Statistical Methods for Bayesian Clinical Trial Design and DNA Methylation Deconvolution

We consider the Bayesian clinical trial design problem in situations where a historical trial is available to inform the design and analysis of a future trial. Currently the FDA requires that all proposed designs exhibit reasonable type I error control. Traditionally, frequentist type I error control has been required. This is currently the case in the Center for Drug Evaluation and Research but no longer in the Center for Devices and Radiological Health. The requirement that a design exhibit frequentist type I error control necessitates that all prior information be discarded. We propose several Bayesian solutions that balance the need to control type I errors with the desire to utilize high quality prior information. For scenarios where the historical trial informs the parameter being tested, we propose Bayesian versions of the type I error rate and power that are defined with respect to the posterior distribution for the parameters given the historical data and conditional on the respective hypothesis being true. We demonstrate that in designs that control the Bayesian type I error rate, meaningful amounts of prior information can be borrowed but that the size of the new trial must be relatively large to justify borrowing a large amount of historical information. We tailor our design methodology for survival applications using proportional hazards and cure rate models. We also develop Bayesian adaptive designs for large cardiovascular outcomes trials (CVOTs) which incorporate control information from a historical CVOT conducted in a similar patient population. We propose an all-or-nothing adaptive design utilizing the power prior as well as a dynamic borrowing adaptive design utilizing a novel extension of the joint power prior. Separately, we present a statistical deconvolution method for DNA methylation data from bisulfite sequencing experiments. We propose a joint model for methylation data from a set of heterogeneous tissue samples and another set of reference tissue samples. Unlike other methylation deconvolution methods, our method allows one to estimate the heterogeneous tissue composition and provides improved estimates of cell type-specific methylation levels through the process of deconvolution. We demonstrate our method using data from DNA mixture tissues and simulation studies.Doctor of Philosoph

An examination of the structure of extension families of irreducible polynomials over finite fields

In this paper we examine the behavior of particular family of polynomial over a nite eld. The family studied is that obtained by composing an irreducible poly- nomial with prime power monomials. We examine methods of testing irreducibility via a new method of discriminant calculation. We also provide new incite into how the members of the given family factor when not irreducible. Further, we provided a nite eld generalization to "Roots Appearing in Quanta", an article presented by Perlis

Optimal Priors for the Discounting Parameter of the Normalized Power Prior

The power prior is a popular class of informative priors for incorporating information from historical data. It involves raising the likelihood for the historical data to a power, which acts as discounting parameter. When the discounting parameter is modelled as random, the normalized power prior is recommended. In this work, we prove that the marginal posterior for the discounting parameter for generalized linear models converges to a point mass at zero if there is any discrepancy between the historical and current data, and that it does not converge to a point mass at one when they are fully compatible. In addition, we explore the construction of optimal priors for the discounting parameter in a normalized power prior. In particular, we are interested in achieving the dual objectives of encouraging borrowing when the historical and current data are compatible and limiting borrowing when they are in conflict. We propose intuitive procedures for eliciting the shape parameters of a beta prior for the discounting parameter based on two minimization criteria, the Kullback-Leibler divergence and the mean squared error. Based on the proposed criteria, the optimal priors derived are often quite different from commonly used priors such as the uniform prior

Exploring the Connection Between the Normalized Power Prior and Bayesian Hierarchical Models

The power prior is a popular class of informative priors for incorporating information from historical data. It involves raising the likelihood for the historical data to a power, which acts as a discounting parameter. When the discounting parameter is modeled as random, the normalized power prior is recommended. Bayesian hierarchical modeling is a widely used method for synthesizing information from different sources, including historical data. In this work, we examine the analytical relationship between the normalized power prior (NPP) and Bayesian hierarchical models (BHM) for \emph{i.i.d.} normal data. We establish a direct relationship between the prior for the discounting parameter of the NPP and the prior for the variance parameter of the BHM. Such a relationship is first established for the case of a single historical dataset, and then extended to the case with multiple historical datasets with dataset-specific discounting parameters. For multiple historical datasets, we develop and establish theory for the BHM-matching NPP (BNPP) which establishes dependence between the dataset-specific discounting parameters leading to inferences that are identical to the BHM. Establishing this relationship not only justifies the NPP from the perspective of hierarchical modeling, but also provides insight on prior elicitation for the NPP. We present strategies on inducing priors on the discounting parameter based on hierarchical models, and investigate the borrowing properties of the BNPP

Case weighted power priors for hybrid control analyses with time-to-event data

We develop a method for hybrid analyses that uses external controls to augment internal control arms in randomized controlled trials (RCTs) where the degree of borrowing is determined based on similarity between RCT and external control patients to account for systematic differences (e.g., unmeasured confounders). The method represents a novel extension of the power prior where discounting weights are computed separately for each external control based on compatibility with the randomized control data. The discounting weights are determined using the predictive distribution for the external controls derived via the posterior distribution for time-to-event parameters estimated from the RCT. This method is applied using a proportional hazards regression model with piecewise constant baseline hazard. A simulation study and a real-data example are presented based on a completed trial in non-small cell lung cancer. It is shown that the case weighted power prior provides robust inference under various forms of incompatibility between the external controls and RCT population

Daily Predictors of ART Adherence Among Young Men Living with HIV Who Have Sex with Men: A Longitudinal Daily Diary Study

Improving adherence to antiretroviral therapy (ART) is essential for limiting HIV disease progression among young sexual minority men living with HIV. Daily diaries allow for a detailed examination of how fluctuations in psychosocial factors are associated with adherence over time. Across three cities in the United States, this study collected 60 days of quantitative data from 44 young men (between 16 and 24 years of age) living with HIV who have sex with men. Lagged transition models explored the associations of mood, stress, social support, substance use, and condomless intercourse with daily ART adherence. Baseline levels of illicit substance use and condomless intercourse, and a higher proportion of days with stress or marijuana use, were associated with lower ART adherence. Lapses in adherence predicted non-adherence the following day. Findings suggest prospective data collection may identify different predictors of adherence compared to retrospective recall. Lapse-management strategies are needed to improve adherence following a missed dose

Case Weighted Power Priors For Hybrid Control analyses With Time-To-Event Data

We develop a method for hybrid analyses that uses external controls to augment internal control arms in randomized controlled trials (RCTs) where the degree of borrowing is determined based on similarity between RCT and external control patients to account for systematic differences (e.g., unmeasured confounders). The method represents a novel extension of the power prior where discounting weights are computed separately for each external control based on compatibility with the randomized control data. The discounting weights are determined using the predictive distribution for the external controls derived via the posterior distribution for time-to-event parameters estimated from the RCT. This method is applied using a proportional hazards regression model with piecewise constant baseline hazard. A simulation study and a real-data example are presented based on a completed trial in non-small cell lung cancer. It is shown that the case weighted power prior provides robust inference under various forms of incompatibility between the external controls and RCT population

Basket trials in oncology: a systematic review of practices and methods, comparative analysis of innovative methods, and an appraisal of a missed opportunity

BackgroundBasket trials are increasingly used in oncology drug development for early signal detection, accelerated tumor-agnostic approvals, and prioritization of promising tumor types in selected patients with the same mutation or biomarker. Participants are grouped into so-called baskets according to tumor type, allowing investigators to identify tumors with promising responses to treatment for further study. However, it remains a question as to whether and how much the adoption of basket trial designs in oncology have translated into patient benefits, increased pace and scale of clinical development, and de-risking of downstream confirmatory trials.MethodsInnovation in basket trial design and analysis includes methods that borrow information across tumor types to increase the quality of statistical inference within each tumor type. We build on the existing systematic reviews of basket trials in oncology to discuss the current practices and landscape. We conceptually illustrate recent innovative methods for basket trials, with application to actual data from recently completed basket trials. We explore and discuss the extent to which innovative basket trials can be used to de-risk future trials through their ability to aid prioritization of promising tumor types for subsequent clinical development.ResultsWe found increasing adoption of basket trial design in oncology, but largely in the design of single-arm phase II trials with a very low adoption of innovative statistical methods. Furthermore, the current practice of basket trial design, which does not consider its impact on the clinical development plan, may lead to a missed opportunity in improving the probability of success of a future trial. Gating phase II with a phase Ib basket trial reduced the size of phase II trials, and losses in the probability of success as a result of not using innovative methods may not be recoverable by running a larger phase II trial.ConclusionInnovative basket trial methods can reduce the size of early phase clinical trials, with sustained improvement in the probability of success of the clinical development plan. We need to do more as a community to improve the adoption of these methods

Pre-exposure Prophylaxis Implementation in Family Planning Services Across the Southern United States: Findings from a Survey Among Staff, Providers and Administrators Working in Title X-Funded Clinics

To improve women's access to pre-exposure prophylaxis (PrEP) in family planning (FP) clinics, we examined readiness to provide PrEP, and barriers and facilitators at the clinic level to integrate PrEP services into Title X-funded FP clinics across the Southern US. Title X-funded FP clinics across DHHS regions III (Mid-Atlantic), IV (Southeast), and VI (Southwest), comprising the Southern US. From February to June, 2018, we conducted a web-based, geographically targeted survey of medical staff, providers and administrators of Title X-funded FP clinics in DHHS regions III (Mid-Atlantic), IV (Southeast), and VI (Southwest). Survey items were developed using the Consolidated Framework for Implementation Research to assess constructs relevant to PrEP implementation. One-fifth of 283 unique Title X clinics across the South provided PrEP. Readiness for PrEP implementation was positively associated with a climate supportive of HIV prevention, leadership engagement, and availability of resources, and negatively associated with providers holding negative attitudes about PrEP's suitability for FP. The Title X FP network is a vital source of sexual health care for millions of individuals across the US. Clinic-level barriers to providing PrEP must be addressed to expand onsite PrEP delivery in Title X FP clinics in the Southern US

State-level clustering in PrEP implementation factors among family planning clinics in the Southern United States

Background: Availability of PrEP-providing clinics is low in the Southern U.S., a region at the center of the U.S. HIV epidemic with significant HIV disparities among minoritized populations, but little is known about state-level differences in PrEP implementation in the region. We explored state-level clustering of organizational constructs relevant to PrEP implementation in family planning (FP) clinics in the Southern U.S. Methods: We surveyed providers and administrators of FP clinics not providing PrEP in 18 Southern states (Feb-Jun 2018, N = 414 respondents from 224 clinics) on these constructs: readiness to implement PrEP, PrEP knowledge/attitudes, implementation climate, leadership engagement, and available resources. We analyzed each construct using linear mixed models. A principal component analysis identified six principal components, which were inputted into a K-means clustering analysis to examine state-level clustering. Results: Three clusters (C1–3) were identified with five, three, and four states, respectively. Canonical variable 1 separated C1 and C2 from C3 and was primarily driven by PrEP readiness, HIV-specific implementation climate, PrEP-specific leadership engagement, PrEP attitudes, PrEP knowledge, and general resource availability. Canonical variable 2 distinguished C2 from C1 and was primarily driven by PrEP-specific resource availability, PrEP attitudes, and general implementation climate. All C3 states had expanded Medicaid, compared to 1 C1 state (none in C2). Conclusion: Constructs relevant for PrEP implementation exhibited state-level clustering, suggesting that tailored strategies could be used by clustered states to improve PrEP provision in FP clinics. Medicaid expansion was a common feature of states within C3, which could explain the similarity of their implementation constructs. The role of Medicaid expansion and state-level policies on PrEP implementation warrants further exploration