Multimorbidity analysis with low condition counts: a robust Bayesian approach for small but important subgroups.

BACKGROUND: Robustly examining associations between long-term conditions may be important in identifying opportunities for intervention in multimorbidity but is challenging when evidence is limited. We have developed a Bayesian inference framework that is robust to sparse data and used it to quantify morbidity associations in the oldest old, a population with limited available data. METHODS: We conducted a retrospective cross-sectional study of a representative dataset of primary care patients in Scotland as of March 2007. We included 40 long-term conditions and studied their associations in 12,009 individuals aged 90 and older, stratified by sex (3039 men, 8970 women). We analysed associations obtained with Relative Risk (RR), a standard measure in the literature, and compared them with our proposed measure, Associations Beyond Chance (ABC). To enable a broad exploration of interactions between long-term conditions, we built networks of association and assessed differences in their analysis when associations are estimated by RR or ABC. FINDINGS: Our Bayesian framework was appropriately more cautious in attributing association when evidence is lacking, particularly in uncommon conditions. This caution in reporting association was also present in reporting differences in associations between sex and affected the aggregated measures of multimorbidity and network representations. INTERPRETATION: Incorporating uncertainty into multimorbidity research is crucial to avoid misleading findings when evidence is limited, a problem that particularly affects small but important subgroups. Our proposed framework improves the reliability of estimations of associations and, more in general, of research into disease mechanisms and multimorbidity. FUNDING: National Institute for Health and Care Research.

Sensing Enhancement on Social Networks: The Role of Network Topology.

Sensing and processing information from dynamically changing environments is essential for the survival of animal collectives and the functioning of human society. In this context, previous work has shown that communication between networked agents with some preference towards adopting the majority opinion can enhance the quality of error-prone individual sensing from dynamic environments. In this paper, we compare the potential of different types of complex networks for such sensing enhancement. Numerical simulations on complex networks are complemented by a mean-field approach for limited connectivity that captures essential trends in dependencies. Our results show that, whilst bestowing advantages on a small group of agents, degree heterogeneity tends to impede overall sensing enhancement. In contrast, clustering and spatial structure play a more nuanced role depending on overall connectivity. We find that ring graphs exhibit superior enhancement for large connectivity and that random graphs outperform for small connectivity. Further exploring the role of clustering and path lengths in small-world models, we find that sensing enhancement tends to be boosted in the small-world regime.

Shadowing and shielding: Effective heuristics for continuous influence maximisation in the voting dynamics.

Influence maximisation, or how to affect the intrinsic opinion dynamics of a social group, is relevant for many applications, such as information campaigns, political competition, or marketing. Previous literature on influence maximisation has mostly explored discrete allocations of influence, i.e. optimally choosing a finite fixed number of nodes to target. Here, we study the generalised problem of continuous influence maximisation where nodes can be targeted with flexible intensity. We focus on optimal influence allocations against a passive opponent and compare the structure of the solutions in the continuous and discrete regimes. We find that, whereas hub allocations play a central role in explaining optimal allocations in the discrete regime, their explanatory power is strongly reduced in the continuous regime. Instead, we find that optimal continuous strategies are very well described by two other patterns: (i) targeting the same nodes as the opponent (shadowing) and (ii) targeting direct neighbours of the opponent (shielding). Finally, we investigate the game-theoretic scenario of two active opponents and show that the unique pure Nash equilibrium is to target all nodes equally. These results expose fundamental differences in the solutions to discrete and continuous regimes and provide novel effective heuristics for continuous influence maximisation.