In the analysis of time-to-event data, the median residual life (MERL) function has been promoted by many researchers as a practically relevant summary of the residual life distribution. Formally the MERL function at a time point is defined as the median of the remaining lifetimes among survivors beyond that particular time point. Despite its widely recognized usefulness, there is no commonly accepted approach to model the median residual life function. In this dissertation we introduce two novel regression techniques that model the relationship between the MERL function and covariates of interest at multiple time points simultaneously; proportional median residual life model and accelerated median residual life model. These models have a conceptual similarity to the well-known proportional hazards and accelerated failure time (AFT) models. Inference procedures that we propose for these models permit the data to be right censored. For the semiparametric analysis under the proportional MERL model, we propose an estimating equation for the regression coefficients. The bootstrap resampling technique is utilized to evaluate the standard errors of the regression coefficient estimates. A simulation study is performed to investigate the proposed inferential approach. The developed method is applied to a real data example from a breast cancer study conducted by the National Surgical Adjuvant Breast and Bowel Project (NSABP). We also propose parametric and semiparametric (under the AFT assumption) inference procedures under the accelerated MERL model. The maximum likelihood inference is considered for the parametric inference and the Buckley and James method is used to estimate the median residual lifetimes semiparametrically under the AFT assumption. A simulation study is performed to validate the proposed maximum likelihood inference procedure. A generated dataset is used to illustrate statistical analysis via both estimation approaches. It is very important from a public health perspective to be able to identify the risk factors for a specific disease or condition. The regression techniques presented in this work enable researchers to identify the patients characteristics that affect their survival experience and describe advantages of a preventive or therapeutic intervention by means of median residual life function in a clinically relevant and intuitively appealing way.

In longitudinal studies of depressive symptoms in elderly patients, analyses are complicated by the presence of nonignorable missing data. In this study, we used data from the Monongahela Valley Independent Elders Survey (MoVIES) of 1,260 rural and elderly residents in western Pennsylvania. The method we used to analyze the evolution of depression is the shared parameter model, which is one of the methods that provide a framework for jointly modeling the longitudinal outcomes and the dropout process through a common frailty or unobserved random effects. When we used 2 different shared parameter models instead of using an unadjusted longitudinal model, we found the following decreases in the ratio of the odds of depression: a 2% decrease for women versus men (OR decreased from 2.05 in the unadjusted model to 2.00 in each shared parameter model); a 3% decrease for individuals with less than a high school education versus individuals with more than or equal to a high school education (OR decreased from 0.33 to 0.32); a 3% decrease for individuals taking fewer than 4 prescription drugs versus individuals taking 4 or more prescription drugs (OR decreased from 0.29 to 0.28); a 5% decrease for individuals using antidepressant drugs versus individuals not using antidepressant drugs (OR decreased from 16.15 to 15.35 in the first shared parameter model and to 15.39 in the second shared parameter model); and a 1% decrease for individuals with functional impairment versus individuals without functional impairment (OR decreased from 4.72 to 4.66 in the first shared parameter model and to 4.67 in the second shared parameter model). Because differences of this magnitude are likely to have an impact on decisions concerning public health policies and funding, it is important to take nonignorable missing data into account when analyzing longitudinal studies. Shared parameter models can be computationally demanding, so their performance should be judged by their goodness of fit and required running time.

Over 800,000 people undergo Coronary Artery Bypass Graft (CABG) surgery annually for management of their Coronary Artery Disease (CAD) worldwide. Postoperative Atrial Fibrillation (PoAF) is a complication with a 30%-40% incidence after CABG surgery. PoAF is believed to cause additional complications and also possibly increase the total duration of hospital stay in these patients. It is also believed that local and systemic inflammation play a role in the development of this complication and the -174 G/C IL-6 gene polymorphism modulates the inflammatory response. A study is underway to evaluate any plausible association between the -174 G/C IL-6 genotype and PoAF in CABG patients at the Presbyterian University Hospital, Pittsburgh, PA. As part of an interim analysis of the study with a proposed enrollment of 380 subjects, the -174 G/C Interleukin 6 genotype variant was determined in 91 CABG patients. Heart rate and rhythm were monitored continuously until discharge. Twenty nine subjects (31.84%) developed PoAF. Multivariate logistic regression analysis included -174 G/C genotype, age, race, sex and other risk factors that are considered to be associated with PoAF. The analysis of the collected data revealed age as a significant predictor of PoAF. Subjects older than 65 years had 2.7 times higher odds of developing PoAF as compared to subjects who were 65 years old or younger. The -174 G/C gene variant or any other predictors were not significantly associated with PoAF in these 91 CABG patients. The length of postoperative hospital stay was not found to be significantly associated with the presence of PoAF. However, this could be attributed to aggressive management of PoAF by our clinical care team. With 15.3 million prevalence (USA-yr 2004) and the leading cause of mortality, CAD and its management are of enormous public health importance. PoAF needs to be explored further due to its ill defined etiopathology and the increasingly older patient population that undergo CABG surgery for their CAD. Any further knowledge derived on PoAF would pave way for better anticipation and prevention of this complication.

Mediational analysis is used to explain how a predictor affects the outcome through an intervening variable called a mediator. In a cross-sectional study, the predictor, the mediator, and the outcome are measured at single time points and these time points need to be chronologically in the same order. In longitudinal mediational models, the outcome and the mediator are measured over the follow-up period also in the chronological order while the predictor is measured at a single time point. The role of a mediator in cross-sectional mediational models with single outcomes is mostly assessed by two parametric tests, Sobel test and Clogg test. We have extended these tests to multiple outcomes. The extensions also include two bootstrap approaches. Simulation results show that in the presence of moderate correlation between the predictor and the mediator, the extended Clogg test has the most reliable Type I error rate and the highest power. For longitudinal mediational models, we have discussed one scenario where the outcome process and the mediational process are described by linear growth curves. The total indirect effect of the predictor is defined as the effect of the predictor on the initial status and the growth rate of the outcome after accounting for the mediating effect of the initial status and the growth rate of the mediator. Inferential methods for the total indirect effect are proposed, using a formulation by random coefficient models. Results indicate the reliability of the proposed methods with large samples. An illustrative example using University of Pittsburgh Physical Activity Study (PittPAS) is given. The study seeks to investigate an important question about the differential effect of gender, if any, on the exercise behavior in young adulthood in relation to the exercise behavior in adolescence. Using the mediational model, we found the differential effect of gender on physical activity in young adulthood was mediated by the previous physical activities experience in adolescence. The public health significance of the present work lies in the development of statistical procedures using cutting-edge methodologies to handle irregularly observed data, small samples and a finer characterization of the longitudinal outcome and mediational processes.

Statistical techniques such as Kaplan-Meier estimate is commonly used and interpreted as the probability of failure in time-to-event data. When used on biomedical survival data, patients who fail from unrelated or other causes (competing events) are often treated as censored observations. This paper reviews and compares two methods of estimating cumulative probability of cause-specific events in the present of other competing events: 1 minus Kaplan-Meier and cumulative incidence estimators. A subset of a breast cancer data with three competing events: recurrence, second primary cancers, and death, was used to illustrate the different estimates given by 1 minus Kaplan-Meier and cumulative incidence function. Recurrence of breast cancer was the event of interest and second primary cancers and deaths were competing risks. The results indicate that the cumulative incidences gives an appropriate estimates and 1 minus Kaplan-Meier overestimates the cumulative probability of cause-specific failure in the presence of competing events. In absence of competing events, the 1 minus Kaplan-Meier approach yields identical estimates as the cumulative incidence function. The public health relevance of this paper is to help researchers understand that competing events affect the cumulative probability of cause-specific events. Researchers should use methods such as the cumulative incidence function to correctly estimate and compare the cause-specific cumulative probabilities.

Traumatic brain injury is one of the leading causes of morbidity and mortality in the United States. A number of different pharmacological and therapeutic based clinical trials have proven to not be efficacious for reversing these trends. In fact, many of these clinical trials have had deleterious effects on patient outcome. Clinical trials with magnesium supplementation are included in this group. The routine use of magnesium may increase the likelihood of secondary hypoxic and anoxia events in these patients, therefore leading to increases in morbidity and mortality in a number of patient populations. The purpose of this study was to investigate the effects of magnesium supplementation on cerebral oxygen tension levels after closed head injury. Nineteen severe head injury patients, who had both cerebral oxygen probe placement and magnesium supplementation within the first 48 hours after injury were included in this study. All interventions were performed under patient consent and Institutional Review Board approval. The cerebral vascular response to magnesium varied by patient, with some patients having dramatic loses or gains in oxygen levels, while others were unaffected. Since only two female patients were included in this group, statistical analysis of data was restricted to the males of the study group. Overall cerebral oxygen levels were clinically unchanged during magnesium infusion periods (27.698 mmHg versus 24.886mmHg) using a mixed model regression adjusting for cerebral perfusion pressure, time after a magnesium infusion and percent of inspired oxygen (p<0.0001). An additional model was constructed controlling for the same variables to investigate the impact of the magnesium dose on tissue oxygenation. Only doses of two or four grams of magnesium improved brain tissue oxygenation (B=8.980 and 8.500 respectively p< 0.001). In conclusion magnesium infusions are not adversely affecting tissue oxygen levels after head injury and a dose of four grams or less during actually improve oxygen levels. The public health significance of this study is that the routine use of intravenous magnesium supplementation may exacerbate tissue injury in patients with impaired blood flow to the brain. The resulting increases in the mortality and morbidity to brain injury patients would have an enormous economic and social cost.

HumanHap550 Genotyping BeadChip provides a platform allowing for genotyping of single nucleotide polymorphisms (SNPs) greater than 550,000 loci. Such SNPs genotyping array technology makes it possible to identify genetic variation in individuals and across populations, profiling somatic mutations in cancer and loss of heterozygosity (LOH) events, amplifying deletions of regions of DNA, as well as possibly evaluating germline mutations in individuals. This study particularly focuses on analysis of clusters of Mendelian inconsistencies (MIs) in the SNPs array for six Russian radiation worker family trios, in order to identify the type of deletion variants for offspring such as inherited parental deletion variants (PDVs), spontaneous mutations (SMs) and germline mutations (GMs). By adapting the Bayesian theorem combining with the hereditary rule, this study presents an exciting result because 96.15% of genotypes in six selected clusters under the investigation could be identified as either PDVs or SMs/GMs, with two clusters are perfectly identified as SMs/GMs. This opens an avenue for further investigation of whether external environmental exposures (e.g., ionizing radiation) can effect the frequency of deletion variants (i.e., germline mutations) occurring in the offspring of highly exposed nuclear workers. While the applied methodology provides a practical means to recognize the genomic variations within the SNPs array some weaknesses of the study have been observed; particularly, the control group which consists of 112 individuals of Yoruba, Han Chinese, Japanese and Mormons is of deficiency on its sample size, diverse ethnicity and DNA process compared to the case group, and unclean potential hemizygous SNPs (i.e., Mendelian inconsistencies). Further statistical investigation and research needs to be conducted in order to overcome the weaknesses observed in the study; hence, the methodology introduced would be further of enhancement in its reliability and validity and it should be more effective when applied. Public health significance: The development of a reliable method to identify and count germline mutations in radiation workers could be generalized to exposures from any form of environmental mutagen (e.g., chemicals). Such a generalized marker could be used to measure the effects of various toxic environmental exposures on specific individuals and to predict genetically determined illness conditions.

The public health significance of this study is to provide researchers and clinicians interested in the study and treatment of Otitis Media with effusion (OME) with a better understanding of the associations between covariates and antibiotic treatment with the resolution of OME, which in turn will inform the decision-to-treat process. In a secondary analysis of the data from a series of three efficacy trials, we focus on the roles of laterality (unilateral vs. bilateral disease) and sidedness (right vs. left ear) as prognostic factors. The D&A trial compared the efficacy of decongestant and antihistamine (D/A) to placebo, the ABI trial was similar but compared amoxicillin (with and without to D/A) to placebo, and the ABII trial compared the efficacy of 2 promising antibiotics to amoxicillin. Each trial assessed subjects for OME at baseline, 2 weeks, and 4 weeks. The prevalence of OME at each time point was described by laterality and sidedness. McNemars test showed no evidence that left and right ears differ with respect to prevalence rates at 2 or 4 weeks (OR = 1.106 and OR = 0.858, respectively). Transition matrices of changes in OME status from 0 to 2 weeks and 2 to 4 weeks described the dependence of prior effusion status on a subjects current OME status. Multinomial regression was used to assess baseline covariates associated with prevalence and transitions of effusion status at each time point. We identified statistically significant prognostic factors of OME, including duration of effusion. Our analyses showed no differences in either prevalence of OME or in transitions of effusion status attributable to sidedness. A Chi Square Goodness-of-Fit test at each timepoint rejected the hypothesis of independence, p < 0.001. An ear-level GEE analysis demonstrated that effusion status of a contralateral ear was a significant predictor of effusion in the other ear (OR = 1.44, p < 0.001). There was no significant effect of sidedness (p = 0.86) and bilateral disease does not resolve at the rate predicted by unilateral resolution. This reanalysis using correlated data methods augments the initial findings by further examining sidedness and documenting transitions over time.

Classification trees are the most popular tool for categorizing individuals into groups and subgroups based on particular outcomes of interest. To date, trees have not been developed for the competing risk situation where survival times are recorded and more than one outcome is possible. In this work we propose three classification trees to analyze survival data with multiple competing risk outcomes, using both univariate and multivariate techniques, respectively. After we describe the method used in growing and pruning the classification trees for competing risks, we demonstrate the performance with simulations in a variety of competing risk model configurations, and compare the competing risk trees to currently available tree-based methods. We also illustrate their use by analyzing survival data concerning patients who had end-stage liver disease and were on the waiting list to receive a liver transplant. Public Health Significance: Competing risks are common in longitudinal studies. The classification tree for competing risks will provide more accurate estimates of risk in distinct subpopulations than the current tree techniques can provide.

An adaptive treatment strategy (ATS) is defined as a sequence of treatments and intermediate responses. ATS' arise when chronic diseases such as cancer and depression are treated over time with various treatment alternatives depending on intermediate responses to earlier treatments. For example, in two-stage adaptive treatment strategies, patients receive one of the induction treatments followed by a maintenance therapy given that the patients responded to the induction treatment they received. Clinical trials are often designed to compare adaptive treatment strategies based on appropriate designs such as sequential randomization designs. One of the main objectives of these trials is to compare two or more treatment strategies in terms of largest patient benefit, such as prolonged survival. Statistical inference from such trials needs to account for the sequential randomization structure of the design. Recent literature suggests several methods of estimation. A comparative review of currently available inferential procedures for analyzing data from such trials is presented. A sample size formula is introduced for comparing the survival probabilities under two treatment strategies sharing the same initial treatment. The formula is based on the large sample properties of inverse-probability- weighted estimator. Monte Carlo simulation study shows strong evidence that the proposed sample size formula guarantees desired power, regardless of the true distributions of survival times. To test for a difference in the effects of different induction and maintenance treatment combinations, a supremum weighted log-rank test is proposed. The test is applied to a dataset from a two-stage randomized trial and the results are compared to those obtained using a standard weighted log-rank test. A sample-size formula is derived based on the limiting distribution of the supremum weighted log-rank statistic. Simulation studies show that the proposed test provides sample sizes which are close to those obtained by standard weighted log-rank test under a proportional hazard alternative. However, the proposed test is more powerful than the standard weighted log-rank test under non-proportional hazard alternatives. The public health significance of this work is to provide a practical guidance of sample size determination and a test procedure in clinical trials that adopt two stage randomization designs.