I was privileged to have David Cox as a supervisor for my PhD (1983–1986) on the flow of water in dry rivers. The topic provoked laughter in the United Kingdom, but was familiar to me as an African born and bred. I learned from David to think about assumptions, and check what mathematicians had already demonstrated on mathematical functions and integrals. I often went to the library to search through the classic volumes informally known to pre-internet mathematicians as Abramowitz and Stegun and Gradshteyn and Ryzhik. I still try to think how I might get an approximate analytical solution to a likelihood function or an estimator rather than immediately resorting to simulation. David’s phrase “with some regularity conditions,” in relation to properties of estimators stayed with me. The phrase was behind a minor but surprisingly controversial article I wrote (Hutton, 2000) on a measure of comparison of rates, “Number needed to treat: properties and problems.” The number needed to treat is the inverse of a difference between two estimated rates, such as cure rates for two treatments (Cook and Sackett, 1995). The authors recommended including ‘Confidence intervals’ formed by inverting the confidence intervals for the difference. If the interval spans zero, a basic condition is violated.
Perhaps my questions about assumptions explain my limited use of Bayesian methods. In my applied work, I rarely see explanatory variables that can be assumed to be mutually independent. David remarked that multivariate independence is a strong assumption, and defining plausible prior distributions is nontrivial. I’ve noticed that the default prior distributions used by various software packages result in almost all of the probability falling outside the plausible ranges for parameters. This is obvious in linear regression with uninformative prior distributions with large variances. I prefer to specify frequentist models, unless I have worked sufficiently in an application area to specify informed prior distributions.
Some London School of Economics philosophers were excited by Bayesian approaches, and arranged a conference on the ethics of statistical methods used in medical studies. The philosopher who initiated the conference lectured on the supremacy of Bayesian methods, which he asserted render randomized controlled trials redundant and unethical. He announced that randomization was as relevant to modern medicine as leeches, obviously unaware that leeches are still used! Bayesian methods render designed experiments redundant, as prior information allowed informed decisions to be made about new treatments. He was confident that all relevant information would be in medical records: “After all, surgeons’ shoe sizes are irrelevant.” Looks were exchanged by those who were easily able to connect shoe size with type and success of surgery. David’s 1985 question, “What is the prior distribution on an unknown variable?” came to mind.
There were many contributions during the discussion. David was brief. He stood up, said “There are books on this topic, which ought to be read,” and sat down. I have enjoyed reading some of David's books, but there is so much more to be read, and reread.
David’s ability to communicate effectively in a difficult situation was matched by his kindness, humor, and humility. Warwick Statistics moved into a new building 20 years ago. Our first seminar was given by David. Unfortunately, the technical aspects of the new facilities challenged us. I found the button to lower a screen. The projector was switched on, and shone in the wrong direction. I climbed up bars attached to the back wall to point the beam at the screen. An increasingly embarrassed colleague tried to connect the computer. David kindly wandered to the other side of the room, so the focus was not on the computer. After 10 minutes, he began giving his seminar on badgers and tuberculosis. He gave a compelling talk without any of his prepared material. Now and again he would say, “and here I would have shown a map, or a graph,” with a quiet smile.
Clarity with regard to assumptions has also been very important in my contributions as an expert witness, as a trustee of a very large pension scheme, and in considering the ethical issues in decision-making under uncertainty. I think David was mildly disappointed by my being distracted by a range of interests, so I was grateful that he encouraged me to keep tackling pensions issues.
David’s work and life has been a source of refreshment for me, not a dry river.
Jane L. Hutton has no financial or non-financial disclosures to share for this article.
Cook, R. J., & Sackett, D. L. (1995) The number needed to treat: A clinically useful measure of treatment effect. BMJ, 310(6977), 452–454. https://doi.org/10.1136/bmj.310.6977.452
Hutton, J. L. (2000). Number needed to treat: Properties and problems. Royal Statistical Society: Series A (Statistics in Society), 163(3), 403–419. https://doi.org/10.1111/1467-985X.00175
©2023 Jane L. Hutton. This article is licensed under a Creative Commons Attribution (CC BY 4.0) International license, except where otherwise indicated with respect to particular material included in the article.