Similar Risk of Kidney Failure among Patients with Blinding Diseases Who Receive Ranibizumab, Aflibercept, and Bevacizumab: An Observational Health Data Sciences and Informatics Network Study.

PURPOSE: To characterize the incidence of kidney failure associated with intravitreal anti-VEGF exposure; and compare the risk of kidney failure in patients treated with ranibizumab, aflibercept, or bevacizumab. DESIGN: Retrospective cohort study across 12 databases in the Observational Health Data Sciences and Informatics (OHDSI) network. SUBJECTS: Subjects aged ≥ 18 years with ≥ 3 monthly intravitreal anti-VEGF medications for a blinding disease (diabetic retinopathy, diabetic macular edema, exudative age-related macular degeneration, or retinal vein occlusion). METHODS: The standardized incidence proportions and rates of kidney failure while on treatment with anti-VEGF were calculated. For each comparison (e.g., aflibercept versus ranibizumab), patients from each group were matched 1:1 using propensity scores. Cox proportional hazards models were used to estimate the risk of kidney failure while on treatment. A random effects meta-analysis was performed to combine each database's hazard ratio (HR) estimate into a single network-wide estimate. MAIN OUTCOME MEASURES: Incidence of kidney failure while on anti-VEGF treatment, and time from cohort entry to kidney failure. RESULTS: Of the 6.1 million patients with blinding diseases, 37 189 who received ranibizumab, 39 447 aflibercept, and 163 611 bevacizumab were included; the total treatment exposure time was 161 724 person-years. The average standardized incidence proportion of kidney failure was 678 per 100 000 persons (range, 0-2389), and incidence rate 742 per 100 000 person-years (range, 0-2661). The meta-analysis HR of kidney failure comparing aflibercept with ranibizumab was 1.01 (95% confidence interval [CI], 0.70-1.47; P = 0.45), ranibizumab with bevacizumab 0.95 (95% CI, 0.68-1.32; P = 0.62), and aflibercept with bevacizumab 0.95 (95% CI, 0.65-1.39; P = 0.60). CONCLUSIONS: There was no substantially different relative risk of kidney failure between those who received ranibizumab, bevacizumab, or aflibercept. Practicing ophthalmologists and nephrologists should be aware of the risk of kidney failure among patients receiving intravitreal anti-VEGF medications and that there is little empirical evidence to preferentially choose among the specific intravitreal anti-VEGF agents. FINANCIAL DISCLOSURES: Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Microbiome analysis of the restricted bacteria in radioactive element-containing water at the Fukushima Daiichi Nuclear Power Station.

A major incident occurred at the Fukushima Daiichi Nuclear Power Station following the tsunami triggered by the Tohoku-Pacific Ocean Earthquake in March 2011, whereby seawater entered the torus room in the basement of the reactor building. Here, we identify and analyze the bacterial communities in the torus room water and several environmental samples. Samples of the torus room water (1 × 109 Bq137Cs/L) were collected by the Tokyo Electric Power Company Holdings from two sampling points between 30 cm and 1 m from the bottom of the room (TW1) and the bottom layer (TW2). A structural analysis of the bacterial communities based on 16S rRNA amplicon sequencing revealed that the predominant bacterial genera in TW1 and TW2 were similar. TW1 primarily contained the genus Limnobacter, a thiosulfate-oxidizing bacterium. γ-Irradiation tests on Limnobacter thiooxidans, the most closely related phylogenetically found in TW1, indicated that its radiation resistance was similar to ordinary bacteria. TW2 predominantly contained the genus Brevirhabdus, a manganese-oxidizing bacterium. Although bacterial diversity in the torus room water was lower than seawater near Fukushima, ~70% of identified genera were associated with metal corrosion. Latent environment allocation-an analytical technique that estimates habitat distributions and co-detection analyses-revealed that the microbial communities in the torus room water originated from a distinct blend of natural marine microbial and artificial bacterial communities typical of biofilms, sludge, and wastewater. Understanding the specific bacteria linked to metal corrosion in damaged plants is important for advancing decommissioning efforts. IMPORTANCE: In the context of nuclear power station decommissioning, the proliferation of microorganisms within the reactor and piping systems constitutes a formidable challenge. Therefore, the identification of microbial communities in such environments is of paramount importance. In the aftermath of the Fukushima Daiichi Nuclear Power Station accident, microbial community analysis was conducted on environmental samples collected mainly outside the site. However, analyses using samples from on-site areas, including adjacent soil and seawater, were not performed. This study represents the first comprehensive analysis of microbial communities, utilizing meta 16S amplicon sequencing, with a focus on environmental samples collected from the radioactive element-containing water in the torus room, including the surrounding environments. Some of the identified microbial genera are shared with those previously identified in spent nuclear fuel pools in countries such as France and Brazil. Moreover, our discussion in this paper elucidates the correlation of many of these bacteria with metal corrosion.

Comparative Effectiveness of Second-line Antihyperglycemic Agents for Cardiovascular Outcomes: A Large-scale, Multinational, Federated Analysis of the LEGEND-T2DM Study.

Background: SGLT2 inhibitors (SGLT2is) and GLP-1 receptor agonists (GLP1-RAs) reduce major adverse cardiovascular events (MACE) in patients with type 2 diabetes mellitus (T2DM). However, their effectiveness relative to each other and other second-line antihyperglycemic agents is unknown, without any major ongoing head-to-head trials. Methods: Across the LEGEND-T2DM network, we included ten federated international data sources, spanning 1992-2021. We identified 1,492,855 patients with T2DM and established cardiovascular disease (CVD) on metformin monotherapy who initiated one of four second-line agents (SGLT2is, GLP1-RAs, dipeptidyl peptidase 4 inhibitor [DPP4is], sulfonylureas [SUs]). We used large-scale propensity score models to conduct an active comparator, target trial emulation for pairwise comparisons. After evaluating empirical equipoise and population generalizability, we fit on-treatment Cox proportional hazard models for 3-point MACE (myocardial infarction, stroke, death) and 4-point MACE (3-point MACE + heart failure hospitalization) risk, and combined hazard ratio (HR) estimates in a random-effects meta-analysis. Findings: Across cohorts, 16·4%, 8·3%, 27·7%, and 47·6% of individuals with T2DM initiated SGLT2is, GLP1-RAs, DPP4is, and SUs, respectively. Over 5·2 million patient-years of follow-up and 489 million patient-days of time at-risk, there were 25,982 3-point MACE and 41,447 4-point MACE events. SGLT2is and GLP1-RAs were associated with a lower risk for 3-point MACE compared with DPP4is (HR 0·89 [95% CI, 0·79-1·00] and 0·83 [0·70-0·98]), and SUs (HR 0·76 [0·65-0·89] and 0·71 [0·59-0·86]). DPP4is were associated with a lower 3-point MACE risk versus SUs (HR 0·87 [0·79-0·95]). The pattern was consistent for 4-point MACE for the comparisons above. There were no significant differences between SGLT2is and GLP1-RAs for 3-point or 4-point MACE (HR 1·06 [0·96-1·17] and 1·05 [0·97-1·13]). Interpretation: In patients with T2DM and established CVD, we found comparable cardiovascular risk reduction with SGLT2is and GLP1-RAs, with both agents more effective than DPP4is, which in turn were more effective than SUs. These findings suggest that the use of GLP1-RAs and SGLT2is should be prioritized as second-line agents in those with established CVD. Funding: National Institutes of Health, United States Department of Veterans Affairs.

Bayesian safety surveillance with adaptive bias correction.

Postmarket safety surveillance is an integral part of mass vaccination programs. Typically relying on sequential analysis of real-world health data as they accrue, safety surveillance is challenged by sequential multiple testing and by biases induced by residual confounding in observational data. The current standard approach based on the maximized sequential probability ratio test (MaxSPRT) fails to satisfactorily address these practical challenges and it remains a rigid framework that requires prespecification of the surveillance schedule. We develop an alternative Bayesian surveillance procedure that addresses both aforementioned challenges using a more flexible framework. To mitigate bias, we jointly analyze a large set of negative control outcomes that are adverse events with no known association with the vaccines in order to inform an empirical bias distribution, which we then incorporate into estimating the effect of vaccine exposure on the adverse event of interest through a Bayesian hierarchical model. To address multiple testing and improve on flexibility, at each analysis timepoint, we update a posterior probability in favor of the alternative hypothesis that vaccination induces higher risks of adverse events, and then use it for sequential detection of safety signals. Through an empirical evaluation using six US observational healthcare databases covering more than 360 million patients, we benchmark the proposed procedure against MaxSPRT on testing errors and estimation accuracy, under two epidemiological designs, the historical comparator and the self-controlled case series. We demonstrate that our procedure substantially reduces Type 1 error rates, maintains high statistical power and fast signal detection, and provides considerably more accurate estimation than MaxSPRT. Given the extensiveness of the empirical study which yields more than 7 million sets of results, we present all results in a public R ShinyApp. As an effort to promote open science, we provide full implementation of our method in the open-source R package EvidenceSynthesis.

Shrinkage-based Random Local Clocks with Scalable Inference.

Molecular clock models undergird modern methods of divergence-time estimation. Local clock models propose that the rate of molecular evolution is constant within phylogenetic subtrees. Current local clock inference procedures exhibit one or more weaknesses, namely they achieve limited scalability to trees with large numbers of taxa, impose model misspecification, or require a priori knowledge of the existence and location of clocks. To overcome these challenges, we present an autocorrelated, Bayesian model of heritable clock rate evolution that leverages heavy-tailed priors with mean zero to shrink increments of change between branch-specific clocks. We further develop an efficient Hamiltonian Monte Carlo sampler that exploits closed form gradient computations to scale our model to large trees. Inference under our shrinkage clock exhibits a speed-up compared to the popular random local clock when estimating branch-specific clock rates on a variety of simulated datasets. This speed-up increases with the size of the problem. We further show our shrinkage clock recovers known local clocks within a rodent and mammalian phylogeny. Finally, in a problem that once appeared computationally impractical, we investigate the heritable clock structure of various surface glycoproteins of influenza A virus in the absence of prior knowledge about clock placement. We implement our shrinkage clock and make it publicly available in the BEAST software package.

Multinational patterns of second line antihyperglycaemic drug initiation across cardiovascular risk groups: federated pharmacoepidemiological evaluation in LEGEND-T2DM.

Objective: To assess the uptake of second line antihyperglycaemic drugs among patients with type 2 diabetes mellitus who are receiving metformin. Design: Federated pharmacoepidemiological evaluation in LEGEND-T2DM. Setting: 10 US and seven non-US electronic health record and administrative claims databases in the Observational Health Data Sciences and Informatics network in eight countries from 2011 to the end of 2021. Participants: 4.8 million patients (≥18 years) across US and non-US based databases with type 2 diabetes mellitus who had received metformin monotherapy and had initiated second line treatments. Exposure: The exposure used to evaluate each database was calendar year trends, with the years in the study that were specific to each cohort. Main outcomes measures: The outcome was the incidence of second line antihyperglycaemic drug use (ie, glucagon-like peptide-1 receptor agonists, sodium-glucose cotransporter-2 inhibitors, dipeptidyl peptidase-4 inhibitors, and sulfonylureas) among individuals who were already receiving treatment with metformin. The relative drug class level uptake across cardiovascular risk groups was also evaluated. Results: 4.6 million patients were identified in US databases, 61 382 from Spain, 32 442 from Germany, 25 173 from the UK, 13 270 from France, 5580 from Scotland, 4614 from Hong Kong, and 2322 from Australia. During 2011-21, the combined proportional initiation of the cardioprotective antihyperglycaemic drugs (glucagon-like peptide-1 receptor agonists and sodium-glucose cotransporter-2 inhibitors) increased across all data sources, with the combined initiation of these drugs as second line drugs in 2021 ranging from 35.2% to 68.2% in the US databases, 15.4% in France, 34.7% in Spain, 50.1% in Germany, and 54.8% in Scotland. From 2016 to 2021, in some US and non-US databases, uptake of glucagon-like peptide-1 receptor agonists and sodium-glucose cotransporter-2 inhibitors increased more significantly among populations with no cardiovascular disease compared with patients with established cardiovascular disease. No data source provided evidence of a greater increase in the uptake of these two drug classes in populations with cardiovascular disease compared with no cardiovascular disease. Conclusions: Despite the increase in overall uptake of cardioprotective antihyperglycaemic drugs as second line treatments for type 2 diabetes mellitus, their uptake was lower in patients with cardiovascular disease than in people with no cardiovascular disease over the past decade. A strategy is needed to ensure that medication use is concordant with guideline recommendations to improve outcomes of patients with type 2 diabetes mellitus.

Accelerating Bayesian inference of dependency between mixed-type biological traits.

Inferring dependencies between mixed-type biological traits while accounting for evolutionary relationships between specimens is of great scientific interest yet remains infeasible when trait and specimen counts grow large. The state-of-the-art approach uses a phylogenetic multivariate probit model to accommodate binary and continuous traits via a latent variable framework, and utilizes an efficient bouncy particle sampler (BPS) to tackle the computational bottleneck-integrating many latent variables from a high-dimensional truncated normal distribution. This approach breaks down as the number of specimens grows and fails to reliably characterize conditional dependencies between traits. Here, we propose an inference pipeline for phylogenetic probit models that greatly outperforms BPS. The novelty lies in 1) a combination of the recent Zigzag Hamiltonian Monte Carlo (Zigzag-HMC) with linear-time gradient evaluations and 2) a joint sampling scheme for highly correlated latent variables and correlation matrix elements. In an application exploring HIV-1 evolution from 535 viruses, the inference requires joint sampling from an 11,235-dimensional truncated normal and a 24-dimensional covariance matrix. Our method yields a 5-fold speedup compared to BPS and makes it possible to learn partial correlations between candidate viral mutations and virulence. Computational speedup now enables us to tackle even larger problems: we study the evolution of influenza H1N1 glycosylations on around 900 viruses. For broader applicability, we extend the phylogenetic probit model to incorporate categorical traits, and demonstrate its use to study Aquilegia flower and pollinator co-evolution.

Adjusting for both sequential testing and systematic error in safety surveillance using observational data: Empirical calibration and MaxSPRT.

Post-approval safety surveillance of medical products using observational healthcare data can help identify safety issues beyond those found in pre-approval trials. When testing sequentially as data accrue, maximum sequential probability ratio testing (MaxSPRT) is a common approach to maintaining nominal type 1 error. However, the true type 1 error may still deviate from the specified one because of systematic error due to the observational nature of the analysis. This systematic error may persist even after controlling for known confounders. Here we propose to address this issue by combing MaxSPRT with empirical calibration. In empirical calibration, we assume uncertainty about the systematic error in our analysis, the source of uncertainty commonly overlooked in practice. We infer a probability distribution of systematic error by relying on a large set of negative controls: exposure-outcome pairs where no causal effect is believed to exist. Integrating this distribution into our test statistics has previously been shown to restore type 1 error to nominal. Here we show how we can calibrate the critical value central to MaxSPRT. We evaluate this novel approach using simulations and real electronic health records, using H1N1 vaccinations during the 2009-2010 season as an example. Results show that combining empirical calibration with MaxSPRT restores nominal type 1 error. In our real-world example, adjusting for systematic error using empirical calibration has a larger impact than, and hence is just as essential as, adjusting for sequential testing using MaxSPRT. We recommend performing both, using the method described here.

Shrinkage with shrunken shoulders: Gibbs sampling shrinkage model posteriors with guaranteed convergence rates.

Use of continuous shrinkage priors - with a "spike" near zero and heavy-tails towards infinity - is an increasingly popular approach to induce sparsity in parameter estimates. When the parameters are only weakly identified by the likelihood, however, the posterior may end up with tails as heavy as the prior, jeopardizing robustness of inference. A natural solution is to "shrink the shoulders" of a shrinkage prior by lightening up its tails beyond a reasonable parameter range, yielding a regularized version of the prior. We develop a regularization approach which, unlike previous proposals, preserves computationally attractive structures of original shrinkage priors. We study theoretical properties of the Gibbs sampler on resulting posterior distributions, with emphasis on convergence rates of the Pólya-Gamma Gibbs sampler for sparse logistic regression. Our analysis shows that the proposed regularization leads to geometric ergodicity under a broad range of global-local shrinkage priors. Essentially, the only requirement is for the prior πlocal(⋅) on the local scale λ to satisfy πlocal(0)<∞. If πlocal(⋅) further satisfies limλ→0πlocal(λ)/λa<∞ for a>0, as in the case of Bayesian bridge priors, we show the sampler to be uniformly ergodic.

Prior-Preconditioned Conjugate Gradient Method for Accelerated Gibbs Sampling in "Large n, Large p" Bayesian Sparse Regression.

In a modern observational study based on healthcare databases, the number of observations and of predictors typically range in the order of 105-106 and of 104-105. Despite the large sample size, data rarely provide sufficient information to reliably estimate such a large number of parameters. Sparse regression techniques provide potential solutions, one notable approach being the Bayesian method based on shrinkage priors. In the "large n and large p" setting, however, the required posterior computation encounters a bottleneck at repeated sampling from a high-dimensional Gaussian distribution, whose precision matrix Φ is expensive to compute and factorize. In this article, we present a novel algorithm to speed up this bottleneck based on the following observation: We can cheaply generate a random vector b such that the solution to the linear system Φß = b has the desired Gaussian distribution. We can then solve the linear system by the conjugate gradient (CG) algorithm through matrix-vector multiplications by Φ; this involves no explicit factorization or calculation of Φ itself. Rapid convergence of CG in this context is guaranteed by the theory of prior-preconditioning we develop. We apply our algorithm to a clinically relevant large-scale observational study with n = 72,489 patients and p = 22,175 clinical covariates, designed to assess the relative risk of adverse events from two alternative blood anti-coagulants. Our algorithm demonstrates an order of magnitude speed-up in posterior inference, in our case cutting the computation time from two weeks to less than a day. Supplementary materials for this article are available online.

International cohort study indicates no association between alpha-1 blockers and susceptibility to COVID-19 in benign prostatic hyperplasia patients.

Purpose: Alpha-1 blockers, often used to treat benign prostatic hyperplasia (BPH), have been hypothesized to prevent COVID-19 complications by minimising cytokine storm release. The proposed treatment based on this hypothesis currently lacks support from reliable real-world evidence, however. We leverage an international network of large-scale healthcare databases to generate comprehensive evidence in a transparent and reproducible manner. Methods: In this international cohort study, we deployed electronic health records from Spain (SIDIAP) and the United States (Department of Veterans Affairs, Columbia University Irving Medical Center, IQVIA OpenClaims, Optum DOD, Optum EHR). We assessed association between alpha-1 blocker use and risks of three COVID-19 outcomes-diagnosis, hospitalization, and hospitalization requiring intensive services-using a prevalent-user active-comparator design. We estimated hazard ratios using state-of-the-art techniques to minimize potential confounding, including large-scale propensity score matching/stratification and negative control calibration. We pooled database-specific estimates through random effects meta-analysis. Results: Our study overall included 2.6 and 0.46 million users of alpha-1 blockers and of alternative BPH medications. We observed no significant difference in their risks for any of the COVID-19 outcomes, with our meta-analytic HR estimates being 1.02 (95% CI: 0.92-1.13) for diagnosis, 1.00 (95% CI: 0.89-1.13) for hospitalization, and 1.15 (95% CI: 0.71-1.88) for hospitalization requiring intensive services. Conclusion: We found no evidence of the hypothesized reduction in risks of the COVID-19 outcomes from the prevalent-use of alpha-1 blockers-further research is needed to identify effective therapies for this novel disease.

Learning and Predicting from Dynamic Models for COVID-19 Patient Monitoring.

COVID-19 has challenged health systems to learn how to learn. This paper describes the context, methods and challenges for learning to improve COVID-19 care at one academic health center. Challenges to learning include: (1) choosing a right clinical target; (2) designing methods for accurate predictions by borrowing strength from prior patients' experiences; (3) communicating the methodology to clinicians so they understand and trust it; (4) communicating the predictions to the patient at the moment of clinical decision; and (5) continuously evaluating and revising the methods so they adapt to changing patients and clinical demands. To illustrate these challenges, this paper contrasts two statistical modeling approaches - prospective longitudinal models in common use and retrospective analogues complementary in the COVID-19 context - for predicting future biomarker trajectories and major clinical events. The methods are applied to and validated on a cohort of 1,678 patients who were hospitalized with COVID-19 during the early months of the pandemic. We emphasize graphical tools to promote physician learning and inform clinical decision making.

Ten Rules for Conducting Retrospective Pharmacoepidemiological Analyses: Example COVID-19 Study.

Since the beginning of the COVID-19 pandemic, pharmaceutical treatment hypotheses have abounded, each requiring careful evaluation. A randomized controlled trial generally provides the most credible evaluation of a treatment, but the efficiency and effectiveness of the trial depend on the existing evidence supporting the treatment. The researcher must therefore compile a body of evidence justifying the use of time and resources to further investigate a treatment hypothesis in a trial. An observational study can provide this evidence, but the lack of randomized exposure and the researcher's inability to control treatment administration and data collection introduce significant challenges. A proper analysis of observational health care data thus requires contributions from experts in a diverse set of topics ranging from epidemiology and causal analysis to relevant medical specialties and data sources. Here we summarize these contributions as 10 rules that serve as an end-to-end introduction to retrospective pharmacoepidemiological analyses of observational health care data using a running example of a hypothetical COVID-19 study. A detailed supplement presents a practical how-to guide for following each rule. When carefully designed and properly executed, a retrospective pharmacoepidemiological analysis framed around these rules will inform the decisions of whether and how to investigate a treatment hypothesis in a randomized controlled trial. This work has important implications for any future pandemic by prescribing what we can and should do while the world waits for global vaccine distribution.

Alpha-1 adrenergic receptor antagonists to prevent hyperinflammation and death from lower respiratory tract infection.

In severe viral pneumonia, including Coronavirus disease 2019 (COVID-19), the viral replication phase is often followed by hyperinflammation, which can lead to acute respiratory distress syndrome, multi-organ failure, and death. We previously demonstrated that alpha-1 adrenergic receptor (⍺1-AR) antagonists can prevent hyperinflammation and death in mice. Here, we conducted retrospective analyses in two cohorts of patients with acute respiratory distress (ARD, n = 18,547) and three cohorts with pneumonia (n = 400,907). Federated across two ARD cohorts, we find that patients exposed to ⍺1-AR antagonists, as compared to unexposed patients, had a 34% relative risk reduction for mechanical ventilation and death (OR = 0.70, p = 0.021). We replicated these methods on three pneumonia cohorts, all with similar effects on both outcomes. All results were robust to sensitivity analyses. These results highlight the urgent need for prospective trials testing whether prophylactic use of ⍺1-AR antagonists ameliorates lower respiratory tract infection-associated hyperinflammation and death, as observed in COVID-19.

Alpha-1 blockers and susceptibility to COVID-19 in benign prostate hyperplasia patients : an international cohort study.

Alpha-1 blockers, often used to treat benign prostate hyperplasia (BPH), have been hypothesized to prevent COVID-19 complications by minimising cytokine storms release. We conducted a prevalent-user active-comparator cohort study to assess association between alpha-1 blocker use and risks of three COVID-19 outcomes: diagnosis, hospitalization, and hospitalization requiring intensive services. Our study included 2.6 and 0.46 million users of alpha-1 blockers and of alternative BPH therapy during the period between November 2019 and January 2020, found in electronic health records from Spain (SIDIAP) and the United States (Department of Veterans Affairs, Columbia University Irving Medical Center, IQVIA OpenClaims, Optum DOD, Optum EHR). We estimated hazard ratios using state-of-the-art techniques to minimize potential confounding, including large-scale propensity score matching/stratification and negative control calibration. We found no differential risk for any of COVID-19 outcome, pointing to the need for further research on potential COVID-19 therapies.

Alpha-1 adrenergic receptor antagonists to prevent hyperinflammation and death from lower respiratory tract infection.

In severe viral pneumonia, including Coronavirus disease 2019 (COVID-19), the viral replication phase is often followed by hyperinflammation, which can lead to acute respiratory distress syndrome, multi-organ failure, and death. We previously demonstrated that alpha-1 adrenergic receptor ($\alpha_1$-AR) antagonists can prevent hyperinflammation and death in mice. Here, we conducted retrospective analyses in two cohorts of patients with acute respiratory distress (ARD, n=18,547) and three cohorts with pneumonia (n=400,907). Federated across two ARD cohorts, we find that patients exposed to $\alpha_1$-AR antagonists, as compared to unexposed patients, had a 34% relative risk reduction for mechanical ventilation and death (OR=0.70, p=0.021). We replicated these methods on three pneumonia cohorts, all with similar effects on both outcomes. All results were robust to sensitivity analyses. These results highlight the urgent need for prospective trials testing whether prophylactic use of $\alpha_1$-AR antagonists ameliorates lower respiratory tract infection-associated hyperinflammation and death, as observed in COVID-19.

Gradients Do Grow on Trees: A Linear-Time O(N)-Dimensional Gradient for Statistical Phylogenetics.

Calculation of the log-likelihood stands as the computational bottleneck for many statistical phylogenetic algorithms. Even worse is its gradient evaluation, often used to target regions of high probability. Order O(N)-dimensional gradient calculations based on the standard pruning algorithm require O(N2) operations, where N is the number of sampled molecular sequences. With the advent of high-throughput sequencing, recent phylogenetic studies have analyzed hundreds to thousands of sequences, with an apparent trend toward even larger data sets as a result of advancing technology. Such large-scale analyses challenge phylogenetic reconstruction by requiring inference on larger sets of process parameters to model the increasing data heterogeneity. To make these analyses tractable, we present a linear-time algorithm for O(N)-dimensional gradient evaluation and apply it to general continuous-time Markov processes of sequence substitution on a phylogenetic tree without a need to assume either stationarity or reversibility. We apply this approach to learn the branch-specific evolutionary rates of three pathogenic viruses: West Nile virus, Dengue virus, and Lassa virus. Our proposed algorithm significantly improves inference efficiency with a 126- to 234-fold increase in maximum-likelihood optimization and a 16- to 33-fold computational performance increase in a Bayesian framework.

Bayesian constraint relaxation.

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without relying on asymptotic approximations. However, sharply constrained priors are not necessary in some settings and tend to limit modelling scope to a narrow set of distributions that are tractable computationally. We propose to replace the sharp indicator function of the constraint with an exponential kernel, thereby creating a close-to-constrained neighbourhood within the Euclidean space in which the constrained subspace is embedded. This kernel decays with distance from the constrained space at a rate depending on a relaxation hyperparameter. By avoiding the sharp constraint, we enable use of off-the-shelf posterior sampling algorithms, such as Hamiltonian Monte Carlo, facilitating automatic computation in a broad range of models. We study the constrained and relaxed distributions under multiple settings and theoretically quantify their differences. Application of the method is illustrated through several novel modelling examples.