There is a growing interest in personalised medicine where individual heterogeneity is incorporated into decision-making and treatments are tailored to individual patients or patient subgroups in order to provide better healthcare. The National Health Service Blood and Transplant (NHSBT) in England aims to move towards a more personalised service and the National Institute for Health Research Blood and Transplant Research Unit (NIHR BTRU) call has mandated research to “identify, characterise and exploit biomarkers in personalising donation strategies to maximise donor health and the blood supply”. The work presented in this thesis was motivated by a large-scale, UK-based blood donation trial called INTERVAL. In INTERVAL, male donors were randomly assigned to 12-week, 10-week, and 8-week inter-donation intervals, and female donors to 16-week, 14-week, and 12-week inter-donation intervals. The outcomes of this trial include the amount of blood collected (primary), the number of low haemoglobin deferrals, and donor's quality of life. The INTERVAL trial has collected a wealth of information on individual donor characteristics, enabling us to explore (i) whether different inter-donation intervals should be recommended for donors with different characteristics (by age, blood measurements, etc.), and (ii) donor stratification schemes, for example, how to partition donors into those who have the capacity to give blood more frequently than the general donor population and those who tend to be deferred more often due to safety concerns than the average donors.

One of the main statistical challenges arising from the development of personalised donation strategies using the data from the INTERVAL trial is that there are three (ordered) randomised groups for each gender in this trial, while the majority of existing statistical approaches developed in the personalised medicine context can only handle two randomised groups and thus are not directly applicable to the INTERVAL data. This thesis aims to address issues related to this added methodological complexity. We hope that the methodologies developed in this thesis can not only help us better analyse the INTERVAL data but also facilitate the analysis of other multi-arm trials in a wider range of medical applications in addition to blood donation.

We begin by summarising methods that can be used to estimate the optimal individualised treatment rule (ITR) in multi-arm trials and comparing their performance in large-scale trials via simulation studies in Chapter 2. We also apply these methods to the data from male donors in the INTERVAL trial to estimate the optimal personalised donation strategies under three different objectives: (i) maximise the total units of blood collected by the blood service, (ii) minimise the low haemoglobin deferral rates, and (iii) maximise a utility score that “discounts” the total units of blood collected by the incidences of low haemoglobin deferrals.

The three inter-donation intervals in the INTERVAL trial exhibit a natural ordering, and applying the ITR estimation methods that ignore the ordinality may result in suboptimal decisions. We are thus motivated to propose a method that effectively incorporates information on the ordinality of randomised groups to identify the optimal ITR in the ordinal-arm setting in Chapter 3. We further develop variable selection methods under the proposed framework to handle situations with noise covariates that are irrelevant for decision-making. Through simulation studies and an application to the data from a target donor population (“much-in-demand but vulnerable”) in the INTERVAL trial, we demonstrate that the proposed method has superior performance over methods that ignore the ordinality.

In Chapter 4, we switch focus to donor (or “patient” in a more general sense) stratification in multi-arm trials and develop a novel method for stratifying subjects with heterogeneous intervention responses and covariate profiles into more homogeneous subgroups using Bayesian clustering techniques. The “imputed” potential outcomes under different randomised groups are linked to subjects’ baseline characteristics nonparametrically through cluster (subgroup) memberships. We examine the performance of our proposed method via simulation studies and we illustrate the utility of the method by applying it to the INTERVAL data to stratify donors based on their capacity to donate.