Locally Adaptive Smoothing with Markov Random Fields and Shrinkage Priors

Adaptive Gaussian Markov random fields for child mortality estimation

The under-5 mortality rate (U5MR), a critical health indicator, is typically estimated from household surveys in lower and middle income countries. Spatio-temporal disaggregation of household survey data can lead to highly variable estimates of U5MR, necessitating the usage of smoothing models which borrow information across space and time. The assumptions of common smoothing models may be unrealistic when certain time periods or regions are expected to have shocks in mortality relative to their neighbors, which can lead to oversmoothing of U5MR estimates. In this paper, we develop a spatial and temporal smoothing approach based on Gaussian Markov random field models which incorporate knowledge of these expected shocks in mortality. We demonstrate the potential for these models to improve upon alternatives not incorporating knowledge of expected shocks in a simulation study. We apply these models to estimate U5MR in Rwanda at the national level from 1985 to 2019, a time period which includes the Rwandan civil war and genocide.

Modeling basal body temperature data using horseshoe process regression

Biomedical data often exhibit jumps or abrupt changes. For example, women's basal body temperature may jump at ovulation, menstruation, implantation, and miscarriage. These sudden changes make these data challenging to model: many methods will oversmooth the sharp changes or overfit in response to measurement error. We develop horseshoe process regression (HPR) to address this problem. We define a horseshoe process as a stochastic process in which each increment is horseshoe-distributed. We use the horseshoe process as a nonparametric Bayesian prior for modeling a potentially nonlinear association between an outcome and its continuous predictor, which we implement via Stan and in the R package HPR. We provide guidance and extensions to advance HPR's use in applied practice: we introduce a Bayesian imputation scheme to allow for interpolation at unobserved values of the predictor within the HPR; include additional covariates via a partial linear model framework; and allow for monotonicity constraints. We find that HPR performs well when fitting functions that have sharp changes. We apply HPR to model women's basal body temperatures over the course of the menstrual cycle.

BayesTME: An end-to-end method for multiscale spatial transcriptional profiling of the tissue microenvironment

Spatial variation in cellular phenotypes underlies heterogeneity in immune recognition and response to therapy in cancer and many other diseases. Spatial transcriptomics holds the potential to quantify such variation, but existing analysis methods are limited by their focus on individual tasks such as spot deconvolution. We present BayesTME, an end-to-end Bayesian method for analyzing spatial transcriptomics data. BayesTME unifies several previously distinct analysis goals under a single, holistic generative model. This unified approach enables BayesTME to deconvolve spots into cell phenotypes without any need for paired single-cell RNA-seq. BayesTME then goes beyond spot deconvolution to uncover spatial expression patterns among coordinated subsets of genes within phenotypes, which we term spatial transcriptional programs. BayesTME achieves state-of-the-art performance across myriad benchmarks. On human and zebrafish melanoma tissues, BayesTME identifies spatial transcriptional programs that capture fundamental biological phenomena such as bilateral symmetry and tumor-associated fibroblast and macrophage reprogramming. BayesTME is open source.

adaPop: Bayesian inference of dependent population dynamics in coalescent models

The coalescent is a powerful statistical framework that allows us to infer past population dynamics leveraging the ancestral relationships reconstructed from sampled molecular sequence data. In many biomedical applications, such as in the study of infectious diseases, cell development, and tumorgenesis, several distinct populations share evolutionary history and therefore become dependent. The inference of such dependence is a highly important, yet a challenging problem. With advances in sequencing technologies, we are well positioned to exploit the wealth of high-resolution biological data for tackling this problem. Here, we present adaPop, a probabilistic model to estimate past population dynamics of dependent populations and to quantify their degree of dependence. An essential feature of our approach is the ability to track the time-varying association between the populations while making minimal assumptions on their functional shapes via Markov random field priors. We provide nonparametric estimators, extensions of our base model that integrate multiple data sources, and fast scalable inference algorithms. We test our method using simulated data under various dependent population histories and demonstrate the utility of our model in shedding light on evolutionary histories of different variants of SARS-CoV-2.

Bayesian Trend Filtering via Proximal Markov Chain Monte Carlo

Proximal Markov Chain Monte Carlo is a novel construct that lies at the intersection of Bayesian computation and convex optimization, which helped popularize the use of nondifferentiable priors in Bayesian statistics. Existing formulations of proximal MCMC, however, require hyperparameters and regularization parameters to be prespecified. In this work, we extend the paradigm of proximal MCMC through introducing a novel new class of nondifferentiable priors called epigraph priors. As a proof of concept, we place trend filtering, which was originally a nonparametric regression problem, in a parametric setting to provide a posterior median fit along with credible intervals as measures of uncertainty. The key idea is to replace the nonsmooth term in the posterior density with its Moreau-Yosida envelope, which enables the application of the gradient-based MCMC sampler Hamiltonian Monte Carlo. The proposed method identifies the appropriate amount of smoothing in a data-driven way, thereby automating regularization parameter selection. Compared with conventional proximal MCMC methods, our method is mostly tuning free, achieving simultaneous calibration of the mean, scale and regularization parameters in a fully Bayesian framework.

Variational Phylodynamic Inference Using Pandemic-scale Data

The ongoing global pandemic has sharply increased the amount of data available to researchers in epidemiology and public health. Unfortunately, few existing analysis tools are capable of exploiting all of the information contained in a pandemic-scale data set, resulting in missed opportunities for improved surveillance and contact tracing. In this paper, we develop the variational Bayesian skyline (VBSKY), a method for fitting Bayesian phylodynamic models to very large pathogen genetic data sets. By combining recent advances in phylodynamic modeling, scalable Bayesian inference and differentiable programming, along with a few tailored heuristics, VBSKY is capable of analyzing thousands of genomes in a few minutes, providing accurate estimates of epidemiologically relevant quantities such as the effective reproduction number and overall sampling effort through time. We illustrate the utility of our method by performing a rapid analysis of a large number of SARS-CoV-2 genomes, and demonstrate that the resulting estimates closely track those derived from alternative sources of public health data.

Highly Specialized Carbohydrate Metabolism Capability in Bifidobacterium Strains Associated with Intestinal Barrier Maturation in Early Preterm Infants

"Leaky gut," or high intestinal barrier permeability, is common in preterm newborns. The role of the microbiota in this process remains largely uncharacterized. We employed both short- and long-read sequencing of the 16S rRNA gene and metagenomes to characterize the intestinal microbiome of a longitudinal cohort of 113 preterm infants born between 240/7 and 326/7 weeks of gestation. Enabled by enhanced taxonomic resolution, we found that a significantly increased abundance of Bifidobacterium breve and a diet rich in mother's breastmilk were associated with intestinal barrier maturation during the first week of life. We combined these factors using genome-resolved metagenomics and identified a highly specialized genetic capability of the Bifidobacterium strains to assimilate human milk oligosaccharides and host-derived glycoproteins. Our study proposes mechanistic roles of breastmilk feeding and intestinal microbial colonization in postnatal intestinal barrier maturation; these observations are critical toward advancing therapeutics to prevent and treat hyperpermeable gut-associated conditions, including necrotizing enterocolitis (NEC). IMPORTANCE Despite improvements in neonatal intensive care, necrotizing enterocolitis (NEC) remains a leading cause of morbidity and mortality. "Leaky gut," or intestinal barrier immaturity with elevated intestinal permeability, is the proximate cause of susceptibility to NEC. Early detection and intervention to prevent leaky gut in "at-risk" preterm neonates are critical for decreasing the risk of potentially life-threatening complications like NEC. However, the complex interactions between the developing gut microbial community, nutrition, and intestinal barrier function remain largely uncharacterized. In this study, we reveal the critical role of a sufficient breastmilk feeding volume and the specialized carbohydrate metabolism capability of Bifidobacterium in the coordinated postnatal improvement of the intestinal barrier. Determining the clinical and microbial biomarkers that drive the intestinal developmental disparity will inform early detection and novel therapeutic strategies to promote appropriate intestinal barrier maturation and prevent NEC and other adverse health conditions in preterm infants.

8000-year doubling of Midwestern forest biomass driven by population- and biome-scale processes

Changes in woody biomass over centuries to millennia are poorly known, leaving unclear the magnitude of terrestrial carbon fluxes before industrial-era disturbance. Here, we statistically reconstructed changes in woody biomass across the upper Midwestern region of the United States over the past 10,000 years using a Bayesian model calibrated to preindustrial forest biomass estimates and fossil pollen records. After an initial postglacial decline, woody biomass nearly doubled during the past 8000 years, sequestering 1800 teragrams. This steady accumulation of carbon was driven by two separate ecological responses to regionally changing climate: the spread of forested biomes and the population expansion of high-biomass tree species within forests. What took millennia to accumulate took less than two centuries to remove: Industrial-era logging and agriculture have erased this carbon accumulation.

Effect of a Nonoptimal Cervicovaginal Microbiota and Psychosocial Stress on Recurrent Spontaneous Preterm Birth

OBJECTIVE

While select cervicovaginal microbiota and psychosocial factors have been associated with spontaneous preterm birth, their effect on the risk of recurrence remains unclear. It is also unknown whether psychosocial factors amplify underlying biologic risk. This study sought to determine the effect of nonoptimal cervicovaginal microbiota and perceived stress on the risk of recurrent spontaneous preterm birth.

STUDY DESIGN

This was a secondary analysis of a prospective pregnancy cohort, Motherhood and Microbiome. The Cohen's Perceived Stress Scale (PSS-14) was administered and cervical swabs were obtained between 16 and 20 weeks of gestation. PSS-14 scores ≥30 reflected high perceived stress. We analyzed cervicovaginal microbiota using 16S rRNA sequencing and classified microbial communities into community state types (CSTs). CST IV is a nonoptimal cervicovaginal microbial community characterized by anaerobes and a lack of Lactobacillus. The final cohort included a predominantly non-Hispanic Black population of women with prior spontaneous preterm birth who had recurrent spontaneous preterm birth or term birth and had stress measurements (n = 181). A subanalysis was performed in the subset of these women with cervicovaginal microbiota data (n = 74). Multivariable logistic regression modeled adjusted associations between CST IV and recurrent spontaneous preterm birth, high stress and recurrent spontaneous preterm birth, as well as high stress and CST IV.

RESULTS

Among the 181 women with prior spontaneous preterm birth, 45 (24.9%) had high perceived stress. We did not detect a significant association between high stress and recurrent spontaneous preterm birth (adjusted odds ratio [aOR] 1.67, 95% confidence interval [CI]: 0.73-3.85). Among the 74 women with prior spontaneous preterm birth and cervicovaginal microbiota analyzed, 29 (39.2%) had CST IV; this proportion differed significantly among women with recurrent spontaneous preterm birth (51.4%) compared with women with term birth (28.2%) (p = 0.04). In models adjusted for race and marital status, the association between CST IV and recurrent spontaneous preterm birth persisted (aOR 3.58, 95% CI: 1.25-10.24). There was no significant interaction between stress and CST IV on the odds of spontaneous preterm birth (p = 0.328). When both stress and CST IV were introduced into the model, their associations with recurrent spontaneous preterm birth were slightly stronger than when they were in the model alone. The aOR for stress with recurrent spontaneous preterm birth was 2.02 (95% CI: 0.61-6.71) and for CST IV the aOR was 3.83 (95% CI: 1.30-11.33). Compared to women with neither of the two exposures, women with both high stress and CST IV had the highest odds of recurrent spontaneous preterm birth (aOR = 6.01, 95% CI: 1.002-36.03).

CONCLUSION

Among a predominantly non-Hispanic Black cohort of women with a prior spontaneous preterm birth, a nonoptimal cervicovaginal microbiota is associated with increased odds of recurrent spontaneous preterm birth. Adjustment for perceived stress may amplify associations between CST IV and recurrent spontaneous preterm birth. Identification of modifiable social or behavioral factors may unveil novel nonpharmacologic interventions to decrease recurrent spontaneous preterm birth among women with underlying biologic risk.

KEY POINTS

· CST IV, a nonoptimal microbiota, is associated with increased odds of recurrent spontaneous preterm birth.. · Adjustment for perceived stress amplified associations between CST IV and recurrent spontaneous preterm birth.. · Identification of modifiable psychosocial factors may unveil novel nonpharmacologic interventions to decrease recurrent preterm birth..

Locally adaptive Bayesian birth-death model successfully detects slow and rapid rate shifts

Birth-death processes have given biologists a model-based framework to answer questions about changes in the birth and death rates of lineages in a phylogenetic tree. Therefore birth-death models are central to macroevolutionary as well as phylodynamic analyses. Early approaches to studying temporal variation in birth and death rates using birth-death models faced difficulties due to the restrictive choices of birth and death rate curves through time. Sufficiently flexible time-varying birth-death models are still lacking. We use a piecewise-constant birth-death model, combined with both Gaussian Markov random field (GMRF) and horseshoe Markov random field (HSMRF) prior distributions, to approximate arbitrary changes in birth rate through time. We implement these models in the widely used statistical phylogenetic software platform RevBayes, allowing us to jointly estimate birth-death process parameters, phylogeny, and nuisance parameters in a Bayesian framework. We test both GMRF-based and HSMRF-based models on a variety of simulated diversification scenarios, and then apply them to both a macroevolutionary and an epidemiological dataset. We find that both models are capable of inferring variable birth rates and correctly rejecting variable models in favor of effectively constant models. In general the HSMRF-based model has higher precision than its GMRF counterpart, with little to no loss of accuracy. Applied to a macroevolutionary dataset of the Australian gecko family Pygopodidae (where birth rates are interpretable as speciation rates), the GMRF-based model detects a slow decrease whereas the HSMRF-based model detects a rapid speciation-rate decrease in the last 12 million years. Applied to an infectious disease phylodynamic dataset of sequences from HIV subtype A in Russia and Ukraine (where birth rates are interpretable as the rate of accumulation of new infections), our models detect a strongly elevated rate of infection in the 1990s.

Horseshoe-based Bayesian nonparametric estimation of effective population size trajectories

Phylodynamics is an area of population genetics that uses genetic sequence data to estimate past population dynamics. Modern state-of-the-art Bayesian nonparametric methods for recovering population size trajectories of unknown form use either change-point models or Gaussian process priors. Change-point models suffer from computational issues when the number of change-points is unknown and needs to be estimated. Gaussian process-based methods lack local adaptivity and cannot accurately recover trajectories that exhibit features such as abrupt changes in trend or varying levels of smoothness. We propose a novel, locally adaptive approach to Bayesian nonparametric phylodynamic inference that has the flexibility to accommodate a large class of functional behaviors. Local adaptivity results from modeling the log-transformed effective population size a priori as a horseshoe Markov random field, a recently proposed statistical model that blends together the best properties of the change-point and Gaussian process modeling paradigms. We use simulated data to assess model performance, and find that our proposed method results in reduced bias and increased precision when compared to contemporary methods. We also use our models to reconstruct past changes in genetic diversity of human hepatitis C virus in Egypt and to estimate population size changes of ancient and modern steppe bison. These analyses show that our new method captures features of the population size trajectories that were missed by the state-of-the-art methods.

Cervicovaginal microbial communities deficient in Lactobacillus species are associated with second trimester short cervix

BACKGROUND

The cervix functions as a barrier to ascending pathogens in pregnancy. Short cervical length and lack of cervicovaginal Lactobacillus species are risk factors for spontaneous preterm birth; however, whether they interact to increase risk remains unknown.

OBJECTIVE

We sought to examine the relationship between cervicovaginal microbiota and short cervix as well as their combined impact on spontaneous preterm birth risk.

STUDY DESIGN

This was a secondary analysis of a prospective nested, case-control pregnancy study. Cervical swabs were collected between 16 and 20 weeks of gestation. Cervical length was measured per standard clinical care during a clinically indicated ultrasound at approximately 20 weeks of gestation. Cervicovaginal microbiota were analyzed with 16S ribosomal RNA gene sequencing and classified into community state types among 67 cases of spontaneous preterm birth, 47 cases of medically indicated preterm birth, and 358 cases of term births. Logistic regression was used to model associations of community state type IV, a community characterized by a paucity of Lactobacillus species and a wide array of anaerobic bacteria, and short cervix (<25 mm) as well as to model the association of a combination of short cervix and community state type IV with the odds of spontaneous preterm birth.

RESULTS

Among the 472 women in the data set, there were 38 with short cervix (8.1%) and 177 with community state type IV (37.5%). Short cervix was associated with spontaneous preterm birth (adjusted odds ratio, 15.59; 95% confidence interval, 6.77-35.92). Women with community state type IV had higher odds of short cervix (adjusted odds ratio, 2.17; 95% confidence interval, 1.04-4.53) as well as spontaneous preterm birth (adjusted odds ratio, 1.97; 95% confidence interval, 1.06-3.65). While the interaction of community state type IV and short cervix was not significant (P = .771), women with both short cervix and community state type IV (n = 20) had higher odds of spontaneous preterm birth compared with women with both normal cervical length and community state types I, II, III, or V (n = 277) (adjusted odds ratio, 21.8; 95% confidence interval, 6.78-70.2).

CONCLUSION

Community state type IV, characterized by a diverse set of strict and facultative anaerobes and a paucity of Lactobacillus species, is associated with increased odds of short cervix. Women with both community state type IV and short cervix have higher odds of spontaneous preterm birth than women with either factor alone. Determining the cascade of events leading to premature cervical shortening, including dysbiosis, may be critical in preventing spontaneous preterm birth.

A modelling approach for correcting reporting delays in disease surveillance data

One difficulty for real-time tracking of epidemics is related to reporting delay. The reporting delay may be due to laboratory confirmation, logistical problems, infrastructure difficulties, and so on. The ability to correct the available information as quickly as possible is crucial, in terms of decision making such as issuing warnings to the public and local authorities. A Bayesian hierarchical modelling approach is proposed as a flexible way of correcting the reporting delays and to quantify the associated uncertainty. Implementation of the model is fast due to the use of the integrated nested Laplace approximation. The approach is illustrated on dengue fever incidence data in Rio de Janeiro, and severe acute respiratory infection data in the state of Paraná, Brazil.

Vaginal microbiota and mucosal pharmacokinetics of tenofovir in healthy women using tenofovir and tenofovir/levonorgestrel vaginal rings

Recent data support that the vaginal microbiota may alter mucosal pharmacokinetics (PK) of topically delivered microbicides. Our team developed an intravaginal ring (IVR) that delivers tenofovir (TFV) (8–10 mg/day) alone or with levonorgestrel (LNG) (20 ug/day). We evaluated the effect of IVRs on the vaginal microbiota, and describe how the vaginal microbiota impacts mucosal PK of TFV. CONRAD A13-128 was a randomized, placebo controlled phase I study. We randomized 51 women to TFV, TFV/LNG or placebo IVR. We assessed the vaginal microbiota by sequencing the V3-V4 regions of 16S rRNA genes prior to IVR insertion and after approximately 15 days of use. We measured the concentration of TFV in the cervicovaginal (CV) aspirate, and TFV and TFV-diphosphate (TFV-DP) in vaginal tissue at the end of IVR use. The change in relative or absolute abundance of vaginal bacterial phylotypes was similar among active and placebo IVR users (all q values >0.13). TFV concentrations in CV aspirate and vaginal tissue, and TFV-DP concentrations in vaginal tissue were not significantly different among users with community state type (CST) 4 versus those with Lactobacillus dominated microbiota (all p values >0.07). The proportions of participants with CV aspirate concentrations of TFV >200,000 ng/mL and those with tissue TFV-DP concentrations >1,000 fmol/mg were similar among women with anaerobe versus Lactobacillus dominated microbiota (p = 0.43, 0.95 respectively). There were no significant correlations between the CV aspirate concentration of TFV and the relative abundances of Gardnerella vaginalis or Prevotella species. Tissue concentrations of TFV-DP did not correlate with any the relative abundances of any species, including Gardnerella vaginalis. In conclusion, active IVRs did not differ from the placebo IVR on the effect on the vaginal microbiota. Local TFV and TFV-DP concentrations were high and similar among IVR users with Lactobacillus dominated microbiota versus CST IV vaginal microbiota.

Trial registration: ClinicalTrials.gov NCT02235662.

Cervicovaginal microbiota and local immune response modulate the risk of spontaneous preterm delivery

Failure to predict and understand the causes of preterm birth, the leading cause of neonatal morbidity and mortality, have limited effective interventions and therapeutics. From a cohort of 2000 pregnant women, we performed a nested case control study on 107 well-phenotyped cases of spontaneous preterm birth (sPTB) and 432 women delivering at term. Using innovative Bayesian modeling of cervicovaginal microbiota, seven bacterial taxa were significantly associated with increased risk of sPTB, with a stronger effect in African American women. However, higher vaginal levels of β-defensin-2 lowered the risk of sPTB associated with cervicovaginal microbiota in an ethnicity-dependent manner. Surprisingly, even in Lactobacillus spp. dominated cervicovaginal microbiota, low β-defensin-2 was associated with increased risk of sPTB. These findings hold promise for diagnostics to accurately identify women at risk for sPTB early in pregnancy. Therapeutic strategies could include immune modulators and microbiome-based therapeutics to reduce this significant health burden.

Microbial Biomarkers of Intestinal Barrier Maturation in Preterm Infants

Intestinal barrier immaturity, or "leaky gut," is the proximate cause of susceptibility to necrotizing enterocolitis in preterm neonates. However, the impact of intestinal microbiota development on intestinal mucosal barrier maturation has not been evaluated in this population. In this study, we investigated a longitudinally sampled cohort of 38 preterm infants < 33 weeks gestation monitored for intestinal permeability (IP) and fecal microbiota during the first 2 weeks of life. Rapid decrease in IP indicating intestinal barrier function maturation correlated with significant increase in community diversity. In particular, members of the Clostridiales and Bifidobacterium were highly transcriptionally active, and progressively increasing abundance in Clostridiales was significantly associated with decreased intestinal permeability. Further, neonatal factors previously identified to promote intestinal barrier maturation, including early exclusive breastmilk feeding and shorter duration antibiotic exposure, associate with the early colonization of the intestinal microbiota by members of the Clostridiales, which altogether are associated with improved intestinal barrier function in preterm infants.

Locally Adaptive Smoothing with Markov Random Fields and Shrinkage Priors

We present a locally adaptive nonparametric curve fitting method that operates within a fully Bayesian framework. This method uses shrinkage priors to induce sparsity in order-k differences in the latent trend function, providing a combination of local adaptation and global control. Using a scale mixture of normals representation of shrinkage priors, we make explicit connections between our method and kth order Gaussian Markov random field smoothing. We call the resulting processes shrinkage prior Markov random fields (SPMRFs). We use Hamiltonian Monte Carlo to approximate the posterior distribution of model parameters because this method provides superior performance in the presence of the high dimensionality and strong parameter correlations exhibited by our models. We compare the performance of three prior formulations using simulated data and find the horseshoe prior provides the best compromise between bias and precision. We apply SPMRF models to two benchmark data examples frequently used to test nonparametric methods. We find that this method is flexible enough to accommodate a variety of data generating models and offers the adaptive properties and computational tractability to make it a useful addition to the Bayesian nonparametric toolbox.