lipids was evaulated by adding height, weight, or BMI and associated interaction terms separately to the basic age-sex models. Height or height gain had a significant negative association with changes in TC, LDL-C and HDL-C. Weight or BMI gain showed positive associations with TC, LDL-C and TC, and a negative relationship with HDL-C. ^ Dynamic changes of blood lipids in school age children and adolescents observed from this analysis suggested that using fixed screening criteria under the current NCEP guidelines for all ages 2–19 may not be appropriate for this age group. The association of increasing BMI or weight to an adverse blood lipid profile found in this analysis also indicated that weight or BMI monitoring could be a future intervention to be implemented in the pediatric population. ^