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Background Precision medicine has led to the development of targeted treatment strategies tailored to individual patients based on their characteristics and disease manifestations. Although precision medicine often focuses on a single health outcome for individualized treatment decision rules (ITRs), relying only on a single outcome rather than all available outcomes information leads to suboptimal data usage when developing optimal ITRs. Methods To address this limitation, we propose a Bayesian multivariate hierarchical model that leverages the wealth of correlated health outcomes collected in clinical trials. The approach jointly models mixed types of correlated outcomes, facilitating the “borrowing of information” across the multivariate outcomes, and results in a more accurate estimation of heterogeneous treatment effects compared to using single regression models for each outcome. We develop a treatment benefit index, which quantifies the relative benefit of the experimental treatment over the control treatment, based on the proposed multivariate outcome model. Results We demonstrate the strengths of the proposed approach through extensive simulations and an application to an international Coronavirus Disease 2019 (COVID-19) treatment trial. Simulation results indicate that the proposed method reduces the occurrence of erroneous treatment decisions compared to a single regression model for a single health outcome. Additionally, the sensitivity analyses demonstrate the robustness of the model across various study scenarios. Application of the method to the COVID-19 trial exhibits improvements in estimating the individual-level treatment efficacy (indicated by narrower credible intervals for odds ratios) and optimal ITRs. Conclusion The study jointly models mixed types of outcomes in the context of developing ITRs. By considering multiple health outcomes, the proposed approach can advance the development of more effective and reliable personalized treatment.

Abiotic and biotic factors are known drivers that modulate community assembly from a regional species pool. Recent evidence has highlighted the intrinsic role of phylogenetic history on communities' response to the environment. Understanding its exact role poses a challenge because community assembly is embedded in a spatio‐temporal context where dispersal capabilities and biotic interactions may also determine species niches, especially in isolated oceanic islands. We unravelled how reef fish abundances from four oceanic islands in the southwestern Atlantic responded to environmental variability through seven years considering their phylogenetic history, functional traits and species co‐occurrence patterns. Species response to environmental variation was assessed through a multivariate hierarchical generalized linear mixed model that allows the inclusion of spatio‐temporal random effects, fitted with Bayesian inference. We found a strong phylogenetic signal (0.98) and a relatively low variance in abundance explained by functional traits, from around 30% in spring to 33% in summer, based on a posterior probability > 0.9. The most important environmental factor was surface chlorophyll‐a concentration, a proxy for primary productivity, explaining up to 23% of abundance variance. The global spatial and temporal effects on abundance were also low, with a maximum of 18% for sampling sites in spring. Our study offers a synthesis of the influence of complex phylogenetic history and geographical isolation on reef fish species niches in isolated oceanic islands, gaining new insights into how assembly processes have shaped these isolated communities.

There are two major theories for setting up ecological communities, the Niche Theory and the Neutral Theory. Both seek to explain the main factors that form a community, which is a great challenge, since each community has its particularities and the environment has different ways to manifest. We devised a process-oriented study that sought to establish the role of environmental niche driven by coastal upwelling in the assembly of reef fish communities from exposed and sheltered environments a few kilometers apart, in the region of Arraial do Cabo (southwestern Atlantic). A multivariate hierarchical generalized linear mixed model fitted with Bayesian inference was applied to abundance and presence-absence data from visual census, together with environmental data from satellite and reanalysis. We found a stronger contribution of random effects to abundance variance with 24% for sites and 20.7% for sheltered vs . exposed locations, and weaker environmental effects with 7.1% for surface chlorophyll-a concentration (SCC) and 5.4% for sea surface temperature (SST). Environmental effects had a stronger contribution in the presence-absence model, with 20.1% for SCC and 14.6% for SST. The overall influence of the upwelling environment across all species was negative, e.g., Gymnothorax moringa and Canthigaster figueiredoi showing negative responses to SCC and Parablennius pilicornis and Malacoctenus delalandii to SST. The joint action of migration-niche mechanisms is inferred from the dominance of spatio-temporal structure, limited influence of life history traits and phylogeny, explaining around 95% of species niches in the abundance model. Our results bring new evidence for the importance of different filters for community assembly other than the environment, such as phylogenetic history and dispersal. We also discuss the balance between niche (environment) and neutral (stochasticity) processes for the assembly of reef fish communities in a tropical-subtropical transition zone.

It is now widely recognized that small area estimation (SAE) needs to be model-based. Global-local (GL) shrinkage priors for random effects are important in sparse situations where many areas’ level effects do not have a significant impact on the response beyond what is offered by covariates. We propose in this paper a hierarchical multivariate model with GL priors. We prove the propriety of the posterior density when the regression coefficient matrix has an improper uniform prior. Some concentration inequalities are derived for the tail probabilities of the shrinkage estimators. The proposed method is illustrated via both data analysis and simulations.

Background Gastrointenstinal nematodes (GIN) present a serious challenge to the health and productivity of grazing stock around the globe. However, the epidemiology of GIN transmission remains poorly understood in northern climates. Combining use of serological diagnostics, GIS mapping technology, and geospatial statistics, we evaluated ecological covariates of spatial and temporal variability in GIN transmission among bovine calves pastured in Alberta, Canada. Methods Sera were collected from 1000 beef calves across Alberta, Canada over three consecutive years (2008–2010) and analyzed for presence of anti-GIN antibodies using the SVANOVIR Ostertagia osteragi -Ab ELISA kit. Using a GIS and Bayesian multivariate spatial statistics, we evaluated the degree to which variation in specific environmental covariates (e.g. moisture, humidity, temperature) was associated with variation in spatial and temporal heterogeneity in exposure to GIN ( Nematodirus and other trichostrongyles, primarily Ostertagia and Cooperia ). Results Variation in growing degree days above a base temperature of 5 °C, humidity, air temperature, and accumulated precipitation were found to be significant predictors of broad–scale spatial and temporal variation in serum antibody concentrations. Risk model projections identified that while transmission in cattle from southeastern and northwestern Alberta was relatively low in all years, rate of GIN transmission was generally higher in the central region of Alberta. Conclusions The spatial variability in risk is attributed to higher average humidity, precipitation and moderate temperatures in the central region of Alberta in comparison with the hot, dry southeastern corner of the province and the cool, dry northwestern corner. Although more targeted sampling is needed to improve model accuracy, our projections represent an important step towards tying treatment recommendations to actual risk of infection.

Recent research has contrasted the travel patterns of young adults of Generation Y (or, synonymously, the Millennial Generation) with the travel patterns of earlier generations of young adults such as those belonging to Generation X. Young adults of Generation Y are found to drive less and in some contexts are found to exhibit more multimodal travel patterns and to use public transit more often. Potential causes for these observed shifts in transport mode use have also been theorised: One view is that period effects in the form of contemporaneous changes in socio-cultural, socio-economic and socio-technical factors are responsible for the observed shifts in transport mode use; another view is that members of Generation Y have inherently different preferences and values due to formative socio-cultural, socio-economic and historical experiences. Motivated by this yet-to-be-resolved dialectic, this paper uses a hierarchical Bayesian multivariate Poisson log-normal model to examine intergenerational differences in transport mode use among young adults. The model is applied to 23 waves of the German Mobility Panel and captures between-cohort and between-period variation of parameters of interest. The trained model informs a counterfactual prediction exercise aiming to decompose intergenerational differences in transport mode use into demography-, cohort-, and period-specific effects. Our findings suggest that all three sets of effects account for intergenerational differences in transport mode use, while the absolute and relative importance of each set of effects vary across transport modes. For the period from 1998 to 2016, two thirds of the decline in car use can be ascribed to period effects; nearly all of the increase in public transit use and 42% of the increase in bicycling can be ascribed to cohort effects.

Because the power properties of traditional repeated measures and hierarchical multivariate linear models have not been clearly determined in the balanced design for longitudinal studies in the literature, the authors present a power comparison study of traditional repeated measures and hierarchical multivariate linear models under 3 variance-covariance structures. The results from a full-crossed simulation design suggest that traditional repeated measures have significantly higher power than do hierarchical multivariate linear models for main effects, but they have significantly lower power for interaction effects in most situations. Significant power differences are also exhibited when power is compared across different covariance structures.

This article provides an efficient algorithm for generating a random matrix according to a Wishart distribution, but with eigenvalues constrained to be less than a given vector of positive values. The procedure of Odell and Feiveson provides a guide, but the modifications here ensure that the diagonal elements of a candidate matrix are less than the corresponding elements of the constraint vector, thus greatly improving the chances that the matrix will be acceptable. The Normal hierarchical model with vector outcomes and the multivariate random effects model provide motivating applications.

Considering the widespread of Covid-19 and its impact on the population health in Russian regions, it is necessary to examine the impact of the pandemic (as excess mortality) on the regional socio-economic development in 2020. Based on a quantitative and qualitative model, the study explains the process of coronavirus diffusion at the regional level, using information from foreign publications, Russian regional statistics and a database of legal documents «Consultant +». The concept of spatial diffusion, developed in the 1950s-1980s, was chosen as the research methodology. The study methods include a cartographic analysis of the monthly dynamics of coronavirus spread in Russian regions and regression analysis of regional differences in excess mortality regarding the most significant explanatory variables. The developed regression model explains the spread of Covid-19 across Russian regions in 2020, while the proposed qualitative model «network-place-scaling» describes the spatial diffusion of the virus. The conducted analysis confirmed the relationship between the spread of the virus and economic specialisation of regions. Simultaneously, such widely discussed factors as physical density, urbanisation level and per capita income did not show significant correlation with excess mortality. The study revealed the following results. There is a significant discrepancy between the actual situation in Russian regions and expected developments according to the simplified centre-periphery model. The important regression variables, explaining the interregional differences in excess mortality in 2020, include the share of employed in contact-intensive wholesale and retail trade and manufacturing (large production teams); proportion of the population over 65; the number of retail facilities per 1000 people. The qualitative model «network-place-scaling» was deemed suitable for explaining the mechanisms of the spread of coronavirus in Russian regions. Future studies should focus on examining the mechanisms and socio-economic consequences of the pandemic at the municipal level of large cities and urban agglomerations in Russia.

Multilevel models are an increasingly popular method to analyze data that originate from a clustered or hierarchical structure. To effectively utilize multilevel models, one must have an adequately large number of clusters; otherwise, some model parameters will be estimated with bias. The goals for this paper are to (1) raise awareness of the problems associated with a small number of clusters, (2) review previous studies on multilevel models with a small number of clusters, (3) to provide an illustrative simulation to demonstrate how a simple model becomes adversely affected by small numbers of clusters, (4) to provide researchers with remedies if they encounter clustered data with a small number of clusters, and (5) to outline methodological topics that have yet to be addressed in the literature.