○Large imaging datasets with hierarchical structure are becoming increasingly commonplace. Examples of such structure can be found in the related subjects of the Human Connectome Project[1] (n=1,200) and in the repeated measures in the Adolescent Brain Cognitive Development study[2] (n=12,000) and the UK Biobank[3] (n=100,000). ○The Linear Mixed effects Model (LMM), a popular extension of the linear model, is used for the analysis of longitudinal, heterogeneous or unbalanced clustered data[4]. ○The LMM utilizes numerical methods for parameter estimation[5]. However, this means heavy overheads are placed on memory and computation time for neuroimaging datasets. ○In addition, variability in the patterns of missing data near the edge of the brain can become problematic as sample sizes increase[6]. This variability can cause shrinkage of the ﬁnal analysis mask if only complete-data voxels are analysed. ○Here we present BLMM ("Big" Linear Mixed Models), an eﬃcient tool for large-scale MRI Mixed Model analyses. BLMM is implemented in python and designed for use on computational clusters. Thomas Maullin-Sapey1, Thomas Nichols1, 2 1. Oxford Big Data Institute, Li Ka Shing Centre for Health Information and Discovery, Nuffield Department of Population Health, University of Oxford, Oxford, UK. 2. Department of Statistics, University of Warwick, UK BLMM: Parallelised Computing for Big Linear Mixed Models Introduction Methods References Conclusion ○BLMM employs a Fisher Scoring algorithm for LMM parameter estimation. This allows for parameter estimation of a wide range of models to be estimated, including: - Hierarchical analyses involving thousands of input images. - Models involving multiple, unbalanced, potentially crossed, random factors. - Random intercept analyses for thousands of input images. ○BLMM accounts for missingness at a given voxel by "zero-ing" out subjects whose brain mask doesn’t include the voxel. The model at voxel v is: MvYv = MvXβv + MvZbv + Mvεv where Mv is a diagonal matrix with 0 diagonal entries for subjects missing data at voxel v. Both bv and εv are random terms with unknown variances. ○BLMM is computationally scalable as it works by partitioning X, Y and Z row-wise and having each processor calculate a part of the product matrices: X’X, X’Y, X’Z, Y’Y, Y’Z and Z’Z. Following this, the original matrices are discarded and the product matrices are used for computation. This means computation does not scale with n, but with the size of the ﬁxed and random effects design. ○We demonstrate BLMM on UK Biobank task fMRI data, faces-shapes effect, modelling data on the 1540 subjects, with up to 2 repeated measures each, with a 2nd imaging visit, for a total of 2833 scans (some data lost to QC failures). The model included random subject intercepts, cross-sectional effect of age (avg age per subject), and longitudinal time (inter-visit time in years, centered by subject) . ○BLMM is a freely available python-based tool for large scale Neuroimaging Linear Mixed Models. It is designed specifically to account for subject mask variability, memory constraints and computational performance. For more information, see: https://github.com/TomMaullin/BLMM 1 - Matthew F. Glasser, et al. (2013). The minimal preprocessing pipelines for the Human Connectome Project. Neuroimage. 80: 105-124. doi: 10.1016/j.neuroimage.2013.04.127 2 - Casey B.J., et al. (2018). The Adolescent Brain Cognitive Development (ABCD) study: Imaging acquisition across 21 sites. Developmental Cognitive Neuroscience. 32:43-54. doi: 10.1016/j.dcn.2018.03.001 3 - Allen N, et al. (2012). UK Biobank: Current status and what it means for epidemiology. Health Policy and Technology, 1(3); 123-126. doi: 10.1016/j.hlpt.2012.07.003] 4 - Laird NM, Ware JH. Random-effects models for longitudinal data. Biometrics. 1982;38(4):963-974. 5 - Demidenko, Eugene. (2013). Mixed Models: Theory and Applications with R. 10.1002/0471728438. 6 - Van Horn JD, et al. (2014). Human neuroimaging