Flexible Bayesian semiparametric mixed-effects model for skewed longitudinal data.

BACKGROUND: In clinical trials and epidemiological research, mixed-effects models are commonly used to examine population-level and subject-specific trajectories of biomarkers over time. Despite their increasing popularity and application, the specification of these models necessitates a great deal of care when analysing longitudinal data with non-linear patterns and asymmetry. Parametric (linear) mixed-effect models may not capture these complexities flexibly and adequately. Additionally, assuming a Gaussian distribution for random effects and/or model errors may be overly restrictive, as it lacks robustness against deviations from symmetry. METHODS: This paper presents a semiparametric mixed-effects model with flexible distributions for complex longitudinal data in the Bayesian paradigm. The non-linear time effect on the longitudinal response was modelled using a spline approach. The multivariate skew-t distribution, which is a more flexible distribution, is utilized to relax the normality assumptions associated with both random-effects and model errors. RESULTS: To assess the effectiveness of the proposed methods in various model settings, simulation studies were conducted. We then applied these models on chronic kidney disease (CKD) data and assessed the relationship between covariates and estimated glomerular filtration rate (eGFR). First, we compared the proposed semiparametric partially linear mixed-effect (SPPLM) model with the fully parametric one (FPLM), and the results indicated that the SPPLM model outperformed the FPLM model. We then further compared four different SPPLM models, each assuming different distributions for the random effects and model errors. The model with a skew-t distribution exhibited a superior fit to the CKD data compared to the Gaussian model. The findings from the application revealed that hypertension, diabetes, and follow-up time had a substantial association with kidney function, specifically leading to a decrease in GFR estimates. CONCLUSIONS: The application and simulation studies have demonstrated that our work has made a significant contribution towards a more robust and adaptable methodology for modeling intricate longitudinal data. We achieved this by proposing a semiparametric Bayesian modeling approach with a spline smoothing function and a skew-t distribution.

Evaluation of a flexible piecewise linear mixed-effects model in the analysis of randomized cross-over trials.

Cross-over designs are commonly used in randomized clinical trials to estimate efficacy of a new treatment. They have received a lot of attention, particularly in connection with regulatory requirements for new drugs. The main advantage of using cross-over designs over conventional parallel designs is increased precision, thanks to within-subject comparisons. In the statistical literature, more recent developments are discussed in the analysis of cross-over trials, in particular regarding repeated measures. A piecewise linear model within the framework of mixed effects has been proposed in the analysis of cross-over trials. In this article, we report on a simulation study comparing performance of a piecewise linear mixed-effects (PLME) model against two commonly cited models-Grizzle's mixed-effects (GME) and Jones & Kenward's mixed-effects (JKME) models-used in the analysis of cross-over trials. Our simulation study tried to mirror real-life situation by deriving true underlying parameters from empirical data. The findings from real-life data confirmed the original hypothesis that high-dose iodine salt have significantly lowering effect on diastolic blood pressure (DBP). We further sought to evaluate the performance of PLME model against GME and JKME models, within univariate modeling framework through a simulation study mimicking a 2 × 2 cross-over design. The fixed-effects, random-effects and residual error parameters used in the simulation process were estimated from DBP data, using a PLME model. The initial results with full specification of random intercept and slope(s), showed that the univariate PLME model performed better than the GME and JKME models in estimation of variance-covariance matrix (G) governing the random effects, allowing satisfactory model convergence during estimation. When a hierarchical view-point is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive-definite. The PLME model is preferred especially in modeling an increased number of random effects, compared to the GME and JKME models that work equally well with random intercepts only. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters.

Pairwise fitting of piecewise mixed models for the joint modeling of multivariate longitudinal outcomes, in a randomized crossover trial.

Many statistical models have been proposed in the literature for the analysis of longitudinal data. One may propose to model two or more correlated longitudinal processes simultaneously, with a goal of understanding their association over time. Joint modeling is then required to carefully study the association structure among the outcomes as well as drawing joint inferences about the different outcomes. In this study, we sought to model the associations among six nutrition outcomes while circumventing the computational challenge posed by their clustered and high-dimensional nature. We analyzed data from a 2 × $\times$ 2 randomized crossover trial conducted in Kenya, to compare the effect of high-dose and low-dose iodine in household salt on systolic blood pressure (SBP) and diastolic blood pressure (DBP) in women of reproductive age and their household matching pair of school-aged children. Two additional outcomes, namely, urinary iodine concentration (UIC) in women and children were measured repeatedly to monitor the amount of iodine excreted through urine. We extended the model proposed by Mwangi et al. (2021, Communications in Statistics: Case Studies, Data Analysis and Applications, 7(3), 413-431) allowing flexible piecewise joint models for six outcomes to depend on separate random effects, which are themselves correlated. This entailed fitting 15 bivariate general linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We analyzed the outcomes separately and jointly using piecewise linear mixed-effects (PLME) model and further validated the results using current state-of-the-art Jones and Kenward methodology (JKME model) used for analyzing randomized crossover trials. The results indicate that high-dose iodine in salt significantly reduced blood pressure (BP) compared to low-dose iodine in salt. Estimates for the random effects and residual error components showed that SBP and DBP had strong positive correlation, with effect of the random slope indicating that significantly related outcomes are strongly associated in their evolution. There was a moderately strong inverse relationship between evolutions of UIC and BP both in women and children. These findings confirmed the original hypothesis that high-dose iodine salt has significant lowering effect on BP. We further sought to evaluate the performance of our proposed PLME model against the widely used JKME model, within the multivariate joint modeling framework through a simulation study mimicking a 2 × 2 $2\times 2$ crossover design. From our findings, the multivariate joint PLME model performed exceptionally well both in estimation of random-effects matrix (G) and Hessian matrix (H), allowing satisfactory model convergence during estimation. It allowed a more complex fit to the data with both random intercepts and slopes effects compared to the multivariate joint JKME model that allowed for random intercepts only. When a hierarchical viewpoint is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive definite. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters. The key highlight in this evaluation shows that multivariate joint JKME model is a powerful tool especially while fitting mixed models with random intercepts only, in crossover design settings. Addition of random slopes may lead to model complexities in most cases, resulting in unsatisfactory model convergence during estimation. To circumvent convergence pitfalls, extention of JKME model to PLME model allows a more flexible fit to the data (generated from crossover design settings), especially in the multivariate joint modeling framework.

Understanding the Evolving Role of Voluntary Medical Male Circumcision as a Public Health Strategy in Eastern and Southern Africa: Opportunities and Challenges.

PURPOSE OF REVIEW: Voluntary male medical circumcision (VMMC) has been a cornerstone of HIV prevention in Eastern and Southern Africa (ESA) and is credited in part for declines in HIV incidence seen in recent years. However, these HIV incidence declines change VMMC cost-effectiveness and how it varies across populations. RECENT FINDINGS: Mathematical models project continued cost-effectiveness of VMMC in much of ESA despite HIV incidence declines. A key data gap is how demand generation cost differs across age groups and over time as VMMC coverage increases. Additionally, VMMC models usually neglect non-HIV effects of VMMC, such as prevention of other sexually transmitted infections and medical adverse events. While small compared to HIV effects in the short term, these could become important as HIV incidence declines. Evidence to date supports prioritizing VMMC in ESA despite falling HIV incidence. Updated modeling methodologies will become necessary if HIV incidence reaches low levels.

Modelling trends of CD4 counts for patients on antiretroviral therapy (ART): a comprehensive health care clinic in Nairobi, Kenya.

BACKGROUND: In resource-limited settings, changes in CD4 counts constitute an important component in patient monitoring and evaluation of treatment response as these patients do not have access to routine viral load testing. In this study, we quantified trends on CD4 counts in patients on highly active antiretroviral therapy (HAART) in a comprehensive health care clinic in Kenya between 2011 and 2017. We evaluated the rate of change in CD4 cell count in response to antiretroviral treatment. We further assessed factors that influenced time to treatment change focusing on baseline characteristics of the patients and different initial drug regimens used. This was a retrospective study involving 432 naïve HIV patients that had at least two CD4 count measurements for the period. The relationship between CD4 cell count and time was modeled using a semi parametric mixed effects model while the Cox proportional hazards model was used to assess factors associated with the first regimen change. RESULTS: Majority of the patients were females and the average CD4 count at start of treatment was 362.1 [Formula: see text]. The CD4 count measurements increased nonlinearly over time and these trends were similar regardless of the treatment regimen administered to the patients. The change of logarithm CD4 cell count rises fast for in the first 450 days of antiretroviral initiation. The average time to first regimen change was 2142 days. Tenoforvir (TDF) based regimens had a lower drug substitution(aHR 0.2682, 95% CI:0.08263- 0.8706) compared to Zidovudine(AZT). CONCLUSION: The backbone used was found to be associated with regimen changes among the patients with fewer switches being observed, with the use of TDF when compared to AZT. There was however no significant difference between TDF and AZT in terms of the rate of change in logarithm CD4 count over time.

Methods for conducting trends analysis: roadmap for comparing outcomes from three national HIV Population-based household surveys in Kenya (2007, 2012, and 2018).

BACKGROUND: For assessing the HIV epidemic in Kenya, a series of independent HIV indicator household-based surveys of similar design can be used to investigate the trends in key indicators relevant to HIV prevention and control and to describe geographic and sociodemographic disparities, assess the impact of interventions, and develop strategies. We developed methods and tools to facilitate a robust analysis of trends across three national household-based surveys conducted in Kenya in 2007, 2012, and 2018. METHODS: We used data from the 2007 and 2012 Kenya AIDS Indicator surveys (KAIS 2007 and KAIS 2012) and the 2018 Kenya Population-based HIV Impact Assessment (KENPHIA 2018). To assess the design and other variables of interest from each study, variables were recoded to ensure that they had equivalent meanings across the three surveys. After assessing weighting procedures for comparability, we used the KAIS 2012 nonresponse weighting procedure to revise normalized KENPHIA weights. Analyses were restricted to geographic areas covered by all three surveys. The revised analysis files were then merged into a single file for pooled analysis. We assessed distributions of age, sex, household wealth, and urban/rural status to identify unexpected changes between surveys. To demonstrate how a trend analysis can be carried out, we used continuous, binary, and time-to-event variables as examples. Specifically, temporal trends in age at first sex and having received an HIV test in the last 12 months were used to demonstrate the proposed analytical approach. These were assessed with respondent-specific variables (age, sex, level of education, and marital status) and household variables (place of residence and wealth index). All analyses were conducted in SAS 9.4, but analysis files were created in Stata and R format to support additional analyses. RESULTS: This study demonstrates trends in selected indicators to illustrate the approach that can be used in similar settings. The incidence of early sexual debut decreased from 11.63 (95% CI: 10.95-12.34) per 1,000 person-years at risk in 2007 to 10.45 (95% CI: 9.75-11.2) per 1,000 person-years at risk in 2012 and to 9.58 (95% CI: 9.08-10.1) per 1,000 person-years at risk in 2018. HIV-testing rates increased from 12.6% (95% CI: 11.6%-13.6%) in 2007 to 56.1% (95% CI: 54.6%-57.6%) in 2012 but decreased slightly to 55.6% [95% CI: 54.6%-56.6%) in 2018. The decrease in incidence of early sexual debut could be convincingly demonstrated between 2007 and 2012 but not between 2012 and 2018. Similarly, there was virtually no difference between HIV Testing rates in 2012 and 2018. CONCLUSIONS: Our approach can be used to support trend comparisons for variables in HIV surveys in low-income settings. Independent national household surveys can be assessed for comparability, adjusted as appropriate, and used to estimate trends in key indicators. Analyzing trends over time can not only provide insights into Kenya's progress toward HIV epidemic control but also identify gaps.

Employing phylogenetic tree shape statistics to resolve the underlying host population structure.

BACKGROUND: Host population structure is a key determinant of pathogen and infectious disease transmission patterns. Pathogen phylogenetic trees are useful tools to reveal the population structure underlying an epidemic. Determining whether a population is structured or not is useful in informing the type of phylogenetic methods to be used in a given study. We employ tree statistics derived from phylogenetic trees and machine learning classification techniques to reveal an underlying population structure. RESULTS: In this paper, we simulate phylogenetic trees from both structured and non-structured host populations. We compute eight statistics for the simulated trees, which are: the number of cherries; Sackin, Colless and total cophenetic indices; ladder length; maximum depth; maximum width, and width-to-depth ratio. Based on the estimated tree statistics, we classify the simulated trees as from either a non-structured or a structured population using the decision tree (DT), K-nearest neighbor (KNN) and support vector machine (SVM). We incorporate the basic reproductive number ([Formula: see text]) in our tree simulation procedure. Sensitivity analysis is done to investigate whether the classifiers are robust to different choice of model parameters and to size of trees. Cross-validated results for area under the curve (AUC) for receiver operating characteristic (ROC) curves yield mean values of over 0.9 for most of the classification models. CONCLUSIONS: Our classification procedure distinguishes well between trees from structured and non-structured populations using the classifiers, the two-sample Kolmogorov-Smirnov, Cucconi and Podgor-Gastwirth tests and the box plots. SVM models were more robust to changes in model parameters and tree size compared to KNN and DT classifiers. Our classification procedure was applied to real -world data and the structured population was revealed with high accuracy of [Formula: see text] using SVM-polynomial classifier.

Multi-level challenges and opportunities in providing antiretroviral treatment to adolescents in Kenya.

Adolescents have poor antiretroviral therapy (ART) outcomes due to multi-level factors. Adolescent and youth-friendly services (AYFS) have been implemented to address this. Adolescents on ART and HIV clinic managers were interviewed on their experiences with HIV care provision. Facility infrastructure was assessed using a standardized checklist. A 10-point criterion was set for AYFS. Descriptive analysis was used for quantitative data while qualitative data were thematically grouped and coded. Eighty-nine adolescents were interviewed including 46 males (52%) and 43 females (48%). The median age was 16.9 years (Interquartile range: 14.6-19.1 years). Some 36 (40.4%) adolescents raised the following facility-level challenges: long turnaround time, 12 (33.3%); clinic-school calendar conflict, 6 (16.7%); lack of digital media, 4 (11.1%); inadequate staff, 4 (11.1%) while another 10 (27.6%) cited lack of privacy, adolescent day and support groups. Clinic managers listed the availability of separate adolescents' days, adolescent-specific support groups, adolescent champion and use of social media as best practices. They listed several facility-related, society-related and adolescent-related challenges. Six facilities met six criteria of adolescent-friendliness (60%), one met five (50%) while two met four (40%). Although progress has been made in providing AYFS, key challenges remain that call for multi-sectoral interventions to ensure good ART outcomes.

Findings of Phlebotomy Practices in Kenya in 2010: Need for Action.

BACKGROUND: Phlebotomy, a commonly performed medical procedure in healthcare, is essential for disease diagnosis and patient management. However, poorly performed phlebotomy can compromise patient safety, healthcare worker (HCW) safety, and specimen quality. We carried out a study between June and July 2010 to assess knowledge, quality and safety of phlebotomy before implementation of a public-private partnership between Becton, Dickinson and Company and the US President's Emergency Plan for AIDS Relief. METHODS: This was a cross-sectional observational study in 8 healthcare facilities within 4 regions of Kenya. HCWs were observed conducting venous and capillary blood collections, and pre- and posttests were offered during HCW training. RESULTS: Of 283 blood samples obtained, 194 were venous draws conducted by 72 HCWs and 89 were capillary draws performed by 33 HCWs. Based on 12 preset quality-associated criteria, none of the 194 observed phlebotomies met the standard. In total, 91 HCWs were trained in phlebotomy. The mean knowledge increase between pre- and posttraining test was 41%, ranging from 39% to 45% (95% confidence interval, 29.3%-53.5%;P< .001). CONCLUSIONS: Inadequate knowledge and imperfect phlebotomy procedures were noted. This formed the basis for the safe phlebotomy partnership to address these deficiencies. To ensure sustainability, safe phlebotomy practices were integrated into preservice training.

Bayesian rank likelihood-based estimation: An application to low birth weight in Ethiopia.

BACKGROUND: Low birth weight is a significant risk factor associated with high rates of neonatal and infant mortality, particularly in developing countries. However, most studies conducted on this topic in Ethiopia have small sample sizes, often focusing on specific areas and using standard models employing maximum likelihood estimation, leading to potential bias and inaccurate coverage probability. METHODS: This study used a novel approach, the Bayesian rank likelihood method, within a latent traits model, to estimate parameters and provide a nationwide estimate of low birth weight and its risk factors in Ethiopia. Data from the Ethiopian Demographic and Health Survey (EDHS) of 2016 were used as a data source for the study. Data stratified all regions into urban and rural areas. Among 15, 680 representative selected households, the analysis included complete cases from 10, 641 children (0-59 months). The evaluation of model performance considered metrics such as the root mean square error, the mean absolute error, and the probability coverage of the corresponding 95% confidence intervals of the estimates. RESULTS: Based on the values of root mean square error, mean absolute error, and probability coverage, the estimates obtained from the proposed model outperform the classical estimates. According to the result, 40.92% of the children were born with low birth weight. The study also found that low birth weight is unevenly distributed across different regions of the country with the highest amounts of variation observed in the Afar, Somali and Southern Nations, Nationalities, and Peoples regions as represented by the latent trait parameter of the model. In contrast, the lowest low birth weight variation was recorded in the Addis Ababa, Dire Dawa, and Amhara regions. Furthermore, there were significant associations between birth weight and several factors, including the age of the mother, number of antenatal care visits, order of birth and the body mass index as indicated by the average posterior beta values of (ß1= -0.269, CI=-0.320, -0.220), (ß2= -0.235, CI=-0.268, -0.202), (ß3= -0.120, CI=-0.162, -0.074) and (ß5= -0.257, CI=-0.291, -0.225). CONCLUSIONS: The study showed that the low birth weight estimates obtained from the latent trait model outperform the classical estimates. The study also revealed that the prevalence of low birth weight varies between different regions of the country, indicating the need for targeted interventions in areas with a higher prevalence. To effectively reduce the prevalence of low birth weight and improve maternal and child health outcomes, it is important to concentrate efforts on regions with a higher burden of low birth weight. This will help implement interventions that are tailored to the unique challenges and needs of each area. Health institutions should take measures to reduce low birth weight, with a special focus on the factors identified in this study.

Modified sharp regression discontinuity model to settings with fuzzy variables.

OBJECTIVE: The goal of this study is to develop a Modified Sharp Regression Discontinuity model to predict alcohol consumption in People Living with Human Immunodeficiency Virus (HIV) and Acquired Immunodeficiency Syndrome (AIDS). Previous studies focused on either fuzzy dependent or fuzzy independent variables separately. However, there is a gap in research that examines the interaction between both types of fuzzy variables thus the model considers both dependent and independent fuzzy variables. METHODS: A statistical model was developed to predict the relationship between alcohol consumption and HIV progression. The model equations are solved numerically using parametric estimation. RESULTS: In simulation studies, as the sample size expanded, the estimates derived from the modified sharp regression discontinuity model exhibited probabilistic convergence towards the true value, thereby validating the estimator of the Average Causal Effect's consistency. Counseling has an average causal effect in the sharp Regression Discontinuity Design (RDD) for compliers that is roughly equal to 0.199. This was the variation in Alcohol Use Detective Identification Test (AUDIT) threshold scores or the change in intercept scores when counseling was effective. Following six months of participation in the counseling program, AUDIT scores decreased, leading to an increase in Cluster of Differentiation 4 (CD4) counts and a decrease in viral loads. CONCLUSION: The Modified Sharp RDD offers a robust approach to handle fuzzy variables in causal inference. Our study contributes to the advancement of RDD methodology and its applicability in real-world settings with uncertain data.

HIV Incidence, Recent HIV Infection, and Associated Factors, Kenya, 2007-2018.

Nationally representative surveys provide an opportunity to assess trends in recent human immunodeficiency virus (HIV) infection based on assays for recent HIV infection. We assessed HIV incidence in Kenya in 2018 and trends in recent HIV infection among adolescents and adults in Kenya using nationally representative household surveys conducted in 2007, 2012, and 2018. To assess trends, we defined a recent HIV infection testing algorithm (RITA) that classified as recently infected (<12 months) those HIV-positive participants that were recent on the HIV-1 limiting antigen (LAg)-avidity assay without evidence of antiretroviral use. We assessed factors associated with recent and long-term (≥12 months) HIV infection versus no infection using a multinomial logit model while accounting for complex survey design. Of 1,523 HIV-positive participants in 2018, 11 were classified as recent. Annual HIV incidence was 0.14% in 2018 [95% confidence interval (CI) 0.057-0.23], representing 35,900 (95% CI 16,300-55,600) new infections per year in Kenya among persons aged 15-64 years. The percentage of HIV infections that were determined to be recent was similar in 2007 and 2012 but fell significantly from 2012 to 2018 [adjusted odds ratio (aOR) = 0.31, p < .001]. Compared to no HIV infection, being aged 25-34 versus 35-64 years (aOR = 4.2, 95% CI 1.4-13), having more lifetime sex partners (aOR = 5.2, 95% CI 1.6-17 for 2-3 partners and aOR = 8.6, 95% CI 2.8-26 for ≥4 partners vs. 0-1 partners), and never having tested for HIV (aOR = 4.1, 95% CI 1.5-11) were independently associated with recent HIV infection. Although HIV remains a public health priority in Kenya, HIV incidence estimates and trends in recent HIV infection support a significant decrease in new HIV infections from 2012 to 2018, a period of rapid expansion in HIV diagnosis, prevention, and treatment.

Forecasting the spread of the COVID-19 pandemic in Kenya using SEIR and ARIMA models.

COVID-19, a coronavirus disease 2019, is an ongoing pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The first case in Kenya was identified on March 13, 2020, with the pandemic increasing to about 237,000 confirmed cases and 4,746 deaths by August 2021. We developed an SEIR model forecasting the COVID-19 pandemic in Kenya using an Autoregressive Integrated moving averages (ARIMA) model. The average time difference between the peaks of wave 1 to wave 4 was observed to be about 130 days. The 4th wave was observed to have had the least number of daily cases at the peak. According to the forecasts made for the next 60 days, the pandemic is expected to continue for a while. The 4th wave peaked on August 26, 2021 (498th day). By October 26, 2021 (60th day), the average number of daily infections will be 454 new cases and 40 severe cases, which would require hospitalization, and 16 critically ill cases requiring intensive care unit services. The findings of this study are key in developing informed mitigation strategies to ensure that the pandemic is contained and inform the preparedness of policymakers and health care workers.

A Flexible Bayesian Parametric Proportional Hazard Model: Simulation and Applications to Right-Censored Healthcare Data.

Survival analysis is a collection of statistical techniques which examine the time it takes for an event to occur, and it is one of the most important fields in biomedical sciences and other variety of scientific disciplines. Furthermore, the computational rapid advancements in recent decades have advocated the application of Bayesian techniques in this field, giving a powerful and flexible alternative to the classical inference. The aim of this study is to consider the Bayesian inference for the generalized log-logistic proportional hazard model with applications to right-censored healthcare data sets. We assume an independent gamma prior for the baseline hazard parameters and a normal prior is placed on the regression coefficients. We then obtain the exact form of the joint posterior distribution of the regression coefficients and distributional parameters. The Bayesian estimates of the parameters of the proposed model are obtained using the Markov chain Monte Carlo (McMC) simulation technique. All computations are performed in Bayesian analysis using Gibbs sampling (BUGS) syntax that can be run with Just Another Gibbs Sampling (JAGS) from the R software. A detailed simulation study was used to assess the performance of the proposed parametric proportional hazard model. Two real-survival data problems in the healthcare are analyzed for illustration of the proposed model and for model comparison. Furthermore, the convergence diagnostic tests are presented and analyzed. Finally, our research found that the proposed parametric proportional hazard model performs well and could be beneficial in analyzing various types of survival data.

Two-year survival rates of proximal atraumatic restorative treatment restorations in relation to glass ionomer cements and Postrestoration meals consumed.

PURPOSE: The purpose of this study was to investigate the influence of 3 glass ionomer cement (GIC) brands and the postrestoration meal consumed on the survival rate of proximal atraumatic restorative treatment (ART) restorations. METHODS: A total of 804 proximal restorations were placed in primary molars by trained operators and assistants using 3 GIC brands. The materials' mixing/placement times, the room temperature and the postrestoration meal consumed by the subjects were documented. The restorations were evaluated soon after placement and after 2 years by trained and calibrated evaluators. RESULTS: After 2 years, approximately 31% of the restorations had survived. There were no statistically significant differences in the survival rate of the restorations in relation to the GIC brands. The postrestoration meal consumed, which was of "hard consistency," was associated with significantly lower survival rate of the restorations. CONCLUSIONS: The survival rate of the proximal restorations was not significantly affected by the glass ionomer cement brands used, but was significantly influenced by the consistency of the next meal consumed by each child.

%svy_freqs: A Generic SAS Macro for Creating Publication-Quality Three-Way Cross-Tabulations.

Cross-tabulations are a simple but important tool for understanding the distribution of socio-demographic characteristics among participants in epidemiological studies. We developed a generic SAS macro, %svy_freqs, to create publication-quality tables from cross-tabulations between a factor and a by-group variable given a third variable using survey or non-survey data. The macro also performs two-way cross-tabulations and provides extra features not available in existing procedures such as ability to incorporate parameters for survey design and replication-based variance estimation methods, performing validation checks for input parameters, transparently formatting variable values from character into numeric and allowing for generalizability. We demonstrate the macro using the 2013-2014 National Health and Nutrition Examination Survey (NHANES), a complex survey designed to assess the health and nutritional status of adults and children in the United States.

Age-structured model for COVID-19: Effectiveness of social distancing and contact reduction in Kenya.

Coronavirus disease 2019 is caused by severe acute respiratory syndrome coronavirus 2. Kenya reported its first case on March 13, 2020 and by March 16, 2020 she instituted physical distancing strategies to reduce transmission and flatten the epidemic curve. An age-structured compartmental model was developed to assess the impact of the strategies on COVID-19 severity and burden. Contacts between different ages are incorporated via contact matrices. Simulation results show that 45% reduction in contacts for 60-days period resulted to 11.5-13% reduction of infections severity and deaths, while for the 190-days period yielded 18.8-22.7% reduction. The peak of infections in the 60-days mitigation was higher and happened about 2 months after the relaxation of mitigation as compared to that of the 190-days mitigation, which happened a month after mitigations were relaxed. Low numbers of cases in children under 15 years was attributed to high number of asymptomatic cases. High numbers of cases are reported in the 15-29 years and 30-59 years age bands. Two mitigation periods, considered in the study, resulted to reductions in severe and critical cases, attack rates, hospital and ICU bed demands, as well as deaths, with the 190-days period giving higher reductions.

Bayesian and Classical Inference for the Generalized Log-Logistic Distribution with Applications to Survival Data.

The generalized log-logistic distribution is especially useful for modelling survival data with variable hazard rate shapes because it extends the log-logistic distribution by adding an extra parameter to the classical distribution, resulting in greater flexibility in analyzing and modelling various data types. We derive the fundamental mathematical and statistical properties of the proposed distribution in this paper. Many well-known lifetime special submodels are included in the proposed distribution, including the Weibull, log-logistic, exponential, and Burr XII distributions. The maximum likelihood method was used to estimate the unknown parameters of the proposed distribution, and a Monte Carlo simulation study was run to assess the estimators' performance. This distribution is significant because it can model both monotone and nonmonotone hazard rate functions, which are quite common in survival and reliability data analysis. Furthermore, the proposed distribution's flexibility and usefulness are demonstrated in a real-world data set and compared to its submodels, the Weibull, log-logistic, and Burr XII distributions, as well as other three-parameter parametric survival distributions, such as the exponentiated Weibull distribution, the three-parameter log-normal distribution, the three-parameter (or the shifted) log-logistic distribution, the three-parameter gamma distribution, and an exponentiated Weibull distribution. The proposed distribution is plausible, according to the goodness-of-fit, log-likelihood, and information criterion values. Finally, for the data set, Bayesian inference and Gibb's sampling performance are used to compute the approximate Bayes estimates as well as the highest posterior density credible intervals, and the convergence diagnostic techniques based on Markov chain Monte Carlo techniques were used.

SEIR model for COVID-19 dynamics incorporating the environment and social distancing.

OBJECTIVE: Coronavirus disease 2019 (COVID-19) is a pandemic respiratory illness spreading from person-to-person caused by a novel coronavirus and poses a serious public health risk. The goal of this study was to apply a modified susceptible-exposed-infectious-recovered (SEIR) compartmental mathematical model for prediction of COVID-19 epidemic dynamics incorporating pathogen in the environment and interventions. The next generation matrix approach was used to determine the basic reproduction number [Formula: see text]. The model equations are solved numerically using fourth and fifth order Runge-Kutta methods. RESULTS: We found an [Formula: see text] of 2.03, implying that the pandemic will persist in the human population in the absence of strong control measures. Results after simulating various scenarios indicate that disregarding social distancing and hygiene measures can have devastating effects on the human population. The model shows that quarantine of contacts and isolation of cases can help halt the spread on novel coronavirus.

Modeling the Effects of Nonpharmaceutical Interventions on COVID-19 Spread in Kenya.

Mathematical modeling of nonpharmaceutical interventions (NPIs) of coronavirus disease (COVID-19) in Kenya is presented. A susceptible-exposed-infected-recovered (SEIR) compartment model is considered with additional compartments of hospitalized population whose condition is severe or critical and the fatality compartment. The basic reproduction number (R 0) is computed by the next-generation matrix approach and later expressed as a time-dependent function so as to incorporate the NPIs into the model. The resulting system of ordinary differential equations (ODEs) is solved using fourth-order and fifth-order Runge-Kutta methods. Different intervention scenarios are considered, and the results show that implementation of closure of education institutions, curfew, and partial lockdown yields predicted delayed peaks of the overall infections, severe cases, and fatalities and subsequently containment of the pandemic in the country.