Familiar statistical tests and estimates are obtained by the direct observation of cases of interest: a clinical trial of a new drug, for instance, will compare the drug’s effects on a relevant set of patients and controls. Sometimes, though, indirect evidence may be temptingly available, perhaps the results of previous trials on closely related drugs. Very roughly speaking, the difference between direct and indirect statistical evidence marks the boundary between frequentist and Bayesian thinking. Twentieth-century statistical practice focused heavily on direct evidence, on the grounds of superior objectivity. Now, however, new scientific devices such as microarrays routinely produce enormous data sets involving thousands of related situations, where indirect evidence seems too important to ignore. Empirical Bayes methodology offers an attractive direct/indirect compromise. There is already some evidence of a shift toward a less rigid standard of statistical objectivity that allows better use of indirect evidence. This article is basically the text of a recent talk featuring some examples from current practice, with a little bit of futuristic speculation.

Indirect evidence is crucial for successful statistical practice. Sometimes, however, it is better used informally. Future efforts should be directed toward understanding better the connection between statistical methods and scientific problems.

The random walk Metropolis (RWM) is one of the most common Markov chain Monte Carlo algorithms in practical use today. Its theoretical properties have been extensively explored for certain classes of target, and a number of results with important practical implications have been derived. This article draws together a selection of new and existing key results and concepts and describes their implications. The impact of each new idea on algorithm efficiency is demonstrated for the practical example of the Markov modulated Poisson process (MMPP). A reparameterization of the MMPP which leads to a highly efficient RWM-within-Gibbs algorithm in certain circumstances is also presented.

In 1951 Robbins and Monro published the seminal article on stochastic approximation and made a specific reference to its application to the “estimation of a quantal using response, nonresponse data.” Since the 1990s, statistical methodology for dose-finding studies has grown into an active area of research. The dose-finding problem is at its core a percentile estimation problem and is in line with what the Robbins–Monro method sets out to solve. In this light, it is quite surprising that the dose-finding literature has developed rather independently of the older stochastic approximation literature. The fact that stochastic approximation has seldom been used in actual clinical studies stands in stark contrast with its constant application in engineering and finance. In this article, I explore similarities and differences between the dose-finding and the stochastic approximation literatures. This review also sheds light on the present and future relevance of stochastic approximation to dose-finding clinical trials. Such connections will in turn steer dose-finding methodology on a rigorous course and extend its ability to handle increasingly complex clinical situations.

During the last twenty years there have been considerable methodological developments in the design and analysis of Phase 1, Phase 2 and Phase 1/2 dose-finding studies. Many of these developments are related to the continual reassessment method (CRM), first introduced by O’Quigley, Pepe and Fisher (1990). CRM models have proven themselves to be of practical use and, in this discussion, we investigate the basic approach, some connections to other methods, some generalizations, as well as further applications of the model. We obtain some new results which can provide guidance in practice.

Traditionally, the major objective in phase I trials is to identify a working-dose for subsequent studies, whereas the major endpoint in phase II and III trials is treatment efficacy. The dose sought is typically referred to as the maximum tolerated dose (MTD). Several statistical methodologies have been proposed to select the MTD in cancer phase I trials. In this manuscript, we focus on a Bayesian adaptive design, known as escalation with overdose control (EWOC). Several aspects of this design are discussed, including large sample properties of the sequence of doses selected in the trial, choice of prior distributions, and use of covariates. The methodology is exemplified with real-life examples of cancer phase I trials. In particular, we show in the recently completed ABR-217620 (naptumomab estafenatox) trial that omitting an important predictor of toxicity when dose assignments to cancer patients are determined results in a high percent of patients experiencing severe side effects and a significant proportion treated at sub-optimal doses.

An early phase clinical trial is the first step in evaluating the effects in humans of a potential new anti-disease agent or combination of agents. Usually called “phase I” or “phase I/II” trials, these experiments typically have the nominal scientific goal of determining an acceptable dose, most often based on adverse event probabilities. This arose from a tradition of phase I trials to evaluate cytotoxic agents for treating cancer, although some methods may be applied in other medical settings, such as treatment of stroke or immunological diseases. Most modern statistical designs for early phase trials include model-based, outcome-adaptive decision rules that choose doses for successive patient cohorts based on data from previous patients in the trial. Such designs have seen limited use in clinical practice, however, due to their complexity, the requirement of intensive, computer-based data monitoring, and the medical community’s resistance to change. Still, many actual applications of model-based outcome-adaptive designs have been remarkably successful in terms of both patient benefit and scientific outcome. In this paper I will review several Bayesian early phase trial designs that were tailored to accommodate specific complexities of the treatment regime and patient outcomes in particular clinical settings.

Optimal design of a Phase I cancer trial can be formulated as a stochastic optimization problem. By making use of recent advances in approximate dynamic programming to tackle the problem, we develop an approximation of the Bayesian optimal design. The resulting design is a convex combination of a “treatment” design, such as Babb et al.’s (1998) escalation with overdose control, and a “learning” design, such as Haines et al.’s (2003) c-optimal design, thus directly addressing the treatment versus experimentation dilemma inherent in Phase I trials and providing a simple and intuitive design for clinical use. Computational details are given and the proposed design is compared to existing designs in a simulation study. The design can also be readily modified to include a first stage that cautiously escalates doses similarly to traditional nonparametric step-up/down schemes, while validating the Bayesian parametric model for the efficient model-based design in the second stage.

Martin Bradbury Wilk was born on December 18, 1922, in Montréal, Québec, Canada. He completed a B.Eng. degree in Chemical Engineering in 1945 at McGill University and worked as a Research Engineer on the Atomic Energy Project for the National Research Council of Canada from 1945 to 1950. He then went to Iowa State College, where he completed a M.Sc. and a Ph.D. degree in Statistics in 1953 and 1955, respectively. After a one-year post-doc with John Tukey, he became Assistant Director of the Statistical Techniques Research Group at Princeton University in 1956–1957, and then served as Professor and Director of Research in Statistics at Rutgers University from 1959 to 1963. In parallel, he also had a 14-year career at Bell Laboratories, Murray Hill, New Jersey. From 1956 to 1969, he was in turn Member of Technical Staff, Head of the Statistical Models and Methods Research Department, and Statistical Director in Management Sciences Research. He wrote a number of influential papers in statistical methodology during that period, notably testing procedures for normality (the Shapiro–Wilk statistic) and probability plotting techniques for multivariate data. In 1970, Martin moved into higher management levels of the American Telephone and Telegraph (AT&T) Company. He occupied various positions culminating as Assistant Vice-President and Director of Corporate Planning. In 1980, he returned to Canada and became the first professional statistician to serve as Chief Statistician. His accomplishments at Statistics Canada were numerous and contributed to a resurgence of the institution’s international standing. He played a crucial role in the reinstatement of the Cabinet-cancelled 1986 Census. He remained active after his retirement, serving as a Senior Advisor to the Privy Council Office as well as on several national commissions. In addition, he chaired the Canadian National Task Forces on Tourism Data and on Health Information. Martin is a former President of the Statistical Society of Canada (SSC) and Vice-President of the American Statistical Association (ASA). He is an elected member of the International Statistical Institute and an honorary member of the SSC. He has received many honors, including the George Snedecor Prize, the Jack Youden Prize, the F.G. Brander Memorial Award, the SSC Gold Medal, and a Distinguished Alumni Achievement Citation from Iowa State University. He is a fellow of the Institute of Mathematical Statistics, the American Statistical Association, the Royal Statistical Society, the American Association for the Advancement of Science, and the New York Academy of Science. He was made an Officer of the Order of Canada in 1999 for his “insightful guidance on important matters related to our country’s national statistical system.”

The following conversation took place at Martin Wilk’s home in Salem, Oregon, October 6–7, 2005.