Thomas A. Murray

Semiparametric Bayesian commensurate survival model for post-market medical device surveillance with non-exchangeable historical data

Trial investigators often have a primary interest in the estimation of the survival curve in a population for which there exists acceptable historical information from which to borrow strength. However, borrowing strength from a historical trial that is non-exchangeable with the current trial can result in biased conclusions. In this article we propose a fully Bayesian semiparametric method for the purpose of attenuating bias and increasing efficiency when jointly modeling time-to-event data from two possibly non-exchangeable sources of information. We illustrate the mechanics of our methods by applying them to a pair of post-market surveillance datasets regarding adverse events in persons on dialysis that had either a bare metal or drug-eluting stent implanted during a cardiac revascularization surgery. We finish with a discussion of the advantages and limitations of this approach to evidence synthesis, as well as directions for future work in this area. The articles Supplementary Materials offer simulations to show our procedures bias, mean squared error, and coverage probability properties in a variety of settings.

Combining nonexchangeable functional or survival data sources in oncology using generalized mixture commensurate priors

Conventional approaches to statistical inference preclude structures that facilitate incorporation of supplemental information acquired from similar circumstances. For example, the analysis of data obtained using perfusion computed tomography to characterize functional imaging biomarkers in cancerous regions of the liver can benefit from partially informative data collected concurrently in non-cancerous regions. This paper presents a hierarchical model structure that leverages all available information about a curve, using penalized splines, while accommodating important between-source features. Our proposed methods flexibly borrow strength from the supplemental data to a degree that reflects the commensurability of the supplemental curve with the primary curve. We investigate our methods properties for nonparametric regression via simulation, and apply it to a set of liver cancer data. We also apply our method for a semiparametric hazard model to data from a clinical trial that compares time to disease progression for three colorectal cancer treatments, while supplementing inference with information from a previous trial that tested the current standard of care.

Flexible bayesian survival modeling with semiparametric time-dependent and shape-restricted covariate effects

Presently, there are few options with available software to perform a fully Bayesian analysis of time-to-event data wherein the hazard is estimated semi- or non-parametrically. One option is the piecewise exponential model, which requires an often unrealistic assumption that the hazard is piecewise constant over time. The primary aim of this paper is to construct a tractable semiparametric alternative to the piecewise exponential model that assumes the hazard is continuous, and to provide modifiable, user-friendly software that allows the use of these methods in a variety of settings. To accomplish this aim, we use a novel model formulation for the log-hazard based on a low-rank thin plate linear spline that readily facilitates adjustment for covariates with time-dependent and proportional hazards effects, possibly subject to shape restrictions. We investigate the performance of our model choices via simulation. We then analyze colorectal cancer data from a clinical trial comparing the effectiveness of two novel treatment regimes relative to the standard of care for overall survival. We estimate a time-dependent hazard ratio for each novel regime relative to the standard of care while adjusting for the effect of aspartate transaminase, a biomarker of liver function, that is subject to a non-decreasing shape restriction.

Utility-based designs for randomized comparative trials with categorical outcomes.

A general utility-based testing methodology for design and conduct of randomized comparative clinical trials with categorical outcomes is presented. Numerical utilities of all elementary events are elicited to quantify their desirabilities. These numerical values are used to map the categorical outcome probability vector of each treatment to a mean utility, which is used as a one-dimensional criterion for constructing comparative tests. Bayesian tests are presented, including fixed sample and group sequential procedures, assuming Dirichlet-multinomial models for the priors and likelihoods. Guidelines are provided for establishing priors, eliciting utilities, and specifying hypotheses. Efficient posterior computation is discussed, and algorithms are provided for jointly calibrating test cutoffs and sample size to control overall type I error and achieve specified power. Asymptotic approximations for the power curve are used to initialize the algorithms. The methodology is applied to re-design a completed trial that compared two chemotherapy regimens for chronic lymphocytic leukemia, in which an ordinal efficacy outcome was dichotomized, and toxicity was ignored to construct the trials design. The Bayesian tests also are illustrated by several types of categorical outcomes arising in common clinical settings. Freely available computer software for implementation is provided. Copyright

Robust Treatment Comparison Based on Utilities of Semi-Competing Risks in Non-Small-Cell Lung Cancer

ABSTRACT A design is presented for a randomized clinical trial comparing two second-line treatments, chemotherapy versus chemotherapy plus reirradiation, for treatment of recurrent non-small-cell lung cancer. The central research question is whether the potential efficacy benefit that adding reirradiation to chemotherapy may provide justifies its potential for increasing the risk of toxicity. The design uses two co-primary outcomes: time to disease progression or death, and time to severe toxicity. Because patients may be given an active third-line treatment at disease progression that confounds second-line treatment effects on toxicity and survival following disease progression, for the purpose of this comparative study follow-up ends at disease progression or death. In contrast, follow-up for disease progression or death continues after severe toxicity, so these are semi-competing risks. A conditionally conjugate Bayesian model that is robust to misspecification is formulated using piecewise exponential distributions. A numerical utility function is elicited from the physicians that characterizes desirabilities of the possible co-primary outcome realizations. A comparative test based on posterior mean utilities is proposed. A simulation study is presented to evaluate test performance for a variety of treatment differences, and a sensitivity assessment to the elicited utility function is performed. General guidelines are given for constructing a design in similar settings, and a computer program for simulation and trial conduct is provided. Supplementary materials for this article are available online.

Bayesian adaptive design for device surveillance

Background Postmarket device surveillance studies often have important primary objectives tied to estimating a survival function at some future time T with a certain amount of precision. Purpose This article presents the details and various operating characteristics of a Bayesian adaptive design for device surveillance, as well as a method for estimating a sample size vector (determined by the maximum sample size and a preset number of interim looks) that will deliver the desired power. Methods We adopt a Bayesian adaptive framework, which recognizes the fact that persons enrolled in a study report their results over time, not all at once. At each interim look, we assess whether we expect to achieve our goals with only the current group or the achievement of such goals is extremely unlikely even for the maximum sample size. Results Our Bayesian adaptive design can outperform two nonadaptive frequentist methods currently recommended by Food and Drug Administration (FDA) guidance documents in many settings. Limitations Our method’s performance can be sensitive to model misspecification and changes in the trial’s enrollment rate. Conclusions The proposed design provides a more efficient framework for conducting postmarket surveillance of medical devices.

A Bayesian Machine Learning Approach for Optimizing Dynamic Treatment Regimes

ABSTRACT Medical therapy often consists of multiple stages, with a treatment chosen by the physician at each stage based on the patient’s history of treatments and clinical outcomes. These decisions can be formalized as a dynamic treatment regime. This article describes a new approach for optimizing dynamic treatment regimes, which bridges the gap between Bayesian inference and existing approaches, like Q-learning. The proposed approach fits a series of Bayesian regression models, one for each stage, in reverse sequential order. Each model uses as a response variable the remaining payoff assuming optimal actions are taken at subsequent stages, and as covariates the current history and relevant actions at that stage. The key difficulty is that the optimal decision rules at subsequent stages are unknown, and even if these decision rules were known the relevant response variables may be counterfactual. However, posterior distributions can be derived from the previously fitted regression models for the optimal decision rules and the counterfactual response variables under a particular set of rules. The proposed approach averages over these posterior distributions when fitting each regression model. An efficient sampling algorithm for estimation is presented, along with simulation studies that compare the proposed approach with Q-learning. Supplementary materials for this article are available online.

A utility-based design for randomized comparative trials with ordinal outcomes and prognostic subgroups: OrdBUB Design with Subgroups

A design is proposed for randomized comparative trials with ordinal outcomes and prognostic subgroups. The design accounts for patient heterogeneity by allowing possibly different comparative conclusions within subgroups. The comparative testing criterion is based on utilities for the levels of the ordinal outcome and a Bayesian probability model. Designs based on two alternative models that include treatment-subgroup interactions are considered, the proportional odds model and a non-proportional odds model with a hierarchical prior that shrinks toward the proportional odds model. A third design that assumes homogeneity and ignores possible treatment-subgroup interactions also is considered. The three approaches are applied to construct group sequential designs for a trial of nutritional prehabilitation versus standard of care for esophageal cancer patients undergoing chemoradiation and surgery, including both untreated patients and salvage patients whose disease has recurred following previous therapy. A simulation study is presented that compares the three designs, including evaluation of within-subgroup type I and II error probabilities under a variety of scenarios including different combinations of treatment-subgroup interactions.

Ranking ultimate teams using a Bayesian score-augmented win-loss model

Abstract Ultimate is a field sport played by two teams, each with seven players on the field. USA Ultimate administers nationwide leagues that consist of a regular season and post-season with Sectional, Regional, and National Championship tournaments. USA Ultimate ranks teams by applying an algorithm to the regular season results, and distributes the sixteen bids for the National Championship to the eight regions based on these rankings. Teams then compete at Regionals to earn the bids granted to their region. This article presents a novel score-augmented win-loss model for ranking Ultimate teams and distributing National Championship bids. The proposed approach facilitates predicting the placement of each qualifying team at the 2016 Club National Championships as well. The key innovations are the use of a pseudo-outcome called the win fraction that splits a win between the two teams based on the final score of their match, and a weighted quasi-likelihood function that facilitates discounting older results. The proposed approach is applied to the 2016 Club Division results. Rankings, bid allocations, and predictive placement probabilities are reported, as well as a comparative evaluation with the USA Ultimate algorithm, a win-loss model, and a point-scoring model.