Bayesian Hierarchical Models can Infer Interpretable Predictions of Leaf Area Index From Heterogeneous Datasets

Environmental scientists often face the challenge of predicting a complex phenomenon from a heterogeneous collection of datasets that exhibit systematic differences. Accounting for these differences usually requires including additional parameters in the predictive models, which increases the probability of overfitting, particularly on small datasets. We investigate how Bayesian hierarchical models can help mitigate this problem by allowing the practitioner to incorporate information about the structure of the dataset explicitly. To this end, we look at a typical application in remote sensing: the estimation of leaf area index of white winter wheat, an important indicator for agronomical modeling, using measurements of reflectance spectra collected at different locations and growth stages. Since the insights gained from such a model could be used to inform policy or business decisions, the interpretability of the model is a primary concern. We, therefore, focus on models that capture the association between leaf area index and the spectral reflectance at various wavelengths by spline-based kernel functions, which can be visually inspected and analyzed. We compare models with three different levels of hierarchy: a non-hierarchical baseline model, a model with hierarchical bias parameter, and a model in which bias and kernel parameters are hierarchically structured. We analyze them using Markov Chain Monte Carlo sampling diagnostics and an intervention-based measure of feature importance. The improved robustness and interpretability of this approach show that Bayesian hierarchical models are a versatile tool for the prediction of leaf area index, particularly in scenarios where the available data sources are heterogeneous.

795. A Bayesian Spatial-temporal Modelling Approach for Prevalence Estimation of a VRE Outbreak in a Tertiary Care Hospital

Background There was a nosocomial outbreak of vancomycin-resistant enterococci (VRE) in our hospital group from 2018-19. The goals of the study were to describe the prevalence trajectory and explore risk factors associated with putative room colonization during the outbreak. Methods We performed a room centric analysis of 12 floors (floors F to R, 264 rooms) of the main bed tower of the hospital, including data on 37’458 patients (23’050 person weeks) over the 104 week period. Patients were assumed to be colonized in the week prior to their first positive test, and thereafter throughout the remainder of their stay until discharge. Poisson Bayesian Hierarchical models were fitted to estimate prevalence per room, including both spatial (conditional autoregressive) and temporal (random walk) random effects terms. Model M1 estimated prevalence for each floor and then used meta-analysis to combine the estimates, whereas model M2 estimated prevalence for “all-floors” simultaneously. Results The oncology department, where the outbreak was thought to have started, experienced slightly higher prevalence (floors O and R; adjusted incidence rate ratio (aIRR) 4.8 [2.6, 8.9], p< 0.001; reference is general medicine; see Figure Panel A), as did both the cardiac surgery (floors G, N, O; aIRR 3.8 [2.0, 7.3], p< 0.001) and abdominal surgery departments (floors H and Q; 3.7 [1.8, 7.6], p< 0.001). There was no discernible difference in prevalence between floors with single and multiple department occupancy. Furthermore, departments spread across multiple floors had similar prevalence on all constituent floors – perhaps indicating transmission by people or devices moving between floors. The “single floor meta-analysis” model (M1) more closely followed the estimated trajectory for the crude prevalence, whereas the “all floors” model (M2) dampened the amplitude of the peaks somewhat, but better estimated periods of low prevalence (Figure Panel B). Figure: Estimates from the Bayesian Hierarchical Models Panel A. Random effect prevalence estimates for each floor (from model M2). Panel B. Crude prevalence (black) and estimates from the “single floor meta-analysis” approach (M1, dashed red) with 95% credible intervals shaded (shaded red), and “all-floors” model (M2, blue ). Conclusion We applied a room centric approach that took into account spatial and temporal dependencies apparent in the nosocomial VRE outbreak. Despite additional complexity, Bayesian Hierarchical Models provide a more flexible platform for studying transmission dynamics and performing hypothesis testing, compared to more traditional methods. Disclosures All Authors: No reported disclosures

Bayesian hierarchical models can infer interpretable predictions of leaf area index from heterogeneous datasets

Environmental scientists often have to predict a complex phenomenon from a heterogeneous collection of datasets. This is particularly challenging if there are systematic differences between them, as is often the case. Accounting for these differences requires a larger number of parameters and thus increases the risk of overfitting. We investigate how Bayesian hierarchical models can help mitigate this problem by allowing the practitioner to explicitly incorporate information about the dataset structure and general domain knowledge. To this end, we look at a typical application in remote sensing: the estimation of leaf area index (of white winter wheat), an important indicator for agronomical modeling, from measurements of reflectance spectra collected at different locations and growth stages. Since the insights gained from such a model could be used to inform policy or business decisions, the interpretability of the model is a primary concern. We, therefore, focus on models that capture the association between leaf area index and the spectral reflectance at various wavelengths by spline-based kernel functions, which can be visually inspected and analyzed. We compare models with three different levels of hierarchy: a non-hierarchical baseline model, a model with hierarchical bias parameter, and a model in which bias and kernel parameters are hierarchically structured. We analyze them using Markov Chain Monte Carlo sampling diagnostics and an intervention-based measure of feature importance. The improved robustness and interpretability of this approach lead us to recommend Bayesian hierarchical models as a versatile tool for environmental sciences and beyond, particularly in scenarios where the available data sources are heterogeneous.

Bayesian Models for Analysis of Inventory and Monitoring Data with Non-ignorable Missingness

We describe the application of Bayesian hierarchical models to the analysis of data from long-term, environmental monitoring programs. The goal of these ongoing programs is to understand status and trend in natural resources. Data are usually collected using complex sampling designs including stratification, revisit schedules, finite populations, unequal probabilities of inclusion of sample units, and censored observations. Complex designs intentionally create data that are missing from the complete data that could theoretically be obtained. This “missingness” cannot be ignored in analysis. Data collected by monitoring programs have traditionally been analyzed using the design-based Horvitz–Thompson estimator to obtain point estimates of means and variances over time. However, Horvitz–Thompson point estimates are not capable of supporting inference on temporal trend or the predictor variables that might explain trend, which instead requires model-based inference. The key to applying model-based inference to data arising from complex designs is to include information about the sampling design in the analysis. The statistical concept of ignorability provides a theoretical foundation for meeting this requirement. We show how Bayesian hierarchical models provide a general framework supporting inference on status and trend using data from the National Park Service Inventory and Monitoring Program as examples. Supplemental Materials Code and data for implementing the analyses described here can be accessed here: https://doi.org/10.36967/code-2287025.

Improving the Estimation of Subgroup Effects for Clinical Trial Participants with Multimorbidity by Incorporating Drug Class-Level Information in Bayesian Hierarchical Models: A Simulation Study

Background There is limited guidance for using common drug therapies in the context of multimorbidity. In part, this is because their effectiveness for patients with specific comorbidities cannot easily be established using subgroup analyses in clinical trials. Here, we use simulations to explore the feasibility and implications of concurrently estimating effects of related drug treatments in patients with multimorbidity by partially pooling subgroup efficacy estimates across trials. Methods We performed simulations based on the characteristics of 161 real clinical trials of noninsulin glucose-lowering drugs for diabetes, estimating subgroup effects for patients with a hypothetical comorbidity across related trials in different scenarios using Bayesian hierarchical generalized linear models. We structured models according to an established ontology—the World Health Organization Anatomic Chemical Therapeutic Classifications—allowing us to nest all trials within drugs and all drugs within anatomic chemical therapeutic classes, with effects partially pooled at each level of the hierarchy. In a range of scenarios, we compared the performance of this model to random effects meta-analyses of all drugs individually. Results Hierarchical, ontology-based Bayesian models were unbiased and accurately recovered simulated comorbidity-drug interactions. Compared with single-drug meta-analyses, they offered a relative increase in precision of up to 250% in some scenarios because of information sharing across the hierarchy. Because of the relative precision of the approaches, a large proportion of small subgroup effects was detectable only using the hierarchical model. Conclusions By assuming that similar drugs may have similar subgroup effects, Bayesian hierarchical models based on structures defined by existing ontologies can be used to improve the precision of treatment efficacy estimates in patients with multimorbidity, with potential implications for clinical decision making.