Optimal, minimax, and Bayesian two-stage designs in two-dose phase II clinical trials

Background: For most cytotoxic and biologic anti-cancer agents, the response rate of the drug is commonly assumed to be non-decreasing with an increasing dose. However, an increasing dose does not always result in an appreciable increase in the response rate. This may especially be true at high doses for a biologic agent. Therefore, in a phase II trial the investigators may be interested in testing the anti-tumor activity of a drug at more than one (often two) doses, instead of only at the maximum tolerated dose (MTD). This way, when the lower dose appears equally effective, this dose can be recommended for further confirmatory testing in a phase III trial under potential long-term toxicity and cost considerations. A common approach to designing such a phase II trial has been to use an independent (e.g., Simon's two-stage) design at each dose ignoring the prior knowledge about the ordering of the response probabilities at the different doses. However, failure to account for this ordering constraint in estimating the response probabilities may result in an inefficient design. In this dissertation, we developed extensions of Simon's optimal and minimax two-stage designs, including both frequentist and Bayesian methods, for two doses that assume ordered response rates between doses. ^ Methods: Optimal and minimax two-stage designs are proposed for phase II clinical trials in settings where the true response rates at two dose levels are ordered. We borrow strength between doses using isotonic regression and control the joint and/or marginal error probabilities. Bayesian two-stage designs are also proposed under a stochastic ordering constraint. ^ Results: Compared to Simon's designs, when controlling the power and type I error at the same levels, the proposed frequentist and Bayesian designs reduce the maximum and expected sample sizes. Most of the proposed designs also increase the probability of early termination when the true response rates are poor. ^ Conclusion: Proposed frequentist and Bayesian designs are superior to Simon's designs in terms of operating characteristics (expected sample size and probability of early termination, when the response rates are poor) Thus, the proposed designs lead to more cost-efficient and ethical trials, and may consequently improve and expedite the drug discovery process. The proposed designs may be extended to designs of multiple group trials and drug combination trials.^

Characterization of E2F1's oncogenic, apoptotic and tumor-suppressive activities utilizing the K5 mouse model

Though E2F1 is deregulated in most human cancers by mutations of the p16-cyclin D-Rb pathway, it also exhibits tumor suppressive activity. A transgenic mouse model overexpressing E2F1 under the control of the bovine keratin 5 (K5) promoter exhibits epidermal hyperplasia and spontaneously develops tumors in the skin and other epithelial tissues after one year of age. In a p53-deficient background, aberrant apoptosis in K5 E2F1 transgenic epidermis is reduced and tumorigenesis is accelerated. In sharp contrast, K5 E2F1 transgenic mice are resistant to papilloma formation in the DMBA/TPA two-stage carcinogenesis protocol. K5 E2F4 and K5 DP1 transgenic mice were also characterized and both display epidermal hyperplasia but do not develop spontaneous tumors even in cooperation with p53 deficiency. These transgenic mice do not have increased levels of apoptosis in their skin and are more susceptible to papilloma formation in the two-stage carcinogenesis model. These studies show that deregulated proliferation does not necessarily lead to tumor formation and that the ability to suppress skin carcinogenesis is unique to E2F1. E2F1 can also suppress skin carcinogenesis when okadaic acid is used as the tumor promoter and when a pre-initiated mouse model is used, demonstrating that E2F1's tumor suppressive activity is not specific for TPA and occurs at the promotion stage. E2F1 was thought to induce p53-dependent apoptosis through upregulation of p19ARF tumor suppressor, which inhibits mdm2-mediated p53 degradation. Consistent with in vitro studies, the overexpression of E2F1 in mouse skin results in the transcriptional activation of the p19ARF and the accumulation of p53. Inactivation of either p19ARF or p53 restores the sensitivity of K5 E2F1 transgenic mice to DMBA/TPA carcinogenesis, demonstrating that an intact p19ARF-p53 pathway is necessary for E2F1 to suppress carcinogenesis. Surprisingly, while p53 is required for E2F1 to induce apoptosis in mouse skin, p19ARF is not, and inactivation of p19ARF actually enhances E2F1-induced apoptosis and proliferation in transgenic epidermis. This indicates that ARF is important for E2F1-induced tumor suppression but not apoptosis. Senescence is another potential mechanism of tumor suppression that involves p53 and p19ARF. K5 E2F1 transgenic mice initiated with DMBA and treated with TPA show an increased number of senescence cells in their epidermis. These experiments demonstrate that E2F1's unique tumor suppressive activity in two-stage skin carcinogenesis can be genetically separated from E2F1-induced apoptosis and suggest that senescence utilizing the p19ARF-p53 pathway plays a role in tumor suppression by E2F1. ^

Forecasting cost based on a stochastic utilization plan and a fixed cost function

The application of Markov processes is very useful to health-care problems. The objective of this study is to provide a structured methodology of forecasting cost based upon combining a stochastic model of utilization (Markov Chain) and deterministic cost function. The perspective of the cost in this study is the reimbursement for the services rendered. The data to be used is the OneCare database of claim records of their enrollees over a two-year period of January 1, 1996–December 31, 1997. The model combines a Markov Chain that describes the utilization pattern and its variability where the use of resources by risk groups (age, gender, and diagnosis) will be considered in the process and a cost function determined from a fixed schedule based on real costs or charges for those in the OneCare claims database. The cost function is a secondary application to the model. Goodness-of-fit will be used checked for the model against the traditional method of cost forecasting. ^

UNDERSTANDING NANOG'S ROLE IN CANCER BIOLOGY

Understanding Nanog’s Role in Cancer Biology Mark Daniel Badeaux Supervisory Professor Dean Tang, PhD The cancer stem cell model holds that tumor heterogeneity and population-level immortality are driven by a subset of cells within the tumor, termed cancer stem cells. Like embryonic or somatic stem cells, cancer stem cells are believed to possess self-renewal capacity and the ability to give rise to a multitude of varieties of daughter cell. Because of cancer’s implied connections to authentic stem cells, we screened a variety of prostate cancer cell lines and primary tumors in order to determine if any notable ‘stemness’ genes were expressed in malignant growths. We found a promising lead in Nanog, a central figure in maintaining embryonic stem cell pluripotency, and through a variety of experiments in which we diminished Nanog expression, found that it may play a significant role in prostate cancer development. We then created a transgenic mouse model in which we targeted Nanog expression to keratin 14-expressing in order to assess its potential contribution to tumorigenesis. We found a variety of developmental abnormalities and altered differentiation patterns in our model , but much to our chagrin we observed neither spontaneous tumor formation nor premalignant changes in these mice, but instead surprisingly found that high levels of Nanog expression inhibited tumor formation in a two-stage skin carcinogenesis model. We also noted a depletion of skin stem cell populations, which underlies the wound-healing defect our mice harbor as well. Gene expression analysis shows a reduction in c-Jun and Bmp5, two genes whose loss inhibits skin tumor development and reduces stem cell counts respectively. As we further explored Nanog’s activity in prostate cancer, it became apparent that the protein oftentimes was not expressed. Emboldened by the competing endogenous RNA (ceRNA) hypothesis, we identified the Nanog 3’UTR as a regulator of the tumor suppressive microRNA 128a (miR-128a), which includes known oncogenes such as Bmi1 among its authentic targets. Future work will necessarily involve discerning instances in which Nanog mRNA is the biologically relevant molecule, as well as identifying additional mRNA species which may serve solely as a molecular sink for miR-128a.

Multiple site phosphorylation of tyrosine hydroxylase: A potential role for protein kinase C in the regulation of catecholamine synthesis

Tyrosine hydroxylase (TH), the initial and rate limiting enzyme in the catecholaminergic biosynthetic pathway, is phosphorylated on multiple serine residues by multiple protein kinases. Although it has been demonstrated that many protein kinases are capable of phosphorylating and activating TH in vitro, it is less clear which protein kinases participate in the physiological regulation of catecholamine synthesis in situ. These studies were designed to determine if protein kinase C (PK-C) plays such a regulatory role.^ Stimulation of intact bovine adrenal chromaffin cells with phorbol esters results in stimulation of catecholamine synthesis, tyrosine hydroxylase phosphorylation and activation. These responses are both time and concentration dependent, and are specific for those phorbol ester analogues which activate PK-C. RP-HPLC analysis of TH tryptic phosphopeptides indicate that PK-C phosphorylates TH on three putative sites. One of these (pepetide 6) is the same as that phosphorylated by both cAMP-dependent protein kinase (PK-A) and calcium/calmodulin-dependent protein kinase (CaM-K). However, two of these sites (peptides 4 and 7) are unique, and, to date, have not been shown to be phosphorylated by any other protein kinase. These peptides correspond to those which are phosphorylated with a slow time course in response to stimulation of chromaffin cells with the natural agonist acetylcholine. The activation of TH produced by PK-C is most closely correlated with the phosphorylation of peptide 6. But, as evident from pH profiles of tyrosine hydroxylase activity, phosphorylation of peptides 4 and 7 affect the expression of the activation produced by phosphorylation of peptide 6.^ These data support a role for PK-C in the control of TH activity, and suggest a two stage model for the physiological regulation of catecholamine synthesis by phosphorylation in response to cholinergic stimulation. An initial fast response, which appears to be mediated by CaM-K, and a slower, sustained response which appears to be mediated by PK-C. In addition, the multiple site phosphorylation of TH provides a mechanism whereby the regulation of catecholamine synthesis appears to be under the control of multiple protein kinases, and allows for the convergence of multiple, diverse physiological and biochemical signals. ^

Bayesian dual threshold design with Dirichlet distribution: An alternative way to frequentist multi-stage phase II designs in oncology

Many phase II clinical studies in oncology use two-stage frequentist design such as Simon's optimal design. However, they have a common logistical problem regarding the patient accrual at the interim. Strictly speaking, patient accrual at the end of the first stage may have to be suspended until all patients have events, success or failure. For example, when the study endpoint is six-month progression free survival, patient accrual has to be stopped until all outcomes from stage I is observed. However, study investigators may have concern when accrual is suspended after the first stage due to the loss of accrual momentum during this hiatus. We propose a two-stage phase II design that resolves the patient accrual problem due to an interim analysis, and it can be used as an alternative way to frequentist two-stage phase II studies in oncology. ^

Factors influencing hurricane evacuation among Hispanic population

The recent hurricanes of Katrina, Rita, and Dolly have brought to light the precarious situation populations place themselves in when they are unprepared to face a storm, or do not follow official orders to evacuate when a destructive hurricane is poised to hit the area. Three counties in southern Texas lie within 60 miles of the Gulf of Mexico, and along the Mexican border. Determining the barriers to hurricane evacuation in this distinct and highly impoverished area of the United States would help aid local, state, and federal agencies to respond more effectively to persons living here.^ The aim of this study was to examine intention to comply with mandatory hurricane evacuation orders among persons living in three counties in South Texas by gender, income, education, acculturation and county of residence. A questionnaire was administered to 3,088 households across the three counties using a two-stage cluster sampling strategy, stratified by all three counties. The door-to-door survey was a 73-item instrument that included demographics, reasons for and against evacuation, and preparedness for a hurricane. Weighted data were used for the analyses.^ Chi-square tests were run to determine whether differences between observed and expected frequencies were statistically significant. A logistic regression model was developed based on that univariate analysis. Results from the logistic regression estimated odds ratios and their 95 percent confidence intervals for the independent variables.^ Logistic regression results indicate that females were less likely than men to follow an evacuation order. Having a higher education meant more likelihood of evacuating. Those respondents with a higher affiliation with Spanish than English were more likely to follow the evacuation orders. Hidalgo County residents were less likely to evacuate than Cameron or Willacy Counties' residents. Local officials need to implement communication efforts specifically tailored for females, residents with less of an affiliation with Spanish, and Hidalgo County residents to ensure their successful evacuation prior to a strong hurricane's landfall.^

The determinants of improvements in health outcomes and of cost reduction in hospital inpatient care

This study aims to address two research questions. First, ‘Can we identify factors that are determinants both of improved health outcomes and of reduced costs for hospitalized patients with one of six common diagnoses?’ Second, ‘Can we identify other factors that are determinants of improved health outcomes for such hospitalized patients but which are not associated with costs?’ The Healthcare Cost and Utilization Project (HCUP) Nationwide Inpatient Sample (NIS) database from 2003 to 2006 was employed in this study. The total study sample consisted of hospitals which had at least 30 patients each year for the given diagnosis: 954 hospitals for acute myocardial infarction (AMI), 1552 hospitals for congestive heart failure (CHF), 1120 hospitals for stroke (STR), 1283 hospitals for gastrointestinal hemorrhage (GIH), 979 hospitals for hip fracture (HIP), and 1716 hospitals for pneumonia (PNE). This study used simultaneous equations models to investigate the determinants of improvement in health outcomes and of cost reduction in hospital inpatient care for these six common diagnoses. In addition, the study used instrumental variables and two-stage least squares random effect model for unbalanced panel data estimation. The study concluded that a few factors were determinants of high quality and low cost. Specifically, high specialty was the determinant of high quality and low costs for CHF patients; small hospital size was the determinant of high quality and low costs for AMI patients. Furthermore, CHF patients who were treated in Midwest, South, and West region hospitals had better health outcomes and lower hospital costs than patients who were treated in Northeast region hospitals. Gastrointestinal hemorrhage and pneumonia patients who were treated in South region hospitals also had better health outcomes and lower hospital costs than patients who were treated in Northeast region hospitals. This study found that six non-cost factors were related to health outcomes for a few diagnoses: hospital volume, percentage emergency room admissions for a given diagnosis, hospital competition, specialty, bed size, and hospital region.^

AN EMPIRICAL ESTIMATION OF MEDICAL AND NON-MEDICAL INPUTS IN THE PRODUCTION OF CARDIO-RESPIRATORY PHYSICAL HEALTH STATUS

The purpose of this study was to examine, in the context of an economic model of health production, the relationship between inputs (health influencing activities) and fitness.^ Primary data were collected from 204 employees of a large insurance company at the time of their enrollment in an industrially-based health promotion program. The inputs of production included medical care use, exercise, smoking, drinking, eating, coronary disease history, and obesity. The variables of age, gender and education known to affect the production process were also examined. Two estimates of fitness were used; self-report and a physiologic estimate based on exercise treadmill performance. Ordinary least squares and two-stage least squares regression analyses were used to estimate the fitness production functions.^ In the production of self-reported fitness status the coefficients for the exercise, smoking, eating, and drinking production inputs, and the control variable of gender were statistically significant and possessed theoretically correct signs. In the production of physiologic fitness exercise, smoking and gender were statistically significant. Exercise and gender were theoretically consistent while smoking was not. Results are compared with previous analyses of health production. ^

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.^

ROLE OF STAT3 IN KERATINOCYTE STEM CELLS DURING SKIN TUMORIGENESIS

STATs play crucial roles in a wide variety of biological functions, including development, proliferation, differentiation, migration and in cancer development. In the present study, we examined the impact of Stat3 deletion or activation on behavior of keratinocytes, including keratinocyte stem cells (KSCs). Deletion of Stat3 specifically in the bulge region of the hair follicle using K15.CrePR1 X Stat3fl/fl mice led to decreased tumor development by altering survival of bulge region KSCs. To further understand the role of KSCs in skin tumorigenesis, K5.Stat3C transgenic (Tg) mice which express a constitutively active/dimerized form of Stat3 called Stat3C via the bovine keratin 5 (K5) promoter were studied. The number of CD34 and α6 integrin positive cells was significantly reduced in Tg mice as compared to non-transgenic (NTg) littermates. There was a concomitant increase in the progenitor populations (Lgr-6, Lrig-1 and Sca-1) in the Tg mice vs. the stem cell population (CD34 and Keratin15). To investigate the mechanism underlying the increase in the progenitor population at the expense of bulge region KSCs we examined if Stat3C expression was involved in inducing migration of the bulge region KSCs. There was altered β-catenin and α6-integrin expression in the hair follicles of Tg mice, which may have contributed to reduced adhesive interactions between the epithelial cells and the basement membrane facilitating migration out of the niche. To further study the effect of Stat3 on differentiation of keratinocytes we analyzed the epidermal keratinocytes in K5.Cre X Stat3fl/fl mice. There was an increase in the expression of epidermal differentiation markers in the Stat3 knockout mice. These data suggest that deletion of Stat3 in the epidermis and hair follicle induced differentiation in these cells. Preliminary studies done with the BK5.Stat3C mouse model suggests that multiple hair follicle stem/progenitor populations may be involved in skin tumor development and progression in this model of skin tumorigenesis. Overall, these data suggest that Stat3 plays an important role in differentiation as well as migration of keratinocytes and that these effects may play a role during epithelial carcinogenesis.

Adaptive clinical trial design for targeted therapy development

The development of targeted therapy involve many challenges. Our study will address some of the key issues involved in biomarker identification and clinical trial design. In our study, we propose two biomarker selection methods, and then apply them in two different clinical trial designs for targeted therapy development. In particular, we propose a Bayesian two-step lasso procedure for biomarker selection in the proportional hazards model in Chapter 2. In the first step of this strategy, we use the Bayesian group lasso to identify the important marker groups, wherein each group contains the main effect of a single marker and its interactions with treatments. In the second step, we zoom in to select each individual marker and the interactions between markers and treatments in order to identify prognostic or predictive markers using the Bayesian adaptive lasso. In Chapter 3, we propose a Bayesian two-stage adaptive design for targeted therapy development while implementing the variable selection method given in Chapter 2. In Chapter 4, we proposed an alternate frequentist adaptive randomization strategy for situations where a large number of biomarkers need to be incorporated in the study design. We also propose a new adaptive randomization rule, which takes into account the variations associated with the point estimates of survival times. In all of our designs, we seek to identify the key markers that are either prognostic or predictive with respect to treatment. We are going to use extensive simulation to evaluate the operating characteristics of our methods.^

Instrumental variable method for the causal relationship between soluble receptor for advanced glycation end-products (sRAGE) and risk of pancreatic cancer

This thesis project is motivated by the potential problem of using observational data to draw inferences about a causal relationship in observational epidemiology research when controlled randomization is not applicable. Instrumental variable (IV) method is one of the statistical tools to overcome this problem. Mendelian randomization study uses genetic variants as IVs in genetic association study. In this thesis, the IV method, as well as standard logistic and linear regression models, is used to investigate the causal association between risk of pancreatic cancer and the circulating levels of soluble receptor for advanced glycation end-products (sRAGE). Higher levels of serum sRAGE were found to be associated with a lower risk of pancreatic cancer in a previous observational study (255 cases and 485 controls). However, such a novel association may be biased by unknown confounding factors. In a case-control study, we aimed to use the IV approach to confirm or refute this observation in a subset of study subjects for whom the genotyping data were available (178 cases and 177 controls). Two-stage IV method using generalized method of moments-structural mean models (GMM-SMM) was conducted and the relative risk (RR) was calculated. In the first stage analysis, we found that the single nucleotide polymorphism (SNP) rs2070600 of the receptor for advanced glycation end-products (AGER) gene meets all three general assumptions for a genetic IV in examining the causal association between sRAGE and risk of pancreatic cancer. The variant allele of SNP rs2070600 of the AGER gene was associated with lower levels of sRAGE, and it was neither associated with risk of pancreatic cancer, nor with the confounding factors. It was a potential strong IV (F statistic = 29.2). However, in the second stage analysis, the GMM-SMM model failed to converge due to non- concaveness probably because of the small sample size. Therefore, the IV analysis could not support the causality of the association between serum sRAGE levels and risk of pancreatic cancer. Nevertheless, these analyses suggest that rs2070600 was a potentially good genetic IV for testing the causality between the risk of pancreatic cancer and sRAGE levels. A larger sample size is required to conduct a credible IV analysis.^