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. ^

Caenorhabditis elegans germinal center kinase (Gck-1) is a p-body component that inhibits precocious ectopic MAP kinase dependent meiotic maturation

The Caenorhabditis elegans germline is an excellent model system for studying meiosis, as the gonad contains germ cells in all stages of meiosis I prophase in a linear temporal and spatial pattern. To form healthy gametes, many events must be coordinated. Failure of any step in the process can reduce fertility. Here, we describe a C. elegans Germinal Center Kinase, GCK-1, that is essential for the accurate progression of germ cells through meiosis I prophase. In the absence of GCK-1, germ cells undergo precocious maturation due to the activation of a specific MAP kinase isoform. Furthermore, GCK-1 localizes to P-bodies, RNP particles that have been implicated in RNA degradation and translational control. Like two other components of C. elegans germline P-bodies, GCK-1 functions to limit physiological germ cell apoptosis. This is the first study to identify a role for a GCK-III kinase in metazoan germ cell development and to link P-body function with MAP kinase activation and germ cell maturation. ^

A multivariate frailty model for disease recurrences and survival

A multivariate frailty hazard model is developed for joint-modeling of three correlated time-to-event outcomes: (1) local recurrence, (2) distant recurrence, and (3) overall survival. The term frailty is introduced to model population heterogeneity. The dependence is modeled by conditioning on a shared frailty that is included in the three hazard functions. Independent variables can be included in the model as covariates. The Markov chain Monte Carlo methods are used to estimate the posterior distributions of model parameters. The algorithm used in present application is the hybrid Metropolis-Hastings algorithm, which simultaneously updates all parameters with evaluations of gradient of log posterior density. The performance of this approach is examined based on simulation studies using Exponential and Weibull distributions. We apply the proposed methods to a study of patients with soft tissue sarcoma, which motivated this research. Our results indicate that patients with chemotherapy had better overall survival with hazard ratio of 0.242 (95% CI: 0.094 - 0.564) and lower risk of distant recurrence with hazard ratio of 0.636 (95% CI: 0.487 - 0.860), but not significantly better in local recurrence with hazard ratio of 0.799 (95% CI: 0.575 - 1.054). The advantages and limitations of the proposed models, and future research directions are discussed. ^

Homeless access to dental health care: Creation of a dental service model

This project involved developing a model for planning a dental emergency treatment center that could function as an embedded component of a shelter for the homeless population. The dental services provided by such a clinic should include treatment for tooth pain, dental caries or cavities, chipped or broken teeth, broken partials, abscessed teeth, emergency cleanings, periodontal disease or gum disease and fillings. These are the dental services that are most often sought by homeless people in hospital emergency rooms.^ The underlying assumption for this project was that the oral health needs of the homeless community can most effectively be addressed by implementing small dental clinics in existing facilities that provide shelter and other services for this population. The model described in this project identifies oral health care services that would be provided by the clinic, facility (physical plant) requirements and associated infrastructure to operate an embedded dental clinic, methods for obtaining funding, strategies of recruiting dental professionals to staff the facility, and methods to assess the outcomes of the embedded clinic strategy. As an example, this project describes a strategy for developing such an embedded clinic at San Antonio Metropolitan Ministries SAMM shelter based on recommendations from community health care leaders, managers of homeless shelters, members of the homeless community and dental professionals^

Comparison of Bayesian and frequentist approaches in clinical outcomes between hospitals

Many public health agencies and researchers are interested in comparing hospital outcomes, for example, morbidity, mortality, and hospitalization across areas and hospitals. However, since there is variation of rates in clinical trials among hospitals because of several biases, we are interested in controlling for the bias and assessing real differences in clinical practices. In this study, we compared the variations between hospitals in rates of severe Intraventricular Haemorrhage (IVH) infant using Frequentist statistical approach vs. Bayesian hierarchical model through simulation study. The template data set for simulation study was included the number of severe IVH infants of 24 intensive care units in Australian and New Zealand Neonatal Network from 1995 to 1997 in severe IVH rate in preterm babies. We evaluated the rates of severe IVH for 24 hospitals with two hierarchical models in Bayesian approach comparing their performances with the shrunken rates in Frequentist method. Gamma-Poisson (BGP) and Beta-Binomial (BBB) were introduced into Bayesian model and the shrunken estimator of Gamma-Poisson (FGP) hierarchical model using maximum likelihood method were calculated as Frequentist approach. To simulate data, the total number of infants in each hospital was kept and we analyzed the simulated data for both Bayesian and Frequentist models with two true parameters for severe IVH rate. One was the observed rate and the other was the expected severe IVH rate by adjusting for five predictors variables for the template data. The bias in the rate of severe IVH infant estimated by both models showed that Bayesian models gave less variable estimates than Frequentist model. We also discussed and compared the results from three models to examine the variation in rate of severe IVH by 20th centile rates and avoidable number of severe IVH cases. ^

A Bayesian analysis for spatial processes with application to mapping

In geographical epidemiology, maps of disease rates and disease risk provide a spatial perspective for researching disease etiology. For rare diseases or when the population base is small, the rate and risk estimates may be unstable. Empirical Bayesian (EB) methods have been used to spatially smooth the estimates by permitting an area estimate to "borrow strength" from its neighbors. Such EB methods include the use of a Gamma model, of a James-Stein estimator, and of a conditional autoregressive (CAR) process. A fully Bayesian analysis of the CAR process is proposed. One advantage of this fully Bayesian analysis is that it can be implemented simply by using repeated sampling from the posterior densities. Use of a Markov chain Monte Carlo technique such as Gibbs sampler was not necessary. Direct resampling from the posterior densities provides exact small sample inferences instead of the approximate asymptotic analyses of maximum likelihood methods (Clayton & Kaldor, 1987). Further, the proposed CAR model provides for covariates to be included in the model. A simulation demonstrates the effect of sample size on the fully Bayesian analysis of the CAR process. The methods are applied to lip cancer data from Scotland, and the results are compared. ^

The application of principal component analysis on human development indicators: Temporal approach from 1999 to 2010

Background and Objective. Ever since the human development index was published in 1990 by the United Nations Development Programme (UNDP), many researchers started searching and corporative studying for more effective methods to measure the human development. Published in 1999, Lai’s “Temporal analysis of human development indicators: principal component approach” provided a valuable statistical way on human developmental analysis. This study presented in the thesis is the extension of Lai’s 1999 research. ^ Methods. I used the weighted principal component method on the human development indicators to measure and analyze the progress of human development in about 180 countries around the world from the year 1999 to 2010. The association of the main principal component obtained from the study and the human development index reported by the UNDP was estimated by the Spearman’s rank correlation coefficient. The main principal component was then further applied to quantify the temporal changes of the human development of selected countries by the proposed Z-test. ^ Results. The weighted means of all three human development indicators, health, knowledge, and standard of living, were increased from 1999 to 2010. The weighted standard deviation for GDP per capita was also increased across years indicated the rising inequality of standard of living among countries. The ranking of low development countries by the main principal component (MPC) is very similar to that by the human development index (HDI). Considerable discrepancy between MPC and HDI ranking was found among high development countries with high GDP per capita shifted to higher ranks. The Spearman’s rank correlation coefficient between the main principal component and the human development index were all around 0.99. All the above results were very close to outcomes in Lai’s 1999 report. The Z test result on temporal analysis of main principal components from 1999 to 2010 on Qatar was statistically significant, but not on other selected countries, such as Brazil, Russia, India, China, and U.S.A.^ Conclusion. To synthesize the multi-dimensional measurement of human development into a single index, the weighted principal component method provides a good model by using the statistical tool on a comprehensive ranking and measurement. Since the weighted main principle component index is more objective because of using population of nations as weight, more effective when the analysis is across time and space, and more flexible when the countries reported to the system has been changed year after year. Thus, in conclusion, the index generated by using weighted main principle component has some advantage over the human development index created in UNDP reports.^

Slope estimation in a parametric measurement error model: A simulation study

In regression analysis, covariate measurement error occurs in many applications. The error-prone covariates are often referred to as latent variables. In this proposed study, we extended the study of Chan et al. (2008) on recovering latent slope in a simple regression model to that in a multiple regression model. We presented an approach that applied the Monte Carlo method in the Bayesian framework to the parametric regression model with the measurement error in an explanatory variable. The proposed estimator applied the conditional expectation of latent slope given the observed outcome and surrogate variables in the multiple regression models. A simulation study was presented showing that the method produces estimator that is efficient in the multiple regression model, especially when the measurement error variance of surrogate variable is large.^

Bayesian adaptive designs for drug combinations in early phase clinical trials

Treating patients with combined agents is a growing trend in cancer clinical trials. Evaluating the synergism of multiple drugs is often the primary motivation for such drug-combination studies. Focusing on the drug combination study in the early phase clinical trials, our research is composed of three parts: (1) We conduct a comprehensive comparison of four dose-finding designs in the two-dimensional toxicity probability space and propose using the Bayesian model averaging method to overcome the arbitrariness of the model specification and enhance the robustness of the design; (2) Motivated by a recent drug-combination trial at MD Anderson Cancer Center with a continuous-dose standard of care agent and a discrete-dose investigational agent, we propose a two-stage Bayesian adaptive dose-finding design based on an extended continual reassessment method; (3) By combining phase I and phase II clinical trials, we propose an extension of a single agent dose-finding design. We model the time-to-event toxicity and efficacy to direct dose finding in two-dimensional drug-combination studies. We conduct extensive simulation studies to examine the operating characteristics of the aforementioned designs and demonstrate the designs' good performances in various practical scenarios.^

Bayesian Adaptive Designs for Early Phase Clinical Trials

My dissertation focuses mainly on Bayesian adaptive designs for phase I and phase II clinical trials. It includes three specific topics: (1) proposing a novel two-dimensional dose-finding algorithm for biological agents, (2) developing Bayesian adaptive screening designs to provide more efficient and ethical clinical trials, and (3) incorporating missing late-onset responses to make an early stopping decision. Treating patients with novel biological agents is becoming a leading trend in oncology. Unlike cytotoxic agents, for which toxicity and efficacy monotonically increase with dose, biological agents may exhibit non-monotonic patterns in their dose-response relationships. Using a trial with two biological agents as an example, we propose a phase I/II trial design to identify the biologically optimal dose combination (BODC), which is defined as the dose combination of the two agents with the highest efficacy and tolerable toxicity. A change-point model is used to reflect the fact that the dose-toxicity surface of the combinational agents may plateau at higher dose levels, and a flexible logistic model is proposed to accommodate the possible non-monotonic pattern for the dose-efficacy relationship. During the trial, we continuously update the posterior estimates of toxicity and efficacy and assign patients to the most appropriate dose combination. We propose a novel dose-finding algorithm to encourage sufficient exploration of untried dose combinations in the two-dimensional space. Extensive simulation studies show that the proposed design has desirable operating characteristics in identifying the BODC under various patterns of dose-toxicity and dose-efficacy relationships. Trials of combination therapies for the treatment of cancer are playing an increasingly important role in the battle against this disease. To more efficiently handle the large number of combination therapies that must be tested, we propose a novel Bayesian phase II adaptive screening design to simultaneously select among possible treatment combinations involving multiple agents. Our design is based on formulating the selection procedure as a Bayesian hypothesis testing problem in which the superiority of each treatment combination is equated to a single hypothesis. During the trial conduct, we use the current values of the posterior probabilities of all hypotheses to adaptively allocate patients to treatment combinations. Simulation studies show that the proposed design substantially outperforms the conventional multi-arm balanced factorial trial design. The proposed design yields a significantly higher probability for selecting the best treatment while at the same time allocating substantially more patients to efficacious treatments. The proposed design is most appropriate for the trials combining multiple agents and screening out the efficacious combination to be further investigated. The proposed Bayesian adaptive phase II screening design substantially outperformed the conventional complete factorial design. Our design allocates more patients to better treatments while at the same time providing higher power to identify the best treatment at the end of the trial. Phase II trial studies usually are single-arm trials which are conducted to test the efficacy of experimental agents and decide whether agents are promising to be sent to phase III trials. Interim monitoring is employed to stop the trial early for futility to avoid assigning unacceptable number of patients to inferior treatments. We propose a Bayesian single-arm phase II design with continuous monitoring for estimating the response rate of the experimental drug. To address the issue of late-onset responses, we use a piece-wise exponential model to estimate the hazard function of time to response data and handle the missing responses using the multiple imputation approach. We evaluate the operating characteristics of the proposed method through extensive simulation studies. We show that the proposed method reduces the total length of the trial duration and yields desirable operating characteristics for different physician-specified lower bounds of response rate with different true response rates.

Bayesian adaptive designs in early phase clinical trials

There are two practical challenges in the phase I clinical trial conduct: lack of transparency to physicians, and the late onset toxicity. In my dissertation, Bayesian approaches are used to address these two problems in clinical trial designs. The proposed simple optimal designs cast the dose finding problem as a decision making process for dose escalation and deescalation. The proposed designs minimize the incorrect decision error rate to find the maximum tolerated dose (MTD). For the late onset toxicity problem, a Bayesian adaptive dose-finding design for drug combination is proposed. The dose-toxicity relationship is modeled using the Finney model. The unobserved delayed toxicity outcomes are treated as missing data and Bayesian data augment is employed to handle the resulting missing data. Extensive simulation studies have been conducted to examine the operating characteristics of the proposed designs and demonstrated the designs' good performances in various practical scenarios.^

On Bayesian seamless phase I-II designs

Early phase clinical trial designs have long been the focus of interest for clinicians and statisticians working in oncology field. There are several standard phse I and phase II designs that have been widely-implemented in medical practice. For phase I design, the most commonly used methods are 3+3 and CRM. A newly-developed Bayesian model-based mTPI design has now been used by an increasing number of hospitals and pharmaceutical companies. The advantages and disadvantages of these three top phase I designs have been discussed in my work here and their performances were compared using simulated data. It was shown that mTPI design exhibited superior performance in most scenarios in comparison with 3+3 and CRM designs. ^ The next major part of my work is proposing an innovative seamless phase I/II design that allows clinicians to conduct phase I and phase II clinical trials simultaneously. Bayesian framework was implemented throughout the whole design. The phase I portion of the design adopts mTPI method, with the addition of futility rule which monitors the efficacy performance of the tested drugs. Dose graduation rules were proposed in this design to allow doses move forward from phase I portion of the study to phase II portion without interrupting the ongoing phase I dose-finding schema. Once a dose graduated to phase II, adaptive randomization was used to randomly allocated patients into different treatment arms, with the intention of more patients being assigned to receive more promising dose(s). Again simulations were performed to compare the performance of this innovative phase I/II design with a recently published phase I/II design, together with the conventional phase I and phase II designs. The simulation results indicated that the seamless phase I/II design outperform the other two competing methods in most scenarios, with superior trial power and the fact that it requires smaller sample size. It also significantly reduces the overall study time. ^ Similar to other early phase clinical trial designs, the proposed seamless phase I/II design requires that the efficacy and safety outcomes being able to be observed in a short time frame. This limitation can be overcome by using validated surrogate marker for the efficacy and safety endpoints.^

Understanding and Characterizing Shared Decision-Making and Behavioral Intent in Medical Uncertainty

Applying Theoretical Constructs to Address Medical Uncertainty Situations involving medical reasoning usually include some level of medical uncertainty. Despite the identification of shared decision-making (SDM) as an effective technique, it has been observed that the likelihood of physicians and patients engaging in shared decision making is lower in those situations where it is most needed; specifically in circumstances of medical uncertainty. Having identified shared decision making as an effective, yet often a neglected approach to resolving a lack of information exchange in situations involving medical uncertainty, the next step is to determine the way(s) in which SDM can be integrated and the supplemental processes that may facilitate its integration. SDM involves unique types of communication and relationships between patients and physicians. Therefore, it is necessary to further understand and incorporate human behavioral elements - in particular, behavioral intent - in order to successfully identify and realize the potential benefits of SDM. This paper discusses the background and potential interaction between the theories of shared decision-making, medical uncertainty, and behavioral intent. Identifying Shared Decision-Making Elements in Medical Encounters Dealing with Uncertainty A recent summary of the state of medical knowledge in the U.S. reported that nearly half (47%) of all treatments were of unknown effectiveness, and an additional 7% involved an uncertain tradeoff between benefits and harms. Shared decision-making (SDM) was identified as an effective technique for managing uncertainty when two or more parties were involved. In order to understand which of the elements of SDM are used most frequently and effectively, it is necessary to identify these key elements, and understand how these elements related to each other and the SDM process. The elements identified through the course of the present research were selected from basic principles of the SDM model and the “Data, Information, Knowledge, Wisdom” (DIKW) Hierarchy. The goal of this ethnographic research was to identify which common elements of shared decision-making patients are most often observed applying in the medical encounter. The results of the present study facilitated the understanding of which elements patients were more likely to exhibit during a primary care medical encounter, as well as determining variables of interest leading to more successful shared decision-making practices between patients and their physicians. Understanding Behavioral Intent to Participate in Shared Decision-Making in Medically Uncertain Situations Objective: This article describes the process undertaken to identify and validate behavioral and normative beliefs and behavioral intent of men between the ages of 45-70 with regard to participating in shared decision-making in medically uncertain situations. This article also discusses the preliminary results of the aforementioned processes and explores potential future uses of this information which may facilitate greater understanding, efficiency and effectiveness of doctor-patient consultations.Design: Qualitative Study using deductive content analysisSetting: Individual semi-structure patient interviews were conducted until data saturation was reached. Researchers read the transcripts and developed a list of codes.Subjects: 25 subjects drawn from the Philadelphia community.Measurements: Qualitative indicators were developed to measure respondents’ experiences and beliefs related to behavioral intent to participate in shared decision-making during medical uncertainty. Subjects were also asked to complete the Krantz Health Opinion Survey as a method of triangulation.Results: Several factors were repeatedly described by respondents as being essential to participate in shared decision-making in medical uncertainty. These factors included past experience with medical uncertainty, an individual’s personality, and the relationship between the patient and his physician.Conclusions: The findings of this study led to the development of a category framework that helped understand an individual’s needs and motivational factors in their intent to participate in shared decision-making. The three main categories include 1) an individual’s representation of medically uncertainty, 2) how the individual copes with medical uncertainty, and 3) the individual’s behavioral intent to seek information and participate in shared decision-making during times of medically uncertain situations.

Regulation of apoptosis during the pathogenesis of non -melanoma skin cancer

Previous studies from our lab have shown distinctive patterns of expression of bcl-2 gene family members in human nonmelanoma skin cancer (NMSC). To further evaluate the significance of these observations and to study the effects of cell death deregulation during skin carcinogenesis, we generated a transgenic mouse model (HK1.bcl-2) using the human keratin 1 promoter to target the expression of a human bcl-2 minigene to the epidermis. Transgenic protein expression was confirmed in all the layers of the epidermis except the stratum corneum using immunohistochemistry. Multifocal epidermal hyperplasia, without associated hyperkeratosis, was observed in newborn HK1.bcl-2 mice. Immunofluorescence staining using monoclonal antibodies specific for a variety of differentiation markers revealed aberrant expression of keratin 6 (K6) in the transgenic epidermis. Epidermal proliferative indexes, assessed by anti-BrdUrd immunofluorescence staining, were similar in control and transgenic newborn mice, but suprabasal proliferating cells were seen within the hyperplastic areas of the transgenic mouse skin. Spontaneous apoptotic indices of the epidermis were similar in both control and HK1.bcl-2 transgenic newborn mice, however, after UV-B irradiation, the number of "sunburn cells" was significantly higher in the control compared to the HK1.bcl-2 transgenic animals.^ Adult HK1.bcl-2 and control littermate mice were used in UV-B and chemical carcinogenesis protocols including DMBA + TPA. UV-B irradiated control and HK1.bcl-2 mice had comparable incidence of tumors than the controls, but the mean latency period was significantly shorter in the HK1.bcl-2 transgenic. Both control and transgenic animals included in chemical carcinogenesis protocols required application of both the initiating (DMBA) and promoting (TPA) agents to develop tumors. The frequency, number, and latency of tumor formation was similar in both groups of animals, however, HK1.bcl-2 mice exhibited a rate of conversion from benign papilloma to carcinoma 2.5 times greater than controls.^ Similar carcinogenesis experiments were performed using newborn mice. HK1.bcl-2 mice treated with UV-B plus TPA have a three fold greater incidence of tumor formation compared to controls littermates. HK1.bcl-2 transgenic animals also exhibited a shorter latency for papilloma formation when treated with DMBA plus TPA.^ HK1.bcl-2/v-Ha-ras double transgenic mice shared phenotypic features of both HK1.v-Ha-ras and HK1.bcl-2 transgenic mice, and exhibited focal areas of augmented hyperplasia. These double transgenic mice were susceptible to tumor formation by treatment with TPA alone.^ Cultures of primary keratinocytes were established from control, HK1.bcl-2, HK1.Ha-ras, and HK1.bcl-2/v-Ha-ras newborn mice. Cell viability was determined after exposure of the cells to UV-B irradiation, DMBA, TPA, or TGF-$\beta$1. Internucleosomal DNA fragmentation ("ladders") and morphological cellular changes compatible with apoptotic cell death were observed after the application of all these agents. HK1.bcl-2 keratinocytes were resistant to cell death induction by all of these agents except TGF-$\beta$1. HK1.Ha-ras cells had a higher spontaneous rate of cell death which could be compensated by co-expression of bcl-2.^ These findings suggest that bcl-2 dependent cell death suppression may be an important component of multistep skin carcinogenesis. ^

Age model and Nd isotope ratios of DSDO Hole 43-386 and ODP Hole 210-1276A

Modern thermohaline circulation plays a role in latitudinal heat transport and in deep-ocean ventilation, yet ocean circulation may have functioned differently during past periods of extreme warmth, such as the Cretaceous. The Late Cretaceous (100-65 Ma) was an important period in the evolution of the North Atlantic Ocean, characterized by opening ocean gateways, long-term climatic cooling and the cessation of intermittent periods of anoxia (oceanic anoxic events, OAEs). However, how these phenomena relate to deep-water circulation is unclear. We use a proxy for deep-water mass composition (neodymium isotopes; e-Nd) to show that, at North Atlantic ODP Site 1276, deep waters shifted in the early Campanian (~78-83 Ma) from e-Nd values of ~-7 to values of ~-9, consistent with a change in the style of deep-ocean circulation but >10 Myr after a change in bottom water oxygenation conditions. A similar, but more poorly dated, trend exists in e-Nd data from DSDP Site 386. The Campanian e-Nd transition observed in the North Atlantic records is also seen in the South Atlantic and proto-Indian Ocean, implying a widespread and synchronous change in deep-ocean circulation. Although a unique explanation does not exist for the change at present, we favor an interpretation that invokes Late Cretaceous climatic cooling as a driver for the formation of Southern Component Water, which flowed northward from the Southern Ocean and into the North Atlantic and proto-Indian Oceans.