Bayesian flexible multilevel nonlinear models in infectious disease modeling using non-informative priors

Bayesian multilevel models—also known as hierarchical or mixed models—are used in situations in which the aim is to model the random effect of groups or levels. In this paper, we conduct a simulation study to compare the predictive ability of 1-level Bayesian multilevel logistic regression models with that of 2-level Bayesian multilevel logistic regression models by using the prior Scaled Beta2 and inverse-gamma distributions to model the standard deviation in the 2-level. Then, these models are employed to estimate the correct answers in two questionnaires administered to university students throughout the first academic semester of 2018. The results show that 2-level models have a better predictive ability and provide more precise probability intervals than 1-level models, particularly when the prior Scaled Beta2 distribution is used to model the standard deviation in the second level. Moreover, the probability intervals of 1-level Bayesian multilevel logistic regression models proved to be more precise when Scaled Beta2 distributions, rather than an inverse-gamma distribution, are employed to model the standard deviation or when 1-level Bayesian multilevel logistic regression models, are used.

Nonlinear mixed models and related approaches in infectious disease modeling: A systematic and critical review

Purpose: Bayesian multilevel models are increasingly used to overcome the limitations of frequentist approaches in the analysis of complex structured data. This tutorial introduces Bayesian multilevel modeling for the specific analysis of speech data, using the brms package developed in R.Method: In this tutorial, we provide a practical introduction to Bayesian multilevel modeling by reanalyzing a phonetic data set containing formant (F1 and F2) values for 5 vowels of standard Indonesian (ISO 639-3:ind), as spoken by 8 speakers (4 females and 4 males), with several repetitions of each vowel.Results: We first give an introductory overview of the Bayesian framework and multilevel modeling. We then show how Bayesian multilevel models can be fitted using the probabilistic programming language Stan and the R package brms, which provides an intuitive formula syntax.Conclusions: Through this tutorial, we demonstrate some of the advantages of the Bayesian framework for statistical modeling and provide a detailed case study, with complete source code for full reproducibility of the analyses (https://osf.io/dpzcb/).Supplemental Material S1. Moderation analysis; lognormal and skew-normal models; session information. Nalborczyk, L., Batailler, C., Loevenbruck, H., Vilain, A., & Burkner, P.-C. (2019). An introduction to Bayesian multilevel models using brms: A case study of gender effects on vowel variability in standard Indonesian. Journal of Speech, Language, and Hearing Research, 62, 1225–1242. https://doi.org/10.1044/2018_JSLHR-S-18-0006

The postnatal period is a critical period for both mothers and their newborns for their health. Lack of early postnatal care (PNC) services during a 2-day period is a life-threatening situation for both the mother and the babies. However, no data have been examined for PNCs in East Africa. Hence, using the more flexible Bayesian multilevel modeling approach, this study aims to investigate the pooled prevalence and potential factors for PNC utilization among women after delivery in East African countries. We retrieved secondary data from the Kids Record (KR) demographic and health surveys (DHS) data from 2015 to 2022 from 10 East African countries. A total of 77,052 weighted women were included in the study. We used R 4.3.2 software for analysis. We fitted Bayesian multilevel logistic regression models. Techniques such as Rhat, effective sample size, density, time series, autocorrelation plots, widely applicable information criterion (WAIC), deviance information criterion (DIC), and Markov Chain Monte-Carlo (MCMC) simulation were used to estimate the model parameters using Hamiltonian Monte-Carlo (HMC) and its extensions, No-U-Turn Sampler (NUTS) techniques. An adjusted odds ratio (AOR) with a 95% credible interval (CrI) in the multivariable model to select variables that have a significant association with PNC was used. The overall pooled prevalence of PNC within 48 hrs. of delivery was about 52% (95% CrI: 39, 66). A higher rate of PNC usage was observed among women aged 25-34 years (AOR = 1.21; 95% CrI: 1.15, 1.27) and 35-49-years (AOR = 1.61; 95% CrI: 1.5, 1.72) as compared to women aged 15-24 years; similarly, women who had achieved primary education (AOR = 1.96; 95% CrI: 1.88, 2.05) and secondary/higher education (AOR = 3.19; 95% CrI: 3.03, 3.36) as compared to uneducated women; divorced or widowed women (AOR = 0.83; 95% CrI: 0.77, 0.89); women who had currently working status (AOR = 0.9; 95% CrI: 0.87, 0.93); poorer women (AOR = 0.88; 95% CrI: 0.84, 0.92), middle-class women (AOR = 0.83; 95% CrI: 0.79, 0.87), richer women (AOR = 0.77; 95% CrI: 0.73, 0.81), and richest women (AOR = 0.59; 95% CrI: 0.55, 0.63) as compared to the poorest women; women who had media exposure (AOR = 1.32; 95% CrI: 1.27, 1.36), were having 3-5 children (AOR = 0.89; 95% CrI: 0.84, 0.94), had >5 children (AOR = 0.69; 95% CrI: 0.64, 0.75), had first birth at age < 20 years (AOR = 0.82; 95% CrI: 0.79, 0.84), had at least one ANC visit (AOR = 1.93; 95% CrI: 1.8, 2.08), delivered at health facilities (AOR = 2.57; 95% CrI: 2.46, 2.68), had average birth size (AOR = 0.94; 95% CrI: 0.91, 0.98) and small birth size child (AOR = 0.88; 95% CrI: 0.84, 0.92), had twin newborns (AOR = 1.15; 95% CrI: 1.02, 1.3), and fourth and above birth order (AOR = 0.88; 95% CrI: 0.82, 0.95) were individual-driven women who have been independently associated with PNC, respectively. Regarding community-level variables, rural women (AOR = 0.76; 95% CrI: 0.72, 0.79), high media exposure communities (AOR = 1.1; 95% CrI: 1.04, 1.18), communities with high wealth levels (AOR = 0.88 95% CrI: 0.83, 0.94), communities with high antenatal care (ANC) utilization (AOR = 1.13, 95% CrI: 1.07, 1.19), and long distance to health facilities (AOR = 1.5; 95% CrI: 1.38, 1.63) were among the community factors associated with PNC, respectively. One of the significant public health priorities in East Africa continues to be the underutilization of immediate PNC. The government ought to prioritize improving maternity and child health services, collaborating with interested parties in the area, reducing health disparities, educating mothers about child health, and other connected issues that are very beneficial.

Maternal mortality is one of the socio-economic problems and widely considered a serious indicator of the quality of a health. Ethiopia is considered to be one of the top six sub-Saharan countries with severe maternal mortality. The objective of this study was to investigate the effects of the Demographic and Socio-economic determinant factors of maternal mortality in Ethiopia. Data from the 2016 Ethiopia Demographic and Health Survey indicated that the sample of women (15–49) was (n = 10,103). The Bayesian multilevel we were used to explore the major risk factors and regional variations in maternal mortality in Ethiopia. Markov chain Monte Carlo methods with non-informative priors have been applied. The Deviance Information Criterion model selection criteria were used to select the appropriate model. The analysis result, 145 (1.43%) mothers were died due to pregnancy. Using model selection criteria Bayesian multilevel random coefficient was found to be appropriate. With this model, Age of mother, marital status, number of living children, wealth index and Education are found to be the significant determinants of maternal mortality in Ethiopia. The study indicated that there was within and between regional variations in maternal mortality. Inference is the fully Bayesian multilevel model based on recent Markov chain Monte Carlo techniques. The socioeconomic, demographic and environmental determinants included in the study were found to be statistically significant. The result of the Bayesian multilevel model in this study has shown that educational attainment, wealth index, an age of mother, status and number of living children was a significant factor of maternal mortality.

Purpose Bayesian multilevel models are increasingly used to overcome the limitations of frequentist approaches in the analysis of complex structured data. This tutorial introduces Bayesian multilevel modeling for the specific analysis of speech data, using the brms package developed in R. Method In this tutorial, we provide a practical introduction to Bayesian multilevel modeling by reanalyzing a phonetic data set containing formant (F1 and F2) values for 5 vowels of standard Indonesian (ISO 639-3:ind), as spoken by 8 speakers (4 females and 4 males), with several repetitions of each vowel. Results We first give an introductory overview of the Bayesian framework and multilevel modeling. We then show how Bayesian multilevel models can be fitted using the probabilistic programming language Stan and the R package brms, which provides an intuitive formula syntax. Conclusions Through this tutorial, we demonstrate some of the advantages of the Bayesian framework for statistical modeling and provide a detailed case study, with complete source code for full reproducibility of the analyses ( https://osf.io/dpzcb /). Supplemental Material https://doi.org/10.23641/asha.7973822.

Bayesian flexible multilevel nonlinear models (FMNLMs) are powerful tools to analyze infectious disease data with asymmetric and unbalanced structures, such as varying epidemic stages across countries. However, the robustness of these models can be undermined by poorly designed estimation methods, particularly due to uncertainties in prior distributions and initial values. This study investigates how varying levels of prior informativeness can influence the model convergence, parameter estimation, and computation time in a Bayesian flexible multilevel nonlinear model (FMNLM). A simulation study was conducted to evaluate the impact of modifying prior assumptions on posterior estimates and their subsequent effects on the interpretations. The framework was applied to COVID-19 data from Francophone West Africa. The results indicate that accurate, informative priors enhance the prediction performance with minimal impact on the computation time. Conversely, non-informative or inaccurate priors for nonlinear parameters led to lower convergence rates and a reduced recovery accuracy, although they may remain viable in standard multilevel nonlinear models.

Introduction: Contraception is a procedure that can be used to avoid pregnancy or childbirth. When women choose to prevent pregnancy or have a longer birth, they frequently use contraceptives. The global prevalence rate of contraceptive use was 64 percent, with Africa responsible for 33 percent. Ethiopia has an estimated rate of 39.2 percent of its population engaging in this activity. Objectives: This study was aimed to identify the predictors of married women’s contraceptive practice using Bayesian and classical approach. In addition, this study has identified the within and between Woredas variation using the hierarchical nature of the data obtained in different woredas. For identifying the better model, researcher has compared the Bayesian and classical multilevel logistic regression models. Methods: This research was conducted in seven Woredas of Assosa zone and was based on a cross-sectional study that primarily focused on married women between the ages of 15 and 49 and the factors that influenced their contraceptive use. Two stage model comparisons were used to approximate the parameters, with the first stage having a null, random intercept, and random slope with a Bayesian approach. Result and Conclusion: The overall contraceptive prevalence rate among 6866 married women 3121(45.46%). According to the intra Woreda correlation of the appropriate model, the between Woreda variance in married women's contraceptive practice was 15.71%, with the remaining 84.29 percent variation attributed to differences in contraceptive practice between women. Finally, predictors for married women contraceptive practice such as women's age, place of residence, women's educational level, husband's educational level, women's job, husband's occupation, wealth index, religion, and knowledge of family planning. The Bayesian multilevel model was found to be the most suitable model for fitting the data after a comparison of classical and Bayesian multilevel models.

Mitigating bias in estimating epidemic severity due to heterogeneity of epidemic onset and data aggregation

Quantitative structure-retention relationships (QSRRs) are used in the field of chromatography to model the relationship between an analyte structure and chromatographic retention. Such models are typically difficult to build and validate for heterogeneous compounds because of their many descriptors and relatively limited analyte-specific data. In this study, a Bayesian multilevel model is proposed to characterize the isocratic retention time data collected for 1026 heterogeneous analytes. The QSRR considers the effects of the molecular mass and 100 functional groups (substituents) on analyte-specific chromatographic parameters of the Neue model (i.e., the retention factor in water, the retention factor in acetonitrile, and the curvature coefficient). A Bayesian multilevel regression model was used to smooth noisy parameter estimates with too few data and to consider the uncertainties in the model parameters. We discuss the benefits of the Bayesian multilevel model (i) to understand chromatographic data, (ii) to quantify the effect of functional groups on chromatographic retention, and (iii) to predict analyte retention based on various types of preliminary data. The uncertainty of isocratic and gradient predictions was visualized using uncertainty chromatograms and discussed in terms of usefulness in decision making. We think that this method will provide the most benefit in providing a unified scheme for analyzing large chromatographic databases and assessing the impact of functional groups and other descriptors on analyte retention.

Different types of math interventions and outcomes naturally yield quantitatively and qualitatively different impacts: Some interventions may produce rapid change whereas others may promote the gradual accumulation of skills. Visual and quantitative analyses require greater continuity to understand the different nuances across types of intervention impacts that may emerge. In the present study, we use data from two separate math interventions among secondary students to examine how Bayesian multilevel models can more effectively integrate both visual and quantitative analysis of single-case designs to quantify and visualize uncertainty. We demonstrate that Bayesian models can augment the analysis of single-case designs without compromising the technical sophistication of quantitative analyses or the interpretive ease of visual analysis. These methods also help understand the degree of uncertainty in effect magnitude, which is especially important when considering the variety of ways effects may emerge in math interventions. We discuss limitations and future directions of the alignment of Bayesian modeling with visual analysis procedures for single-case math interventions and beyond. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

Religious group size, demographic composition, and the dynamics thereof are of interest in many areas of social science including migration, social cohesion, parties and voting, and violent conflict. Existing estimates however are of varying and perhaps poor quality because many countries do not collect official data on religious identity. We propose a method for accurately measuring religious group demographics using existing survey data: Bayesian multilevel regression models with poststratification. We illustrate this method by estimating the demography of Muslims, Hindus, and Jews in Great Britain over a 20-year period and validate it by comparing our estimates to UK census data on religious demography. Our estimates are very accurate, differing from true population proportions by as little as 0.29 (Muslim) to 0.04 (Jewish) percentage points. These findings have implications for the measurement of religious demography as well as small group attributes more generally.

Religious group size, demographic composition, and the dynamics thereof are of interest in many areas of social science, including migration, social cohesion, parties and voting, and violent conflict. Existing estimates however are of varying and perhaps poor quality because many countries do not collect official data on religious identity. We propose a method for accurately measuring religious group demographics using existing survey data: Bayesian multilevel regression models with post-stratification, or MRP. We illustrate this method by estimating the demography of Muslims, Hindus, and Jews in Great Britain over a 20-year period, and validate it by comparing our estimates to UK census data on religious demography. Our estimates are very accurate, differing from true population proportions by as little as 0.29 (Muslim) to 0.04 (Jewish) percentage points. These findings have implications for the measurement of religious demography as well as small group attributes more generally.

In this study, I explore the impact of different Bayesian inference techniques—Hamiltonian Monte Carlo (HMC) and Maximum A Posteriori (MAP)—on personalized dosing strategies within pharmacokinetic modeling for apixaban. I present a Bayesian model that incorporates informative priors to derive personalized dosing recommendations based on desired trough concentrations following an initial dose. Through extensive simulation, I demonstrate significant discrepancies between dosing strategies derived from HMC and MAP, particularly in terms of predicted concentration uncertainties. While MAP provides a point estimate that is computationally efficient and familiar, it leads to different decision-making outcomes compared to HMC, which accounts for uncertainty more comprehensively. My findings reveal that MAP and HMC can lead to markedly different dosing recommendations, highlighting the importance of considering inference methods beyond point predictions in Bayesian pharmacokinetic modeling. I recommend practitioners use HMC alongside MAP to validate and compare results, thereby enhancing the transparency and reproducibility of personalized dosing strategies.

Bayesian compartmental infectious disease models yield important inference on disease transmission by appropriately accounting for the dynamics and uncertainty of infection processes. In addition to estimating transition probabilities and reproductive numbers, these statistical models allow researchers to assess the probability of disease risk and quantify the effectiveness of interventions. These infectious disease models rely on data collected from all individuals classified as positive based on various diagnostic tests. In infectious disease testing, however, such procedures produce both false‐positives and false‐negatives at varying rates depending on the sensitivity and specificity of the diagnostic tests being used. We propose a novel Bayesian spatio‐temporal infectious disease modeling framework that accounts for the additional uncertainty in the diagnostic testing and classification process that provides estimates of the important transmission dynamics of interest to researchers. The method is applied to data on the 2006 mumps epidemic in Iowa, in which over 6,000 suspected mumps cases were tested using a buccal or oral swab specimen, a urine specimen, and/or a blood specimen. Although all procedures are believed to have high specificities, the sensitivities can be low and vary depending on the timing of the test as well as the vaccination status of the individual being tested.