Sofía Villar is a postdoctoral research associate member of Adrian Mander’s trial design research programme, in Design and Analysis of Randomised Trials (DART) of the Medical Research Council (MRC) Biostatistics Unit (BSU).
Sofia currently works on an MRC funded project “Designing and analysing multi-arm multi-stage clinical trials with one or more endpoints”. The project is a cross-institutional initiative between the Statistics Groups at the University of Lancaster and the MRC Biostatistics Unit Hub for Trials Methodology Research in Cambridge led by Thomas Jaki (Lancaster), Jack Bowden and James Wason (Cambridge).
She has recently also been awarded a Biometrika Trust fellowship. It is the first Biometrika Trust fellowship to be awarded, so it a great achievement. This is a two-year research fellowship, for junior researchers in statistical theory and methodology, “aimed at those among the most outstanding recent PhD graduates who are capable of self-direction.”
The BSU, as host department will provide a stimulating and inclusive research environment, and Sofía’s career development will be supported through mentoring and her ongoing collaboration with Jack Bowden and James Wason. Her research will also be supported by collaborations with Lancaster University (Thomas Jaki and Peter Jacko) and MD. Anderson Cancer Center, in Houston U.S. (Don Berry).
Current research work
Clinical trials are prospective research studies on human subjects that are designed to answer specific questions about the effectiveness of treatment interventions. A particular goal of some clinical trials is to choose the most efficacious drug among several options. In this setting a trial design can be considered ‘optimal’ if it maximises the number of patients receiving the truly best treatment, since this maximises the benefit to patients who take part.
The methodological approach applied in Sofía’s PhD thesis is part of a large body of theoretical literature known as bandit problems, accumulated during the past 50 years and which has long been motivated by the optimal design of multi-arm clinical trials. It provides a rationale for efficiently learning which treatment is the best and then exploiting this knowledge for the benefit of future patients. Despite this long standing theoretical work developed in this area, bandit methods have never actually been applied in a real clinical trial.
Sofía’s research during the past year and a half has focused on identifying the limitations to the use of bandit approaches in practice. Her future research plan is based on developing the necessary methodological extensions to overcome them, so that they can be fully exploited in future clinical research.
Why is this research important? Why is it timely? What impact will it have?
Possibly the most relevant limitation to the bandit results, and the one with the largest impact, is to extend the methodology to deal with the more general case in which there is an unknown delay in observing patient outcomes, as it is the case in cancer trials where the outcome is ‘time until death’. This is one of the key research lines Sofia plans to pursue as part of her fellowship.
This line of Sofía’s work also led her to start a dialogue about bandit models and clinical trial design with Prof. Donald Berry, whose background includes both Bayesian Statistics and bandit problems and whose research has impacted health-research broadly, and most notably in cancer. This contact led to her recent research visit in February-March 2014 to the M.D. Anderson Center of the University of Texas.
Additionally, developing trials based on these optimisation ideas can be a solution for rare diseases, for which there are substantial methodological difficulties due to patient recruitment constraints. Such trials would learn within the trial so as to maximise the successful treatment of patients in the trial and that of future patients, taking into consideration the size of the population of patients with a disease to do so.
The impact of developing efficient research methodologies of rare disease is likely to become larger, as disease categories are being fragmented into finer and finer entities. Also, as stratified medicine tries to identify and develop treatments that are effective for particular groups of patients, based on identifying subgroups of patients with distinct mechanisms of disease through genomic approaches. Therefore, trials in the future can be expected to have smaller patient populations.
Origins of this research work
Sofia Villar received her PhD in Business Administration and Quantitative Methods from Universidad Carlos III de Madrid, Spain, for her research within the field of sequential estimation and optimization. Her doctoral thesis led to the presentation and publication of three articles in leading-edge applied conference proceedings and she also received an outstanding PhD thesis award from her former University.
In her PhD thesis she studied problems arising in modern sensing systems and developed rules for improving their performance. Modern sensing technologies offer the possibility of efficiently performing tasks (e.g. tracking multiple moving objects) by adaptively deploying its sensing resources based on the information extracted from past measurements.
However, deriving optimal adaptive rules for such tasks based on mathematical formulations, at least for realistic scenarios, typically have a prohibitively large computational cost, which dramatically delays its practical application.
Sofia’s work contributed to addressing this limitation by proposing heuristic methods (a simpler solution requiring less computational intensity), based on a novel methodological approach to dynamic optimisation problems, which are computational feasible and nearly optimal. This may facilitate a faster implementation and better performance of modern sensing technologies in the near future.
The figure shows the results of a simulation replicating 10000 trials of 423 patients each, in which 4 treatments were being studied, a control arm vs. 3 experimental arms. The outcome measured in patients was binary, i.e., 1 stands for a successful patient treated (e.g., remission of a tumour), while 0 stands for a failure. In all the replicas one of the experimental arms was assumed to be better than all the other arms (in particular, the success rate of it was of 5 successes in 10 patients in average while for all the others treatments it was of 3 out of 10).
The simulation compared 6 different trials a design, broadly classified into traditional & other designs and bandit based. Two properties are displayed: on the horizontal axis: power, which is the probability of a trial ending with the conclusion that the experimental is better than the control treatment. On the vertical axis: the average number of successfully treated patients.
The figure illustrates the tension between these two attractive properties (power and average number of successes). Designs that achieve a high power do so by allocating patients to all treatments and this naturally works contrary to maximising successes which is attained by allocating more patients to the best treatment. On the top left corner of this figure there is a bandit design that attains the best balance between the two goals, i.e., it manages to attain a high power level and a high number of mean number of successes. This so called ‘controlled’ bandit approach is a combination of the two type of designs which tries to ensure a sufficient number in the control treatment while it uses the bandit ideas for allocating patients among the experimental treatments.
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