Liverpool Centre for Mathematics in Healthcare

8th March 2019 - Seminar - Application of a hierarchical mixed model to longitudinal bone mineral density data with measurements at multiple sites - Ms Rachel Tribbick (University of Lancaster)

Time: 13:00-14:00

Venue: MATH-104, First Floor, Department of Mathematical Science Building

Abstract: Modern studies of biological systems increasingly collect high-dimensional longitudinal data: repeated measurements of data on large numbers of outcomes over time. We can often assume correlation between observations from a single patient, both across time and outcomes. This correlation itself may be of scientific interest, but even when it is not, properly accounting for it can improve the parameter estimates of interest. Methods for jointly modelling multiple outcomes exist, but current literature demonstrating the application of this family of models to more than three outcomes is sparse. 

In this talk I will describe an approach for modelling an unbalanced longitudinal data set with 12 outcomes: bone mineral density (BMD) measurements at different sites across the skeleton. This data has been collected on over 4000 patients as part of routine NHS scans for diagnosis osteoporosis. In order to be able to model the latent processes underlying the measurements, I developed a hierarchical mixed model in which both fixed and random effects are shared among measurements through a layer of latent variables. This layer is then linked to the observations at each site through a link matrix, the elements of which are also estimated. The observations are conditionally independent (both across time and sites) given the latent layer.

I will share the results and limitations of applying this model to the BMD data, aiming to answer the following questions of scientific interest:

(1) Do significant relationships exist between covariates and BMD/BMD loss at the femoral neck? 

(2) What is the relationship among BMD measurements across sites? 

(3) Do covariates have the same relationships with BMD/BMD loss across all sites?