Variational Approximation Approaches for Efficient Clinical Predictions

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Motivation: High-dimensional data is now routinely collected in many medical settings. The data may be high-dimensional due to the number of different variables being measured on a single patient (e.g. genetic or metabolomics studies) or the number of times a variable is repeatedly measured (e.g. longitudinal studies). In addition the number of individuals with available data in a study is now increasing (through the availability of Biobanks for example).One way in which this data can be used is in screening or monitoring patients to determine their risk of developing a disease or requiring an intervention, or to classify patients into various risk groups.Objective: In recent years joint models for multiple longitudinal (mainly continuous) and time-to-event data have been developed, which make use of mixed models. The popularity of these methods is evidenced by the success of software packages for joint models.These methods provide personalised predictions of a patient's risk of experiencing an event. However, a key limitation of current models is the computational burden required to fit such models. This burden occurs if there is a high number of patients (many thousands instead of a few hundred), many repeated observations per patient, or multiple clinical biomarkers under consideration. These factors have limited the uptake of joint-modelling methodology to generally small sample sizes and only a few (2-4) longitudinal biomarkers.In the machine learning literature variational approximation methods have been shown to give fast and accurate estimates of model parameters in a variety of settings. Recent statistical work has introduced these methods in univariate generalised linear mixed models, and in some genetic settings.My proposal is to derive a mean-field variational Bayes (MFVB) approach to estimating joint models for multiple longitudinal biomarkers of different type (continuous, counts, binary, etc.) and time-to-event data. The basic idea of the approach is to avoid estimating the model parameters from the full likelihood function but instead, split the likelihood function into a product of more tractable functions, which can then be more easily estimated. The rationale is that by sacrificing a little in terms of model accuracy, we gain the ability to fit multivariate joint model within a reasonable period of time (seconds/minutes instead of hours/days). Making it practicable to fit such models in a reasonable time frame, will allow personalised risk-prediction and diagnostics to be performed in real-time and make a substantial contribution towards stratified medical treatment and intelligent medical systems.Clinical Applications: The models developed will be used to assess the influence of covariates, and the correlation between at least 10 markers over time that have known links to a patient developing sight threatening diabetic retinopathy (STDR). Considering that the ISDR dataset contains over 20,000 patients, even fitting a univariate mixed model to assess the evolution over time is computationally intensive with current methods. Fitting a model to assess the correlation over time between all of these markers would be infeasible. My approach will lead to an improved understanding of the complex relationship between various clinical markers and their changes over time. I will derive personalised risk prediction models for STDR, which will provide increased understanding of risk factors and will provide patient specific assessment of their risk of STDR within clinically relevant timeframes. Some markers that appear to have a significant association in univariate analysis may be found to be no longer significant when multiple markers are considered. The models will allow us to inform clinicians as to the most crucial markers influencing risk of developing a disease and also to determine the best time to plan the patient's next visit.