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Randomized clinical trials have been the mainstay of clinical research, but are prohibitively expensive and subject to increasingly difficult patient recruitment. Recently, there is a movement to use real-world data (RWD) from electronic health records, patient registries, claims data and other sources in lieu of or supplementing controlled clinical trials. This process of combining information from diverse sources calls for inference under a Bayesian paradigm. We review some of the currently used methods and a novel non-parametric Bayesian (BNP) method. Carrying out the desired adjustment for differences in patient populations is naturally done with BNP priors that facilitate understanding of and adjustment for population heterogeneities across different data sources. We discuss the particular problem of using RWD to create a synthetic control arm to supplement single-arm treatment only studies. At the core of the proposed approach is the model-based adjustment to achieve equivalent patient populations in the current study and the (adjusted) RWD. This is implemented using common atoms mixture models. The structure of such models greatly simplifies inference. The adjustment for differences in the populations can be reduced to ratios of weights in such mixtures. This article is part of the theme issue ‘Bayesian inference: challenges, perspectives, and prospects’. 

Abstract Large stocks of soil carbon (C) and nitrogen (N) in northern permafrost soils are vulnerable to remobilization under climate change. However, there are large uncertainties in present‐day greenhouse gas (GHG) budgets. We compare bottom‐up (data‐driven upscaling and process‐based models) and top‐down (atmospheric inversion models) budgets of carbon dioxide (CO₂), methane (CH₄) and nitrous oxide (N₂O) as well as lateral fluxes of C and N across the region over 2000–2020. Bottom‐up approaches estimate higher land‐to‐atmosphere fluxes for all GHGs. Both bottom‐up and top‐down approaches show a sink of CO₂in natural ecosystems (bottom‐up: −29 (−709, 455), top‐down: −587 (−862, −312) Tg CO₂‐C yr⁻¹) and sources of CH₄(bottom‐up: 38 (22, 53), top‐down: 15 (11, 18) Tg CH₄‐C yr⁻¹) and N₂O (bottom‐up: 0.7 (0.1, 1.3), top‐down: 0.09 (−0.19, 0.37) Tg N₂O‐N yr⁻¹). The combined global warming potential of all three gases (GWP‐100) cannot be distinguished from neutral. Over shorter timescales (GWP‐20), the region is a net GHG source because CH₄dominates the total forcing. The net CO₂sink in Boreal forests and wetlands is largely offset by fires and inland water CO₂emissions as well as CH₄emissions from wetlands and inland waters, with a smaller contribution from N₂O emissions. Priorities for future research include the representation of inland waters in process‐based models and the compilation of process‐model ensembles for CH₄and N₂O. Discrepancies between bottom‐up and top‐down methods call for analyses of how prior flux ensembles impact inversion budgets, more and well‐distributed in situ GHG measurements and improved resolution in upscaling techniques. 

Evolutionary biologists typically envision a trait’s genetic basis and fitness effects occurring within a single species. However, traits can be determined by and have fitness consequences for interacting species, thus evolving in multiple genomes. This is especially likely in mutualisms, where species exchange fitness benefits and can associate over long periods of time. Partners may experience evolutionary conflict over the value of a multi-genomic trait, but such conflicts may be ameliorated by mutualism’s positive fitness feedbacks. Here, we develop a simulation model of a host–microbe mutualism to explore the evolution of a multi-genomic trait. Coevolutionary outcomes depend on whether hosts and microbes have similar or different optimal trait values, strengths of selection and fitness feedbacks. We show that genome-wide association studies can map joint traits to loci in multiple genomes and describe how fitness conflict and fitness feedback generate different multi-genomic architectures with distinct signals around segregating loci. Partner fitnesses can be positively correlated even when partners are in conflict over the value of a multi-genomic trait, and conflict can generate strong mutualistic dependency. While fitness alignment facilitates rapid adaptation to a new optimum, conflict maintains genetic variation and evolvability, with implications for applied microbiome science.