Peter Müller, Ph.D.
Pre-Posterior Simulation and Bayesian Optimal Design

Many Bayesian design problems require the solution of analytically intractable integration and optimization problems. We will discuss three related approaches. The first is optimal design by curve fitting of Monte Carlo samples. Second, we will propose an approach to exploring expected utility surfaces by pre-posterior simulation.  By artificially augmenting the usual statistical model, p (theta, y) for a parameter, theta, and data, y, to a probability model h (d, theta, y) that includes the decision vector, d, the optimal design problem is recast as a problem of simulating from this augmented distribution. We will also discuss a generalization of this augmented probability model that is similar to the power transformation in simulated annealing.  Another practically important but notoriously difficult class of problems is sequential decision-making. We will discuss some recent simulation-based methods for approximate solutions to sequential design problems.  We will begin with a general review of simulation-based methods in Bayesian inference, including designs based on inference loss, expected utility optimization, and stylized Bayesian design. Biostatistical applications will include adaptive dose allocation in phase I/II trials, dose individualization, and optimal sampling for longitudinal data.

Robert E. Kass, Ph.D.
Bayesian Curve Fitting and Neuron Firing Patterns

One of the most important techniques in learning about brain function has involved examining neuronal activity in laboratory animals under varying experimental conditions.  Neural information is represented and communicated through series of action potentials, or spike trains, and a fundamental question in neuroscience is precisely how this is accomplished, that is, what physiological significance should be attached to a particular neuron firing pattern. My colleagues and I have framed scientific questions in terms of point process intensity functions, and have used Bayesian methods to fit the point process models to neuronal data.

I will describe the neurophysiological setting, and then use it as background to discuss a general approach to curve fitting with free-knot splines and reversible-jump MCMC, which may be applied in the point process setting.  With this analytical foundation in place I will outline the progress we’ve made and the substantive problems we hope to address in the next few years.

Andy P. Grieve, Ph.D.
Implementing a Complex Bayesian Design in a Regulated Environment: A Case Study

The context of our case study will be a dose-response study in the treatment of acute stroke. Such studies are an extremely important part of the drug development process as knowledge of the relationship between response and dose is an essential requirement for making informed decisions about dosage.  One potential difficulty in the use of a limited number of doses in a parallel group design to investigate dose response is the danger that the steep part of the dose-response curve may fall between two doses and little is learned. The use of a large number of doses in order to circumvent this problem is potentially wasteful in its use of patients because a large number of patients will either be receiving doses which are little different from placebo or, at the other extreme, receiving doses which have a greater potential for causing adverse side effects. Ideally, the vast majority of patients should receive doses in the steepest part of the dose-response function. The design decided upon was a sequential Bayesian adaptive design in which knowledge of the dose-response curve was updated on an on-going basis in order to inform two decisions. First, the dose that should be allocated to the next patient; second whether the study should continue or should be stopped.

There have been two major hindrances to the use of Bayesian methods in pharmaceutical R&D, one of which is practical, the other more philosophical.  The practical constraint has been the lack of availability of methods and software for their implementation. The philosophical constraint has been a perceived antipathy from regulators to the use of priors.

We will discuss aspects of these issues in the practical implementation of the proposed design.  In particular we will consider:

• choice of dose-response function
• simulation adaptive clinical trials to sample size the study and to provide details of the operating characteristic of the design
• use of prior information
• software validation
• interaction with regulatory authorities

Gary L. Rosner, Sc.D.
Bayesian Dose Individualization: A Case Study in Anticancer Transplant Therapy

I will highlight various Bayesian methods we use to design and analyze population-based studies of anticancer therapy.  In particular, we use Bayesian nonparametric models and combine information across studies and patients within studies by hierarchical modeling. 

The specific application concerns predicting the optimal dose for a leukemia patient undergoing high doses of chemotherapy, followed by bone marrow transplantation.  The optimization seeks to find the dose that minimizes the expected loss, where the loss function associates costs when the area under the concentration-time curve (AUC), a measure of systemic exposure, is either below or above the limits of a target range.  By first giving a patient a sub-therapeutic test dose of the anticancer drug, we estimate the patient-specific pharmacokinetics and use this information to predict the patient’s AUC as a function of dose.  The study design uses data from the following sources.  First, we have historical data on leukemia patients who underwent the same high-dose chemotherapy.  These data consist of pharmacokinetics and clinical outcomes.  A subsequent study collected pharmacokinetic information on patients who received a fixed low dose and a non-individualized high-dose of the drug.  In the third study, patients receive a low, test dose of the drug, the same low dose as in the second study.  We fit a pharmacokinetic model to the concentrations of the drug measured in the patient after administration of the test dose to infer the patient-specific parameters in the model of drug disposition.  We determine the optimal dose by averaging a loss function with respect to the predictive distribution for the patient’s AUC as a function of dose.  The patient will then receive the optimal dose, which is the dose that is associated with the smallest expected loss for the patient.  Our design incorporates historical information from the other two studies, along with the current patient’s data, borrowing strength to improve the precision of the prediction.

Lurdes Y. T. Inoue, Ph.D.
Seamlessly Expanding a Randomized Phase II Trial to Phase III

A sequential Bayesian phase II/III design is proposed for comparative clinical trials.  The design is based on both survival time and discrete early events that may be related to survival through a parametric mixture model.  Phase II involves a small number of centers.  Patients are randomized between treatments throughout, and sequential decisions are based on predictive probabilities of concluding superiority of the experimental treatment. Whether to stop early, continue, or shift into phase III is assessed repeatedly in phase II.  Phase III begins when additional institutions are incorporated into the ongoing phase II trial. Using simulation studies in the context of a non-small-cell lung cancer trial, we will show that the proposed method maintains overall size and power while usually requiring substantially smaller sample size and shorter trial duration when compared to conventional group-sequential phase III designs.

Peter F. Thall, Ph.D.
Practical Adaptive Decision-Making in Oncology Clinical Trials

Outcome-adaptive decision-making during an ongoing experiment uses the data that become available at successive times as a basis for deciding what to do next.  This is especially useful in clinical trials, where the decisions may be what dose or treatment to give the next patient, whether to drop a treatment arm, or whether to continue or terminate the trial.  The Bayesian paradigm provides a natural basis for this process.  The posterior is updated repeatedly as new data become available, and decisions are based on posterior or predictive probabilities.  This talk will consist of several examples of oncology trials using adaptive Bayesian methods, including (1) a trial of allogeneic donor lymphocytes for treating relapsed acute leukemia patients in which adaptive randomization is used to optimize the lymphocyte infusion time of each patient, (2) a new method for dose-finding in phase I trials where the doses of two different agents used in combination are varied, and (3) a trial to determine whether Gleevec has substantive anti-disease activity in sarcoma that uses a hierarchical model to account for multiple disease subtypes.

Dalene Stangl, Ph.D.
Meta-Analysis: Recent Advances and Future Needs

Conflicting conclusions between large clinical trials and meta-analyses fuel a debate about the usefulness of meta-analysis.  Much of the controversy is overstated, stemming from the disregard of naturally occurring variation between studies.  This course will discuss the controversy, review some basic concepts, and introduce recent methodological developments in meta-analysis.  New developments will include methods for incorporating 1) inconsistency between designs and outcomes across studies, 2) study-level covariates (including measures of study quality), and 3) adjustments for publication bias. Methods will be taught through the presentation of examples from clinical and community trials, epidemiology, and health policy.

Giovanni Parmigiani, Ph.D.
Can Nothing Teach Us Something?
Bayesian Meta-analysis of Sparse Contingency Tables

Over the last decade Bayesian hierarchical models have been increasingly used in numerous areas, including clinical trials and epidemiological studies. This is now a well established methodology for handling study-to-study heterogeneity, small sample sizes, heterogeneous study designs, publication bias, and other complexities.  The necessary computations for fitting Bayesian hierarchical models in a wide range of situations can be carried out conveniently using standard software packages such as BUGS.  As results from Bayesian hierarchical models are increasingly used to support clinical and policy decision making, the issue arises of whether they provide a sound way for comparing treatments. In this case study we will consider a meta-analysis of 2x2 tables, each arising from a study comparing adverse event counts for a treatment arm and a control arm. Our analysis will highlight strengths as well as important potential limitations of Bayesian hierarchical approaches, and will emphasize approaches that ensure robustness of conclusions to modeling choices such as parameterization, distributional assumptions and prior hyperparameters.

Bradley P. Carlin, Ph.D.
Hierarchical Models for Spatio-Temporally Correlated Survival Data

Survival models have a long history in the biomedical and biostatistical literature, and are enormously popular in the analysis of time-to-event data.  Very often these data will be grouped into strata, such as clinical sites, geographic regions, and so on.  Such data will often be available over multiple time periods, and for multiple diseases.  In this talk we will consider spatial survival models from two general points of view: {\em geostatistical approaches}, where we use the exact geographic locations (e.g., latitude and longitude) of the strata, and {\em lattice approaches}, where we use only the positions of the strata relative to each other (e.g., which counties neighbor which others).  We will compare these approaches in the context of a data set on infant mortality in Minnesota counties between 1992 and 1996.

We will then consider hierarchical spatial process models for multivariate survival data sets which are spatio-temporally arranged. Such models must account for correlations between survival rates in neighboring spatial regions, adjacent time periods, and similar diseases (say, different forms of cancer).  We will investigate Cox semiparametric survival modeling approaches, adding spatial and temporal effects in a hierarchical structure.  Here, a multivariate lattice model for the region-specific frailties is most convenient. Exemplification will be provided using time-to-event data for various cancers from the National Cancer Institute’s Surveillance, Epidemiology, and End Results (SEER) database.

Donald A. Berry, Ph.D.
Decision Analysis in Drug Development

A Bayesian statistical approach to decision making from a medical perspective can be helpful in pharmaceutical company decision making. I will show how the Bayesian approach can be used to develop efficient designs for clinical trials. I will apply a decision-analytic approach to the question of proceeding to the next phase of drug development and address the optimal design of future trials. I will present case studies of trial designs that have the goal of maximizing information while minimizing cost, where cost is measured in terms of time, money and patient resources.