Functional Regression Models with Functional Response: New Approaches and a Comparative Study

This paper proposes three new approaches for additive functional regression models with functional responses. The first one is a reformulation of the linear regression model, and the last two are on the yet scarce case of additive nonlinear functional regression models. Both proposals are based on extensions of similar models for scalar responses. One of our nonlinear models is based on constructing a Spectral Additive Model (the word "Spectral" refers to the representation of the covariates in an \mcal{L}_2 basis), which is restricted (by construction) to Hilbertian spaces. The other one extends the kernel estimator, and it can be applied to general metric spaces since it is only based on distances. We include our new approaches as well as real datasets in an R package. The performances of the new proposals are compared with previous ones, which we review theoretically and practically in this paper. The simulation results show the advantages of the nonlinear proposals and the small loss of efficiency when the simulation scenario is truly linear. Finally, the supplementary material provides a visualization tool for checking the linearity of the relationship between a single covariate and the response.Comment: Submitte

Partial agonism improves the anti-hyperglycaemic efficacy of an oxyntomodulin-derived GLP-1R/GCGR co-agonist

OBJECTIVE: Glucagon-like peptide-1 and glucagon receptor (GLP-1R/GCGR) co-agonism can maximise weight loss and improve glycaemic control in type 2 diabetes and obesity. In this study we investigated the cellular and metabolic effects of modulating the balance between G protein and β-arrestin-2 recruitment at GLP-1R and GCGR using oxyntomodulin (OXM)-derived co-agonists. This strategy has been previously shown to improve the duration of action of GLP-1R mono-agonists by reducing target desensitisation and downregulation. METHODS: Dipeptidyl dipeptidase-4 (DPP-4)-resistant OXM analogues were generated and assessed for a variety of cellular readouts. Molecular dynamic simulations were used to gain insights into the molecular interactions involved. In vivo studies were performed in mice to identify effects on glucose homeostasis and weight loss. RESULTS: Ligand-specific reductions in β-arrestin-2 recruitment were associated with slower GLP-1R internalisation and prolonged glucose-lowering action in vivo. The putative benefits of GCGR agonism were retained, with equivalent weight loss compared to the GLP-1R mono-agonist liraglutide in spite of a lesser degree of food intake suppression. The compounds tested showed only a minor degree of biased agonism between G protein and β-arrestin-2 recruitment at both receptors and were best classified as partial agonists for the two pathways measured. CONCLUSIONS: Diminishing β-arrestin-2 recruitment may be an effective way to increase the therapeutic efficacy of GLP-1R/GCGR co-agonists. These benefits can be achieved by partial rather than biased agonism