Predictive inference for clinical trials with the parametric bootstrap

The development of cutting-edge medical treatments requires targeted statistical methods for the analysis of clinical trial data. In this arena, many questions of interest have a distinctively causal flavor. What is the expected effect of a new drug or vaccine on patient outcomes over time? How does that effect vary across different subgroups of the population? Can these conclusions be strengthened by incorporating observational or historical data? It is clear that 21st-century biomedical research necessitates thoughtful and original advancements in the area of causal inference.

The general aim of this project is to develop the theory and practice of predictive inference within a Bayesian framework as a novel and unique approach to these questions. Given observed data from an unknown parametric sampling distribution, the standard Bayesian approach would be to elicit a prior density and likelihood function, then derive the posterior density. The predictive approach, however, notes that the statistical uncertainty in this posterior arises entirely from the fact that we can only observe a limited sample of data and are therefore missing observations. If we could observe infinite data, then any parameter of interest would be fully defined.

An alternative method is therefore to directly model the predictive density and then impute further observations through a bootstrap resampling procedure, effectively transforming the statistical inference problem into a missing data problem. This predictive resampling viewpoint provides an interesting lens through which to view the analysis of clinical trials. In particular, the focus of a clinical trial is generally on how the treatment will affect patient outcomes. The predictive approach therefore addresses this question more directly by taking the actual future data points as the objects of inference, rather than working through a parameter which may be an artifical model construct.

Bayesian predictive inference also provides a novel perspective on questions related to uncertainty quantification and hypothesis testing. A standard frequentist hypothesis test would likely attempt to derive a density function for some estimator, then use it to calculate confidence intervals and p-values. Instead, our approach again considers the concept of sampling the missing or unobserved data repeatedly in order to generate several complete datasets. Any hypothesis can then be evaluated with respect to the multiverse of "true parameters" arising from these datasets. The final result is a prior-free Bayesian alternative to traditional methods of hypothesis testing. Through our collaboration with Novo Nordisk, we will apply these methods to real-world clinical trial data, including treatments for heart disease and diabetes.

This project falls under the "Statistics and applied probability" EPSRC research area, which involves "statistical methodology and development of new probabilistic techniques inspired by applications". It is co-funded by Novo Nordisk and supervised by Professor Chris Holmes, with additional collaboration from Professor Stephen Walker.

The primary CDT impact will be training 75 PhD graduates as the next generation of leaders in statistics and statistical machine learning. These graduates will lead in industry, government, health care, and academic research. They will bridge the gap between academia and industry, resulting in significant knowledge transfer to both established and start-up companies. Because this cohort will also learn to mentor other researchers, the CDT will ultimately address a UK-wide skills gap. The students will also be crucial in keeping the UK at the forefront of methodological research in statistics and machine learning.
After graduating, students will act as multipliers, educating others in advanced methodology throughout their career. There are a range of further impacts:
- The CDT has a large number of high calibre external partners in government, health care, industry and science. These partnerships will catalyse immediate knowledge transfer, bringing cutting edge methodology to a large number of areas. Knowledge transfer will also be achieved through internships/placements of our students with users of statistics and machine learning.
- Our Women in Mathematics and Statistics summer programme is aimed at students who could go on to apply for a PhD. This programme will inspire the next generation of statisticians and also provide excellent leadership training for the CDT students.
- The students will develop new methodology and theory in the domains of statistics and statistical machine learning. It will be relevant research, addressing the key questions behind real world problems. The research will be published in the best possible statistics journals and machine learning conferences and will be made available online. To maximize reproducibility and replicability, source code and replication files will be made available as open source software or, when relevant to an industrial collaboration, held as a patent or software copyright.