Streamlined solutions to multilevel sparse matrix problems

We define and solve classes of sparse matrix problems that arise in multilevel modelling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation, in which data on level-1 units are grouped within a two-level structure. We provide full solutions for two-level and three-level problems, and their derivations provide blueprints for the challenging, albeit rarer in applications, higher-level versions of the problem. While our linear system solutions are a concise recasting of existing results, our matrix inverse sub-block results are novel and facilitate streamlined computation of standard errors in frequentist inference as well as allowing streamlined mean field variational Bayesian inference for models containing higher-level random effects. doi: 10.1017/S144618112000006

A patient-centric modeling framework captures recovery from SARS-CoV-2 infection.

The biology driving individual patient responses to severe acute respiratory syndrome coronavirus 2 infection remains ill understood. Here, we developed a patient-centric framework leveraging detailed longitudinal phenotyping data and covering a year after disease onset, from 215 infected individuals with differing disease severities. Our analyses revealed distinct 'systemic recovery' profiles, with specific progression and resolution of the inflammatory, immune cell, metabolic and clinical responses. In particular, we found a strong inter-patient and intra-patient temporal covariation of innate immune cell numbers, kynurenine metabolites and lipid metabolites, which highlighted candidate immunologic and metabolic pathways influencing the restoration of homeostasis, the risk of death and that of long COVID. Based on these data, we identified a composite signature predictive of systemic recovery, using a joint model on cellular and molecular parameters measured soon after disease onset. New predictions can be generated using the online tool http://shiny.mrc-bsu.cam.ac.uk/apps/covid-19-systemic-recovery-prediction-app , designed to test our findings prospectively

A patient-centric modeling framework captures recovery from SARS-CoV-2 infection.

The biology driving individual patient responses to severe acute respiratory syndrome coronavirus 2 infection remains ill understood. Here, we developed a patient-centric framework leveraging detailed longitudinal phenotyping data and covering a year after disease onset, from 215 infected individuals with differing disease severities. Our analyses revealed distinct 'systemic recovery' profiles, with specific progression and resolution of the inflammatory, immune cell, metabolic and clinical responses. In particular, we found a strong inter-patient and intra-patient temporal covariation of innate immune cell numbers, kynurenine metabolites and lipid metabolites, which highlighted candidate immunologic and metabolic pathways influencing the restoration of homeostasis, the risk of death and that of long COVID. Based on these data, we identified a composite signature predictive of systemic recovery, using a joint model on cellular and molecular parameters measured soon after disease onset. New predictions can be generated using the online tool http://shiny.mrc-bsu.cam.ac.uk/apps/covid-19-systemic-recovery-prediction-app , designed to test our findings prospectively