PhD Opportunities - MRC Biostatistics Unit

Brian Tom (Precision Medicine) brian.tom@mrc-bsu.cam.ac.uk

Paul Kirk (Biostatistical Machine Learning) - paul.kirk@mrc-bsu.cam.ac.uk

Background: In many settings there is a need to either prioritise certain types of data, regulate the influence of different pieces of information or remove irrelevant variables when performing regression or clustering. For example, when certain types of variables are either of better quality than others, it may be better to up-weight these variables relative to others to get more reliable and stable models. If certain variables/modalities are easier to measure, cheaper to collect or more routinely used in clinical settings, then it may be preferable to adopt a more decision-theoretic solution where costs are traded-off with the benefits of better information. Moreover, situations arise when prioritisation allows targeted solutions to the specific clinical question at hand. Applied motivation for investigating prioritisation of variables comes from collaborations in osteoarthritis and dementia where to a lesser or greater extent, clinical outcome has had a minor or major role in determining cluster structure. In the mixture regression model context (e.g. two-part, latent class mixed model and joint latent class models), where intrinsically linked sub-models are formulated as regressions with common subset of covariates, it is unclear how best to do variable selection. Adaptive regularisation may be an option.

Aim of Project: To investigate and provide recommendations on how best to prioritise, regulate or perform variable selection for mixture models used to uncover latent structures.

Methods: We envisage that there will be various approaches amenable to the general problem of prioritisation. The exact approach may be dependent on the reasons for up- or down-weighting variables and the clinical questions addressed. However, possible strategies could involve (i) weighted likelihoods; (ii) adaptive regularisation; (iii) informative priors; and (iv) decision-based or multi-task learning approaches with loss functions.

Supervisors: This project will be supervised by Dr Brian Tom, Programme Leader in Precision Medicine Theme, Dr Paul Kirk, Programme Leader in Biostatistical Machine Learning and Professor Sylvia Richardson (Emeritus Professor and former Director of the MRC Biostatistics Unit)

David Robertson (Efficient Study Design) - david.robertson@mrc-bsu.cam.ac.uk

Traditional clinical trials follow a design that is fixed in advance, with the data only analysed after completion when all trial participants have been recruited and have accrued outcome data. In contrast, adaptive designs allow for pre-planned modifications to the trial's course based on accumulating data from participants in the trial.

Appropriate estimation of treatment effects is a key part of the validity of any clinical trial, which includes point estimates and the quantification of uncertainty as given by confidence intervals (CIs). A fundamental problem for ADs is that the use of standard methods to construct point estimators and CIs (i.e., methods that do not account for the fact an AD has been used) can result in undesirable properties, such as bias and undercoverage [1-4]. The aim of this PhD project is to develop and extend methods to construct adjusted point estimators and CIs that take into account the adaptive design used, as well as open-source software to implement the methods in practice. One key unresolved question that the PhD will focus on is when conditional or unconditional inference is more appropriate, i.e., when the analysis should be conducted conditional on the observed design. A recent proposal [5] provides a general framework for exploring this question for point estimation, which could be extended and used for different types of adaptive designs.

[1] Robertson et al. (2023a). Point estimation for adaptive trial designs I: A methodological review. https://doi.org/10.1002/sim.9605

[2] Robertson et al. (2023b). Point estimation for adaptive trial designs II: Practical considerations and guidance. https://doi.org/10.1002/sim.9734

[3] Robertson et al. (2024a). Confidence Intervals for Adaptive Trial Designs I: A Methodological Review. https://doi.org/10.1002/sim.70174

[4] Robertson et al. (2024b). Confidence Intervals for Adaptive Trial Designs II: Case Study and Practical Guidance.https://doi.org/10.1002/sim.70202

[5] Marschner (2021). A General Framework for the Analysis of Adaptive Experiments. https://doi.org/10.1214/20-STS803

Anne Presanis (Population Health) - anne.presanis@mrc-bsu.cam.ac.uk

Sofia Villar (ESD) - sofia.villar@mrc-bsu.cam.ac.uk

Human Immunodeficiency Virus (HIV) and other sexually transmitted infections (STIs) can cause severe health problems and outcomes, impacting different population groups unequally. England has therefore set goals to eliminate HIV transmission by 2030 and reduce harms from and inequalities associated with STIs. Monitoring the incidence and undiagnosed prevalence of HIV and STIs is crucial for achieving these goals and evaluating the effectiveness of interventions to reach them. These are quantities that cannot be observed: nevertheless, they can be estimated, through the careful synthesis, in a Bayesian framework, of multiple data sources that, together, indirectly inform prevalence and incidence (Presanis et al, 2021; Brizzi, Birrell et al, 2021). Prevalence estimates have been so far stratified by age group, sex, exposure, ethnicity, year and broad region; and incidence estimates by age group only for one exposure group. 

To effectively monitor progress, it is crucial that trends in incidence and undiagnosed prevalence are obtained at finer granularity than so far developed, particularly by geography (e.g. local authority). However, it is challenging to obtain finely-stratified estimates, due to small sample sizes leading to privacy concerns and large uncertainty in estimates. This challenge can be overcome using hierarchical modelling assumptions of exchangeability across strata, allowing borrowing of strength across strata. However there are trade-offs in the strength of such assumptions and levels of granularity of estimates that are required to ensure local prevention, testing and treatment interventions are designed, implemented and evaluated effectively. Furthermore, these objectives, and the optimal targeting of interventions to key population groups, may vary over time as an epidemic and available resources evolve. 

Focussing on HIV and syphilis, and building on previous evidence syntheses (Presanis et al, 2021), this PhD will first develop Bayesian hierarchical spatial models integrating multiple data sources to estimate local area prevalence. Then there will be opportunities to develop these models further to estimate incidence; and to apply methods for optimal surveillance of infectious disease (e.g. Cheng et al, 2020) to the problem of jointly updating local area estimates and targeting HIV and syphilis testing and prevention efforts to population groups most in need. This project will be carried out in close collaboration with colleagues at the UK Health Security Agency; and with Daniela De Angelis and Christopher Jackson in the Population Health theme at the MRC Biostatistics Unit.

Dominique-Laurent Couturier (Efficient Study Design) - dominique.couturier@mrc-bsu.cam.ac.uk

Thomas Jaki (Efficient Study Design) - thomas.jaki@mrc-bsu.cam.ac.uk

Background to the project: Digital healthcare is a very dynamic field aiming to enhance patient health, from diagnostic to treatment, through the collection and analysis of increasingly larger digital health records. Examples include the use of deep learning (DL) algorithms to improve disease detection and diagnosis based on medical images such as MRIs and CT scans [1,2], the use of machine learning (ML) algorithms to inform patient treatment based on clinical and genomic profiles [3], and the use of wearable devices to monitor patient health [4,5]. These algorithms and devices are regularly updated to follow the latest developments in DL/ML theory [5], in medical knowledge, with, for example, the availability of new or different health data [6], as well as the latest technological improvements, possibly leading to more affordable and improved health devices [7].

What the studentship will encompass: While guidance on how to use adaptive designs to evaluate medical devices exist [8], no such recommendation is available when considering updates of such algorithms and devices. This project aims to fill this gap by focusing on developing novel efficient adaptive designs for the evaluation of updates to algorithms and devices in digital healthcare when a re-evaluation is deemed necessary. The project will focus on two scenarios:

• Update of healthcare devices:

Nowadays wearable health devises typically provide a multitude of longitudinal outcomes, like, for example, heart and respiratory rates, physical activity, sleep patterns, body temperature and glucose levels. A device producer may be interested in verifying that such measures are the same following an update related to the use of an improved technology and/or a change in production. Existing methods in (adaptive) equivalence testing are typically design dependent and consider a small number of outcomes [9,10]. A first aim of this project is therefore to develop more efficient and general adaptive methods in equivalence testing in the context of large number of dependent outcomes.

• Update of healthcare algorithms:

Improved algorithms are typically expected to be developed regularly and to do as well or better than their previous versions. A second aim of this project is therefore to develop adaptive methods in non-inferiority testing able to exclude that such changes led to a decrease in quality like a decrease in specificity and sensitivity for diagnosis classifier algorithms, for example, through time. A particular emphasis will therefore focus on methods allowing to preserve power when hypotheses are tested sequentially, as data becomes available, without knowledge of future algorithm improvements [11].

Detail of supervision: The project will be undertaken under the supervision Dr Dominique-Laurent Couturier and Professor Thomas Jaki at the MRC Biostatistics Unit (BSU), University of Cambridge, where the student will be based.

Collaborations: This project will be conducted in close collaboration with an industry partner, Pfizer US, with regular interactions to enhance the project's inputs and outcomes.

PPI:  Training on Patient and Public Involvement will be provided (e.g. through the NIHR Cambridge BRC). Input on the practicability of the proposed methods will be discussed on the basis of concrete applications with patient representatives when appropriate.

[1] Litjens, G. et al. (2017), A survey on deep learning in medical image analysis. Med. Image Anal. https://doi.org/10.1016/j.media.2017.07.005 

[2] Liu, X. et al. (2019), A comparison of deep learning performance against health-care professionals in detecting diseases from medical imaging: a systematic review and meta-analysis. The Lancet Digital Health. https://doi.org/10.1016/S2589-7500(19)30123-2 [3] Quazi S. (2022), Artificial intelligence and machine learning in precision and genomic medicine. Med Oncol. https://doi.org/10.1007/s12032-022-01711-1

[4] Smith, A.A. et al (2023), Reshaping healthcare with wearable biosensors. Sci Rep 13. https://doi.org/10.1038/s41598-022-26951-z [5] Shickel, B. et al (2018), Deep EHR: A survey of recent advances in deep learning techniques for electronic health record (EHR) analysis. IEEE J. Biomed. Health Inform. https://doi.org/10.1109/JBHI.2017.2767063

[6] Savage, N. (2023), Synthetic data could be better than real data. Nature. https://doi.org/10.1038/d41586-023-01445-8

[7] Iqbal, S.M.A. et al. (2021), Advances in healthcare wearable devices. NPJ Flexible Electronics. https://doi.org/10.1038/s41528-021-00107-x 

[8] FDA (2016), Adaptive Designs for Medical Device Clinical Studies - Guidance for Industry and Food and Drug Administration Staff, https://www.regulations.gov/docket/FDA-2015-D-1439

[9] Pallmann, P. and Jaki, T. (2017), Simultaneous confidence regions for multivariate bioequivalence. Statistics in Medicine. https://doi.org/10.1002/sim.7446

[10] Grayling, M. et al (2019), Two-Stage Adaptive Designs for Three-Treatment Bioequivalence Studies. Stat Biopharm Res. https://doi.org/10.1080/19466315.2019.1654911

[11] Tian, J. and Ramdas, A. (2022). Online control of the familywise error rate. Statistical Methods in Medical Research. https://doi.org/10.1177/0962280220983381

Kyriakos Flouris (Biomedical Machine Learning) - kyriakos.flouris@mrc-bsu.cam.ac.uk

Oscar Rueda (Precision Medicine) - oscar.rueda@mrc-bsu.cam.ac.uk

Background

Histopathology using haematoxylin and eosin (H&E) staining remains the clinical gold standard for diagnosing disease and guiding treatment decisions. However, H&E images capture only morphological features, while the mechanisms underlying prognosis, drug response, and resistance are fundamentally molecular. Emerging platforms such as Spatial Transcriptomics offer genome-wide gene expression resolved across tissue architecture, revealing rich biological states inaccessible to conventional microscopy. Yet these modalities are expensive, low-throughput, and suffer from significant technical variability across different scanners, staining protocols, and institutions. This "domain gap" prevents models trained on one dataset from generalizing to another. The opportunity lies in overcoming this barrier: by using transfer learning to robustly align these complex molecular maps with widely available tissue transcriptomics, we can unlock the ability to predict patient outcomes at scale, regardless of where the data was collected.

Aim of Project

To develop robust transfer learning and domain adaptation frameworks that leverage spatial transcriptomics to align heterogeneous tissue datasets for improved prognosis and drug response prediction.

Methods

We envisage a machine learning approach focused on generalization across diverse biological contexts. The methodology will likely involve (i) utilizing transfer learning from large-scale computational pathology foundation models to extract robust morphological features; (ii) developing domain adaptation strategies to mathematically align feature distributions across different cohorts, neutralizing the impact of scanner or staining variability; (iii) training models to map the rich, spatially-resolved molecular signals from spatial transcriptomics onto the more abundant bulk tissue profiles; and (iv) applying these unified representations to predict prognosis and therapeutic response in independent clinical validation sets.

Kyriakos Flouris (Biomedical Machine Learning) - kyriakos.flouris@mrc-bsu.cam.ac.uk

Biostatistics-Inspired Generative AI and Foundation Models

Biomedical systems are inherently complex, high-dimensional, and heterogeneous, often involving interactions across multiple scales and modalities. Traditional mechanistic models, based on differential equations, networks, or regulatory constraints, offer interpretability and generalizability but often require simplifications that omit emergent patterns or patient-specific variations. Modern machine learning, including deep generative models, excels at capturing high-dimensional nonlinear structures but can lack adherence to known mechanistic principles, limiting interpretability and reliability. Mechanistic-inspired generative models offer a promising middle ground: by incorporating domain knowledge as priors or constraints within flexible generative architectures, these models can produce realistic and interpretable synthetic data, reconstruct missing observations, and explore latent structure across patients or experimental conditions. This approach has broad applications, from modelling spatial tissue heterogeneity to integrating multi-modal imaging and omics data, and from predicting intervention effects to generating synthetic datasets for hypothesis testing.

Aims

To develop mechanistic-inspired generative models that integrate domain knowledge with high-dimensional biomedical data, enabling interpretable simulations, data reconstruction, and/or the discovery of latent biological structure.

Methods

The project will proceed through several key stages: (i) the exploration of flexible generative modelling approaches, including variational autoencoders, diffusion models, flow-based models, and emerging biomedical foundation models, (ii) the augmentation of these architectures with mechanistic or structure-preserving constraints derived from prior biological knowledge, curated networks, or physical principles, (iii) the training of models on diverse biomedical datasets, such as multi-modal imaging, spatial omics, or patient-level clinical measurements, (iv) the rigorous evaluation of these models for realism, interpretability, and utility for downstream tasks, including synthetic data generation, intervention exploration, or latent marker discovery, and (v) the development of extensions to integrate multiple data modalities or condition generative models on experimental or clinical covariates to explore hypothetical scenarios or interventions.

Kyriakos Flouris (Biomedical Machine Learning) - kyriakos.flouris@mrc-bsu.cam.ac.uk

Oscar Rueda (Precision Medicine) - oscar.rueda@mrc-bsu.cam.ac.uk

Background

Predicting how diseases progress over time and how patients respond to interventions is a central challenge in biomedical research and patient care. Learning the dynamics of disease evolution under treatment, particularly from high-dimensional molecular and imaging data, has enormous potential to discover personalized predictive markers. Such insights could form the basis for more equitable and effective patient care. Traditional mechanistic models, grounded in differential equations, provide interpretability regarding tumor growth and drug diffusion but often require simplifications that omit emergent features in heterogeneous clinical data. Modern machine learning methods, including deep learning, excel at capturing complex spatial patterns in tissue but are typically agnostic to the underlying biological laws driving resistance or response. Generative modeling offers a promising framework to integrate mechanistic knowledge with observational data. By combining spatial characterisation of the tumor microenvironment (e.g., via histology or spatial transcriptomics) with longitudinal treatment outcomes, we can create Digital Twins that simulate patient-specific responses to therapies, accounting for the complex interplay between tumor architecture and molecular state.

Aims

To develop new generative models that integrate mechanistic simulation with pre- and post-treatment molecular data to simulate disease evolution and predict therapeutic responses, enabling patient-specific digital twins for precision oncology.

Methods

The project will focus on breast cancer cohorts with paired molecular and imaging characterisation before and after treatment. The approach will: (i) Leverage generative modeling (e.g., latent variable models, diffusion models) to learn the high-dimensional mapping between pre-treatment spatial architecture and post-treatment molecular states. (ii) Incorporate mechanistic priors derived from tumor growth inhibition models or immune-interaction networks to constrain predictions, ensuring that simulated responses respect biological plausibility. (iii) Evaluate models for their ability to predict clinical endpoints (such as Pathological Complete Response vs. Resistance) and generalizability across different treatment regimens. (iv) Extend the framework to integrate multi-modal data.

Daniela De Angelis (Population Health) - daniela.deangelis@mrc-bsu.cam.ac.uk

Kyriakos Flouris (Biomedical Machine Learning) - kyriakos.flouris@mrc-bsu.cam.ac.uk

Alex Zarebski (Population Health) - alex.zarebski@mrc-bsu.cam.ac.uk

Background

During outbreaks, complex mechanistic models are increasingly replied upon to inform public health reponse and decision-making, and to understand transmission dynamics, behaviour change and the effects of interventions. Yet the models we rely on are often too simplified to capture important details of the social and biological processes that underlie the spread of infection. This oversimplification can lead to biased and overconfident forecasts. However, as models grow in realism and, therefore, complexity, their calibration becomes prohibitively expensive, limiting how quickly (e.g., in real time) and how precisely (e.g., at local geographic scales) they can provide insights to inform an effective response. Deep learning offers a compelling opportunity to transform outbreak analysis. Neural estimators [1] have proved highly effective for complex estimation tasks by learning flexible mappings between model outputs (i.e., potentially observed data) and model parameters (the quantities we need to understand the epidemic). In scientific domains where large datasets are unavailable, training data are often simulated using computational models that encode domain knowledge and span wide ranges of plausible parameters. Neural estimators convert a hard estimation problem into the simpler computational task of simulating epidemics. However, generating the large number of simulations needed to train deep learning models is not easy, especially for complex, high-fidelity epidemic models developed in response to an emerging threat.

This project tackles the computational challenge. You will develop data-efficient deep learning methods to analyse epidemics with complex models. By reducing the number of simulations required for training neural estimators and making better use of existing data, these methods will be more suitable for deployment during public health emergencies. The ambition is to bridge the gap between state-of-the-art machine learning methods and the operational constraints of real-world response modelling, enabling faster, more reliable insights when they matter most.

Aim of the project

Develop data-efficient and robust techniques for producing emulators of complex models and neural estimators for inference. This will culminate in new methods and the creation of guidance on best practice for applying these methods during public health emergency responses, with the ambition of changing how AI supports decision-making in outbreaks.

Methods

We propose a focused programme of computational research to develop data-efficient and robust methods for emulating complex epidemic models and training neural estimators for inference. The approach will evolve with initial findings, but is likely to include: (i) developing neural network-based emulators of high-fidelity simulators [2], including fine-tuning time-series foundation models on simulator-generated data and using data augmentation to reduce reliance on expensive simulations; (ii) improving how simulation data are generated and used [3]; and (iii) improving the training of neural estimators, exploring approaches that help models learn to make accurate predictions over longer forecast horizons [4].

All methods will be evaluated on realistic epidemic models, with emphasis on robustness, uncertainty quantification, and computational efficiency. The out-comes will be used to generate practical guidance on deploying deep learning-based emulation and inference in time-critical public health response settings.

The student will be supervised by Alexander Zarebski and Daniela De Angelis (Population Health Theme), and Kyriakos Flouris (Biomedical Machine Learning Theme), and will benefit from interaction with colleagues at the UK Health Security Agency (Paul Birrell).

References

[1] Matthew Sainsbury-Dale et al. “Likelihood-Free Parameter Estimation with Neural Bayes Estimators”. In: The American Statistician (2024). doi: 10.1080/00031305.2023.2249522.

[2] Stefania Scheurer et al. “Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Models”. In: arXiv e-prints (2025). doi: 10.48550/arXiv.2505.08683.

[3] Angelos Katharopoulos et al. “Not All Samples Are Created Equal: Deep Learning with Importance Sampling”. In: arXiv e-prints (2018). doi: 10.48550/arXiv.1803.00942.

[4] Alex Lamb et al. “Professor Forcing: A New Algorithm for Training Recurrent Networks”. In: arXiv e-prints (2016). doi: 10.48550/arXiv.1610.09038.

Daniela De Angelis (Population Health) - daniela.deangelis@mrc-bsu.cam.ac.uk

Kyriakos Flouris (Biomedical Machine Learning) - kyriakos.flouris@mrc-bsu.cam.ac.uk

Alex Zarebski (Population Health) - alex.zarebski@mrc-bsu.cam.ac.uk

Background

Understanding the hidden dynamics of infectious diseases is one of the most urgent challenges in global health security. While the recent proliferation of data offers unprecedented opportunities, transforming noisy observational data into actionable biological insights remains a formidable challenge [1]. A prime example is the difficulty of inferring the true, unobserved number of infections solely from indirect data (e.g., lagged hospitalization records). Traditional models often rely on rigid assumptions about the relationship between observed data and the underlying epidemic, leading to biased estimates if this relationship is mis-specified. Conversely, “Foundation Models” and generative AI offer the power to learn these complex, non-linear mappings directly from data, effectively “discovering” the unknown mechanism connecting infections to clinical outcomes. However, without structural constraints, these models frequently hallucinate dynamics that violate basic biological constraints [2]. A critical frontier in this field lies in distinguishing whether a model has genuinely “learned” the under-lying mechanism (generalization) or is merely memorizing the training data (overfitting). Recent theoretical developments in Learning Theory [3] and the phenomenon of “grokking”, where a model suddenly transitions from memorization to understanding, offer a promising path to address this question [4]. There is a need for new frameworks that leverage the flexibility of generative deep learning while strictly enforcing the structural constraints of dynamical systems.

Aim of the project

To develop and validate robust frameworks for parameter estimation in infectious disease epidemiological systems by bridging deep learning with mechanistic modelling principles.

Methods

We envisage a series of machine learning, computational, and theoretical investigations to address the challenge of estimating parameters from noisy time series data. The specific approach will adapt based on initial findings, but likely strategies include: (i) developing generative and deep learning architectures that are constrained by, or embedded within, dynamical systems to ensure physical plausibility; (ii) utilizing metrics from Learning Theory to detect phase transitions during the learning process, distinguishing between models that have “grokked” the mechanism versus merely memorizing patterns; (iii) investigating the impact of model misspecification, specifically analyzing how well parameter estimation performs when the mathematical model is slightly incorrect; and (iv) validating these approaches on simulated test datasets before applying them to estimate parameters from real-world epidemic datasets. This project will be supervised by Kyriakos Flouris (Biomedical Machine Learning Theme), Alexander Zarebski and Daniela De Angelis (Population Health Theme), and will benefit from interaction with colleagues at the UK Health Security Agency (Paul Birrell).

References

[1] Roy M Anderson et al. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, 1992.

[2] Christopher Rackauckas et al. “Universal Differential Equations for Scientific Machine Learning”. In: arXiv e-prints (2020). doi: 10.48550/arXiv.2001.04385.

[3] Sumio. Watanabe. Algebraic Geometry and Statistical Learning Theory. Cambridge University Press, 2009.

[4] Alethea Power et al. “Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets”. In: arXiv e-prints (2022). doi: 10.48550/arXiv.2201.02177.

Daniela De Angelis (Population Health) - daniela.deangelis@mrc-bsu.cam.ac.uk

Paul Birrell (Population Health) - paul.birrell@mrc-bsu.cam.ac.uk

Angelos Alexopoulos (Athens University of Economics and Business) 

In any real world epidemic, the underlying infection process is unobserved, but can be reconstructed using an array of indirect (e.g lagged and biased) data sources either on infection incidence (e.g. hospital admissions or deaths) or infection prevalence (e.g. cross-sectional testing of the population) [1]. Typically, such reconstruction is carried out by linking such data to SIR-type ordinary differential equation (ODE)-based transmission models, which have been the ‘go-to’ model framework for capturing epidemic transmission dynamics for over 100-years. However, these ODE-driven models describe idealised, population-level dynamics that ignore the demographic (not all people are equally likely to transmit infection) and environmental stochasticity (due to behaviour, policy or virological changes) that characterise real-world epidemics. Both sources should be accounted for when seeking to make sense of temporal patterns of infection and SIR models have been suitably adapted to include them. Environmental stochasticity, for instance, is typically accounted for by replacing β, the transmission parameter representing the likelihood of infection between pairs of individuals, with a suitably transformed stochastic process, βt. In making this switch, in the discrete-time case, the dimension of a model’s parameter space increases by orders of magnitude. This makes model-fitting through computational Bayesian methods (e.g. MCMC or SMC) much harder, as algorithms take longer to converge, and potentially many millions of model evaluations are required. This becomes even more challenging when transmission models are highly stratified and/or are used to capture the dynamics of long-running epidemics (such as SARS-CoV-2).

The proposed PhD project will investigate methods of generating epidemic inference from fully stochastic SIR-type models through the use of model approximations and emulation. Chiefly model approximations will be employed to mitigate the increase in dimension of the problem, and emulation to replace complex transmission models with simpler statistical proxy models that are more readily evaluated and for which standard inference methods exist.

Model Approximations

If B is expressed as a diffusion process, we can approximate it using a finite path-wise expansion of basis functions the coefficients of which are, a priori, random variables N(0, 1) (see [2]). The number of terms that should be used in such an expansion has been guided by general rules of thumb, but work is needed to understand how the model’s predictive performance can be used to identify the optimal number of terms. We propose to further investigate the use of such approximations by integrating them into a fully stochastic system using linear noise approximations (LNAs) for the whole Stochastic Differential Equation system [3, 4], adapting standard LNA methodology to account for non-normal epidemic data.

Bayesian Emulation

Emulators of dynamic epidemic processes have been shown to alleviate the real-time computational burden of epidemic inference [5]. Emulation of models incorporating diffusion processes would involve integrating over all possible trajectories of the diffusion process for each input parameter value. However, the use of the pathwise approximations can offer a scalable solution, for a modest increase in the dimension of the input parameter space. We propose to investigate the use of emulators in the presence of diffusion-driven transmission potentials, extending the work of [5] to the case where the data model cannot be assumed to be approximately Gaussian (as is the case with much epidemic data which is typically in the form of overdispersed count data), and to remove the repeated smoothing steps that can be computationally expensive as pandemic time series increase in length (as was the case with SARS-CoV-2). More scalable emulation strategies include deep GP emulation with stochastic imputation (e.g. [6]) which, in combination with the above model approximations, offers a computationally efficient route to more flexible surrogate models. The candidate will investigate inducing-variable variational methods [7] and stochastic variational GP learning [8] to enable larger training datasets and iterative simulator refinement as new data arrive, building capacity for the real-time use of emulators in real-world pandemic inference.

[1] Birrell PJ, Blake J, Kandiah J, Alexopoulos A, van Leeuwen E, Pouwels KB, Ghosh S, Starr C, Walker AS, House TA, Gay N, Finnie T, Gent N, Charlett A, De Angelis D (2025). Real-time modelling of the SARS-CoV-2 pandemic in England 2020–2023: a challenging data integration, J. R. Stat. Soc. Ser. A Stat. Soc, qnaf030

[2] Ghosh S, Birrell PJ, De Angelis D (2023). An approximate diffusion process for environmental stochasticity in infectious disease transmission modelling. PLoS Comput Biol 19(5) 2023.

[3] Fintzi J, Wakefield J, Minin VN (2022). A Linear Noise Approximation for Stochastic Epidemic Models Fit to Partially Observed Incidence Counts, Biometrics, Volume 78(4) 1530–1541

[4] Swallow B, Rand DA, Minas G (2024). Bayesian Inference for Stochastic Oscillatory Systems Using the Phase-Corrected Linear Noise Approximation, Bayesian Anal. Advance Publication 1 - 30, 2024.

[5] Farah, M., Birrell, P. J., Conti, S., and De Angelis, D. (2014). Bayesian Emulation and Calibration of a Dynamic Epidemic Model for A/H1N1 Influenza. Journal of the American Statistical Association, 109(508), 1398–1411.

[6] Ming, D., Williamson, D., and Guillas, S. (2023). Deep Gaussian Process Emulation Using Stochastic Imputation. Technometrics, 65(2), 150–161.

[7] Titsias, M. K. (2009). Variational Learning of Inducing Variables in Sparse Gaussian Processes. In Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 5, 567–574.

[8] Hensman, J., Fusi, N., and Lawrence, N. D. (2013). Gaussian Processes for Big Data. In Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence (UAI 2013), 282–290.

Anne Presanis (Population Health) - anne.presanis@mrc-bsu.cam.ac.uk

Daniela De Angelis (Population Health) - daniela.deangelis@mrc-bsu.cam.ac.uk

Hannah Fraser (Bristol)

Alison Brown (UKHSA)

Background

England has set an ambition to reduce HIV transmission by 90% between 2010 and 2030 and thereafter work to sustain transmission at low level. Ending HIV transmission is achievable because the necessary tools already exist: frequent HIV testing, provision of pre-exposure prophylaxis (PrEP) to those most at risk, and—when diagnosed—rapid linkage to care, treatment, and ongoing support to remain in care and achieve an undetectable viral load. By maximizing the proportion of people who stay HIV-negative and ensuring those living with HIV maintain viral suppression, transmission can be significantly reduced. To date, most progress has been among white gay men, where HIV diagnoses have fallen by 11%, from 517 in 2020 to 461 in 2024. This decline, combined with high testing rates, suggests reduced transmission, supported by estimates of incidence from CD4 back-calculation models (Brizzi, Birrell et al, 2021). However, among heterosexual adults from African heritage communities, diagnoses have increased—from 290 in 2020 to 683 in 2024—despite testing levels having not increased over this period (Quinn et al, 2026). Ongoing transmission in this population has been indicated by initial results from a back-calculation model for heterosexuals. This trend is thought to reflect lower uptake of HIV testing and PrEP in this population, even though anti-retroviral therapy (ART) coverage and viral suppression remain high and comparable to other groups. There is an urgent need to verify these hypotheses if ending HIV transmission by 2030 is to remain an achievable goal.

Project aims

To characterise the groups at risk of infection among African heritage heterosexuals in England, quantify HIV transmission and investigate the level of combination prevention (e.g. testing and PreP) needed to reduce transmission. This information will be used to assess and guide the scale of response required in this population to meet and maintain transmission elimination targets.  

Approach
This work will require integration of data from multiple sources to estimate population sizes, HIV prevalence, incidence and transmission dynamics; and to investigate the prevention coverage needed to reduce transmission. Data sources include: population surveys (Office for National Statistics (ONS) and National Survey of Sexual Attitudes and Lifestyles (Natsal); data from UKHSA surveillance systems (e.g. attendance at sexual health services [SHS], testing  and PrEP uptake,  information on CD4 counts at diagnosis, linkage to care, treatment coverage, viral suppression, and retention in care); and existing evidence on ongoing interventions in the community (e.g. Common Ambition Bristol).

The project comprises four key steps:

1. Estimation of the size of the African heritage population at risk of HIV acquisition by demographic and behavioural characteristics (eg age, region of birth, SHS attendance), using ONS and Natsal-4 data.
2. Characterisation of HIV acquisition among the African heritage population resident in England according to country of birth (e.g. born abroad, with HIV acquired but undiagnosed before arriving in England; born abroad and HIV acquired after arriving in England), through CD4 back-calculation using information on date of diagnosis supplemented by genomic data.  
3. Development of the back-calculation model in 2. into a dynamic HIV transmission model approximating the infection mechanism and progression through disease states (susceptible, on PrEP, living with undiagnosed HIV [stratified by CD4 count], diagnosed but untreated, on ART).
4. Investigation, through the model in 3., of the levels of prevention interventions, including HIV testing, PrEP uptake, linkage to care, ART initiation, retention in care and treatment, needed to achieve viral suppression and reduce transmission.

Candidate requirements:

Degree in quantitative science (e.g. Mathematics, Physics, Engineering, Computer Science) with at least a 2.1 degree (or equivalent). Possession of a relevant Master's degree and/or equivalent research experience, particularly in infectious disease modelling, is desirable.  

Funding

The studentship is fully funded by Health Protection Research Unit in Evaluation and Behavioural Science (HPRU EBS) for three years. The funding covers tuition fees for home students, a stipend at the UKRI rate (£20,780 in 2025/2026).

Overseas students are welcome to apply but you must pay the difference between the home and overseas fees. You must state clearly on your application how you will be paying the difference.

MRC-BSU

MRC-BSU is one of Europe's leading biostatistics research institutions. Our focus is to develop and apply new analytical and computational strategies based on sound statistical principles for the challenging tasks facing biomedicine and public health. The Unit is situated on the Cambridge Biomedical Campus, one of the world's most vibrant centres of biomedical research, which includes the University of Cambridge's Clinical School, two major hospitals, the MRC Laboratory of Molecular Biology, and the world headquarters of Astra Zeneca.

University of Bristol, Bristol Medical School

Bristol Medical School is the largest and one of the most diverse Schools in the University of Bristol, with approximately 930 members of staff and over 300 postgraduate doctoral research students. The School is a leading centre for research and teaching across Population Health Sciences and Translational Health Sciences. Research in the School is collaborative and multi-disciplinary, with staff coming from a wide range of academic disciplines and clinical specialties. Within the Medical School are several major research centres, groups and programmes. More details can be found on the Medical School website.

UK Health Security Agency

The UK Health Security Agency (UKHSA) and its predecessors have been undertaking the surveillance of HIV and AIDS since the start of the epidemic.  The HIV team, situated with the Blood Safety, Hepatitis, STI and HIV Division are world leaders in surveillance and HIV epidemiology. In addition to owning comprehensive data on every HIV diagnosis and episodes of clinical care, and HIV testing and PrEP activity in sexual health services, the team routinely provide national and international expert advice on HIV epidemiology. The team also hosts expertise in data matching and interpretation. The UKHSA has provided a critical role in the creation of the HIV Action Plans (2021 and 2025) which aim to end HIV transmission, including provide advice on targets that are to be met if this ambition is to be realised.  UKHSA has been co-supervisors for several successful PhD students, including collaboration with University of Cambridge, UCL, Imperial and the LSHTM over the past ten years.

Kyriakos Flouris (Biostatistical Machine Learning) - kyriakos.flouris@mrc-bsu.cam.ac.uk

One of the most challenging and still unresolved problems in artificial intelligence is forecasting, particularly the ability of machine learning models to reliably extrapolate beyond the data they were trained on. This challenge is especially pronounced in biomedical settings, where systems are fundamentally dynamic: physiological processes evolve over time, disease trajectories unfold across multiple biological scales, and clinical decision-making relies on temporal patterns observed in patient data. These systems are increasingly measured through heterogeneous modalities, including longitudinal electronic health records (EHR), imaging, physiological monitoring, and molecular assays, creating rich but complex multimodal datasets.Traditional mechanistic models, often expressed as ordinary or partial differential equations, provide principled descriptions of biological dynamics such as diffusion, transport, and regulation. Yet they often rely on simplifying assumptions and cannot fully capture the high-dimensional variability across patients and data modalities. Modern machine learning models, by contrast, excel at modeling nonlinear patterns in large datasets but typically lack explicit mechanistic structure or physical constraints. Integrating machine learning with time-dependent modeling offers an exciting opportunity to bridge this gap: by embedding continuous structures and domain knowledge within flexible ML architectures, we can build models that capture both mechanistic dynamics and data-driven variability. Such models could enable more accurate prediction of disease progression, reconstruction of missing observations in longitudinal data, and the discovery of latent temporal biomarkers across heterogeneous patient populations.

Aims
This project aims to develop state-of-the-art methods for understanding and predicting the dynamics of complex biomedical systems. Specifically, it will develop machine learning models for time-dependent biomedical systems that integrate mechanistic structure with multimodal biomedical data, enabling interpretable modeling of disease dynamics, multimodal integration, and predictive simulation.

Methods
The project will proceed through several stages: (i) Development of time-aware machine learning architectures, for example biomedical foundation models, capable of representing temporal processes and irregularly sampled longitudinal data. (ii) Integration of mechanistic structure, incorporating known biological or physical dynamics operator-learning approaches (iii) Multimodal data integration, combining heterogeneous data to capture interactions between clinical trajectories and underlying biological mechanisms. (iv) ML training on large-scale longitudinal datasets, leveraging modern representation learning and generative modeling approaches to learn shared latent temporal structure. (v) Evaluation and downstream applications, including forecasting disease trajectories, reconstructing incomplete patient histories, identifying latent temporal biomarkers, and simulating hypothetical interventions or treatment scenarios within a mechanistically informed ML framework.

Pantelis Samartsidis (Population Health) - pantelis.samartsidis@mrc-bsu.cam.ac.uk

Assessing the impact of an intervention using observational data is a problem that is encountered frequently in various fields of applied research including epidemiology, public health, econometrics and political science. Such data often take the form of time-series observed at an aggregate level, e.g. by hospital or by geographical region. An advantage of using time-series data for evaluating interventions is that they offer the opportunity to tackle the issue of unobserved confounding, which is very difficult when using cross-sectional data. 

Despite recent developments [1,2] in the field, current methods lack the flexibility to deal with challenges posed by complex real-world interventions. The objective of this project will be to improve existing approaches for causal inference using time-series data. Some possible directions depending on the student’s interests include:

1. Using tree-based methods to model the effect of observed confounders on the outcome, and to allow for interactions between observed and unobserved confounders.
2. Extending existing approaches to allow for multiple interventions applied to the units concurrently. 
3. Estimating spillover intervention effects to neighbouring units using count data.
4. Exploring the potential of copula models to relax parametric assumptions taken by current approaches. 

The proposed methods will be developed under the Bayesian paradigm to obtain automatic uncertainty quantification, and to make use of regularising priors that can enable flexible models to be fit to a limited amount of data. They will be used to assess various interventions in the field of public health (in collaboration with the UK Health Security Agency) and in economics.

References:

[1] Samartsidis et al (2019). Assessing the Causal Effect of Binary Interventions from Observational Panel Data with Few Treated Units. Statistical Science 34 (3), 486-503. 

[2] Arkhangelsky and Imbens (2024). Causal models for longitudinal and panel data: a survey. The Econometrics Journal 27 (3), C1-C61.

Pavel Mozgunov (Efficient Study Design) - pavel.mozgunov@mrc-bsu.cam.ac.uk

This project will develop novel approaches to combine the information for early phase trials starting from dose-escalation in monotherapy, followed by dose-escalations of combinations, to make recommendations and ensure efficient decision-making regarding later stages of development (typically Phase 3 directly).

The student will review the currently available designs and common approaches to Oncology Phase 1 monotherapy and combination trials.

They will then propose different approaches that assess these jointly and incorporate existing/occurring information in an ongoing fashion for improved decision-making. The performance of the developed frameworks will then be studied from a theoretical perspective (investigating its statistical properties) and via an extensive simulation study, with clear metrics of speed, decision characteristics, and patient numbers.

Kyriakos Flouris (Biostatistical Machine Learning) - kyriakos.flouris@mrc-bsu.cam.ac.uk 

To develop and rigorously evaluate agentic LLM systems for biostatistics research, in which language-model reasoning is grounded in verifiable tools, mechanistic knowledge, and principled statistical inference, enabling trustworthy automation of hypothesis generation, evidence synthesis, digital-twin construction, and data analysis.

The project will proceed through several key stages: (i) the design of agentic architectures for biomedical tasks, including tool use, retrieval over curated knowledge sources, planning and decomposition, memory, and multi-agent configurations in which specialised agents propose, execute, and adversarially critique analyses; (ii) the grounding of these agents in trusted computational substrates, including statistical and causal inference engines, mechanistic simulators, ontologies, and curated biological networks, so that claims are constrained by, or checked against, formal machinery rather than generated freely; (iii) the application of these systems to patient-level digital twins, in which the agent assembles a personalised model from an individual's data, fits and simulates it, and reports calibrated predictions and candidate interventions rather than unqualified point estimates; (iv) the treatment of uncertainty and reliability as first-class objects of study, through calibration, abstention, self-consistency, verifier models, and quantification of how errors propagate through multi-step agentic pipelines; and (v) the construction of realistic benchmarks and evaluation protocols, beginning with publicly available electronic health record resources such as MIMIC-IV and eICU, where results are reproducible and openly comparable, before extending to restricted cohort, biobank, imaging, or omics data, and measuring not only task accuracy but reproducibility, sensitivity to prompt and context, faithfulness of stated reasoning, and utility to a domain expert.

1. Gao, S., Fang, A., Huang, Y., Giunchiglia, V., Noori, A., Schwarz, J. R., Ektefaie, Y., Kondic, J. and Zitnik, M. (2024). Empowering biomedical discovery with AI agents. Cell 187(22), 6125-6151. doi:10.1016/j.cell.2024.09.022. 

2. Swanson, K., Wu, W., Bulaong, N. L., Pak, J. E. and Zou, J. (2025). The Virtual Lab of AI agents designs new SARS-CoV-2 nanobodies. Nature 646(8085), 716-723. doi:10.1038/s41586-025-09442-9. 

3. Boiko, D. A., MacKnight, R., Kline, B. and Gomes, G. (2023). Autonomous chemical research with large language models. Nature 624(7992), 570-578. doi:10.1038/s41586-023-06792-0.