The current AI paradigm at best reveals correlations between model input and output variables. This falls short of addressing health and healthcare challenges where knowing the causal relationship between interventions and outcomes is necessary and desirable. In addition, biases and vulnerability in AI systems arise, as models may pick up unwanted, spurious correlations from historic data, resulting in the widening of already existing health inequalities. Causal AI is the key to unlock robust, responsible and trustworthy AI and transform challenging tasks such as early prediction, diagnosis and prevention of disease. The Causality in Healthcare AI with Real Data (CHAI) Hub will bring together academia, industry, healthcare, and policy stakeholders to co-create the next-generation of world-leading artificial intelligence solutions that can predict outcomes of interventions and help choose personalised treatments, thus transforming health and healthcare. The CHAI Hub will develop novel methods to identify and account for causal relationships in complex data. The Hub will be built by the community for the community, amassing experts and stakeholders from across the UK to 1) push the boundaries of AI innovation; 2) develop cutting-edge solutions that drive desperately needed efficiency in resource-constrained healthcare systems; and 3) cement the UK's standing as a next-gen AI superpower. The data complexity in heterogeneous and distributed environments such as healthcare exacerbates the risks of bias and vulnerability and introduces additional challenges that must be addressed. Modern clinical investigations need to mix structured and unstructured data sources (e.g. patient health records, and medical imaging exams) which current AI cannot integrate effectively. These gaps in current AI technology must be addressed in order to develop algorithms that can help to better understand disease mechanisms, predict outcomes and estimate the effects of treatments. This is important if we want to ensure the safe and responsible use of AI in personalised decision making. Causal AI has the potential to unearth novel insights from observational data, formalise treatment effects, assess outcome likelihood, and estimate 'what-if' scenarios. Incorporating causal principles is critical for delivering on the National AI Strategy to ensure that AI is technically and clinically safe, transparent, fair and explainable. The CHAI Hub will be formed by a founding consortium of powerhouses in AI, healthcare, and data science throughout the UK in a hub-spoke model with geographic reach and diversity. The hub will be based in Edinburgh's Bayes Centre (leveraging world-class expertise in AI, data-driven innovation in health applications, a robust health data ecosystem, entrepreneurship, and translation). Regional spokes will be in Manchester (expertise in both methods and translation of AI through the Institute for Data Science and AI, and Pankhurst Institute), London (hosted at KCL, representing also UCL and Imperial, leveraging London's rapidly growing AI ecosystem) and Exeter (leveraging strengths in philosophy of causal inference and ethics of AI). The hub will develop a UK-wide multidisciplinary network for causal AI. Through extended collaborations with industry, policymakers and other stakeholders, we will expand the hub to deliver next-gen causal AI where it is needed most. We will work together to co-create, moving beyond co-ideation and co-design, to co-implementation, and co-evaluation where appropriate to ensure fit-for-purpose solutions Our programme will be flexible, will embed trusted, responsible innovation and environmental sustainability considerations, will ensure that equality diversity and inclusion principles are reflected through all activities, and will ensure that knowledge generated through CHAI will continue to have real-world impact beyond the initial 60 months.

We live in the "Era of Mathematics" (UKRI, 2018), in which mathematics research has deep and widespread impact. Medical imaging is enhanced using the theory of inverse problems. Predicting sewage contamination in waterways after storms requires solving complicated systems of hydrodynamic equations. Machine learning tools are revolutionising data-intensive computing and, handled with proper mathematical care, have vast potential benefits for science and society. These are examples of the ongoing explosion in mathematical innovation driving, and being driven by, the analysis and modelling of data running through every aspect of life. Cutting-edge research now sits at the interface of data science and mathematical modelling. Methods and fields such as compressed sensing, stochastic optimisation, neural networks, Bayesian hierarchical models - to name but a few - have become interwoven and contributed to the delivery of a new domain of research. We refer to this research interface as "statistical applied mathematics". Established in 2014, the Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa, samba.ac.uk) delivers leading research and training in this space. In the development of this bid, we have consulted widely with academic, industrial, and governmental partners, who consistently report a large and widening gap between demand and supply for highly skilled graduates. Our vision is to create a new generation of statistical applied mathematicians ready to lead high-impact, data-driven, mathematically-robust research in academia and industry. We will nurture a vibrant culture of cohort learning, enabling internationally-leading training in modern mathematical data science. A particularly important research focus will be the synthesis of data-driven methods with robust mathematical modelling frameworks. Tomorrow's industrial mathematicians and statisticians must understand when machine learning tools are (and are not) appropriate to use and be able to conduct the underpinning research to improve these tools by integrating scientific domain knowledge. This research challenge is informed by deep partnerships with a range of industry and government bodies. Our long-term partners such as BT, Syngenta, Novartis, the NHS, and the Environment Agency co-create our vision and our training. They are emphatic that we must address the urgent need for mathematical data science talent in this key strategic area for the UK economy. Many of our students will work directly on industry challenges during their PhD either in their core research or with internships. Our unique Integrative Think Tanks are the key mechanism for exploring new research ideas with industry. These are week-long events where SAMBa students, leading academics, and partners work together on industrial and societal problems. SAMBa graduates will be able to develop and apply new ideas and methods to harness the power of data to tackle challenges affecting society, the economy, and the environment. Our students will move into academia, providing sustainability to the UK's capacity in this field, as well as industry and government, providing impact through societal benefits and driving economic growth. Many alumni now hold permanent positions at leading UK universities and senior positions in a range of businesses. The CDT will be embedded within the University of Bath's Department of Mathematical Sciences, where 98% of the research is world leading or internationally excellent (REF2021). The CDT is supported by 58 academics in maths, with similar numbers of co-supervisors from industry and other departments. The centre will be co-delivered with 22 industry and government partners. A vital international perspective is provided by a worldwide network of 11 academic institutions sharing our scientific vision.

Digital Health technologies can make a positive difference to the outcomes of patient treatment, management and care. Improving digital services and the sharing and use of data will also save time and resources so that staff can better focus on delivering medical and social care. Examples of such technologies include data collected through smartphones. For example, the ZOE COVID Symptom Study App used during the pandemic was jointly developed by King's College London, and now has more than four million users. Other digital technologies include wearable devices which can help monitor heart rate, activity and sleep and remotely assess and help manage a wide range of conditions. For example, the £23M Innovative Medicines Initiative RADAR-CNS led by King's has pioneered their use in depression, multiple sclerosis and epilepsy. Our aim is to enable the development of new digital technologies and reduce the time it takes for these to benefit patient care. The King's Health Partner (KHP) Digital Health Hub will do this by helping researchers, health and social care staff, patients and industry to work together better. We also hope to increase the availability of such technologies nationally by offering support to enable new businesses to grow rapidly, thereby making a more immediate difference to patients' lives. Digital health technologies have lots of potential but their widespread use is limited by: - A lack of examples of how clinicians, academics, engineers, quality assurance experts, health economists, patients and end users can best work together during development - Specific gaps in training and knowledge amongst the different groups, for example: - Academic and industry technologists may have trouble understanding NHS systems and fail to engage with the end users of the technologies they are trying to develop, such as health care providers, patients and carers. They may not know about or understand the complex regulatory pathway which needs to be followed before such technologies can be used in clinical practice. - Clinical specialists may lack the appropriate technical skills such as data analyses, coding and programming languages to help them develop digital applications they think will be helpful to their patients. The KHP Digital Health Hub will help to overcome the barriers to the rapid development and use of digital technologies nationally. It will be an accessible "ecosystem" comprising specialists from different sectors working together to improve understanding and use of digital technologies and addressing the government's long-term goals for health and social care. With our partners, we will connect the digital health research community to the substantial opportunities for investment in London and our diverse and world leading healthcare research environment. We have brought together a wealth of expertise from across KHP, including King's College London and partner NHS Trusts, patients and industry collaborators, to provide support and training, and create opportunities for the acceleration of digital health across the UK. KHP includes seven mental health and physical healthcare hospitals and many community sites with ~4.8 million patient contacts each year and a combined annual turnover of more than £3.7 billion. The KHP Digital Health Hub will provide: - proven expertise, infrastructure and experience of co-creation and commercialisation - a three-way clinical, academic and industry partnership - a physical location where technology developers can work collaboratively, and - an excellent track record in training which will be offered to all our partners across the health and social care sectors. With the right support and networks in place, digital health technologies have the power to transform patient care and experiences across the UK. The knowledge and expertise is all there, and together we can make sure it is shared, translated and built upon, at every step of the way.