Estimating the Under-Five Mortality Rate Using a Bayesian Hierarchical Time Series Model

Background: Millennium Development Goal 4 calls for a reduction in the under-five mortality rate by two-thirds between 1990 and 2015, which corresponds to an annual rate of decline of 4.4%. The United Nations Inter-Agency Group for Child Mortality Estimation estimates under-five mortality in every country to measure progress. For the majority of countries, the estimates within a country are based on the assumption of a piece-wise constant rate of decline. Methods and Findings: This paper proposes an alternative method to estimate under-five mortality, such that the underlying rate of change is allowed to vary smoothly over time using a time series model. Information about the average rate of decline and changes therein is exchanged between countries using a Bayesian hierarchical model. Cross-validation exercises suggest that the proposed model provides credible bounds for the under-five mortality rate that are reasonably well calibrated during the observation period. The alternative estimates suggest smoother trends in under-five mortality and give new insights into changes in the rate of decline within countries. Conclusions: The proposed model offers an alternative modeling approach for obtaining estimates of under-five mortality which removes the restriction of a piece-wise linear rate of decline and introduces hierarchy to exchange information between countries. The newly proposed estimates of the rate of decline in under-5 mortality and the uncertaint

Extreme and rapid bursts of functional adaptations shape bite force in amniotes

Adaptation is the fundamental driver of functional and biomechanical evolution. Accordingly, the states of biomechanical traits (absolute or relative trait values) have long been used as proxies for adaptations in response to direct selection. However, ignoring evolutionary history, in particular ancestry, passage of time and the rate of evolution, can be misleading. Here, we apply a recently developed phylogenetic statistical approach using significant rate shifts to detect instances of exceptional rates of adaptive changes in bite force in a large group of terrestrial vertebrates, the amniotes. Our results show that bite force in amniotes evolved through multiple bursts of exceptional rates of adaptive changes, whereby whole groups—including Darwin's finches, maniraptoran dinosaurs (group of non-avian dinosaurs including birds), anthropoids and hominins (fossil and modern humans)—experienced significant rate increases compared to the background rate. However, in most parts of the amniote tree of life, we find no exceptional rate increases, indicating that coevolution with body size was primarily responsible for the patterns observed in bite force. Our approach represents a template for future studies in functional morphology and biomechanics, where exceptional rates of adaptive changes can be quantified and potentially linked to specific ecological factors underpinning major evolutionary radiation

Analysis of human mini-exome sequencing data from Genetic Analysis Workshop 17 using a Bayesian hierarchical mixture model

Next-generation sequencing technologies are rapidly changing the field of genetic epidemiology and enabling exploration of the full allele frequency spectrum underlying complex diseases. Although sequencing technologies have shifted our focus toward rare genetic variants, statistical methods traditionally used in genetic association studies are inadequate for estimating effects of low minor allele frequency variants. Four our study we use the Genetic Analysis Workshop 17 data from 697 unrelated individuals (genotypes for 24,487 autosomal variants from 3,205 genes). We apply a Bayesian hierarchical mixture model to identify genes associated with a simulated binary phenotype using a transformed genotype design matrix weighted by allele frequencies. A Metropolis Hasting algorithm is used to jointly sample each indicator variable and additive genetic effect pair from its conditional posterior distribution, and remaining parameters are sampled by Gibbs sampling. This method identified 58 genes with a posterior probability greater than 0.8 for being associated with the phenotype. One of these 58 genes, PIK3C2B was correctly identified as being associated with affected status based on the simulation process. This project demonstrates the utility of Bayesian hierarchical mixture models using a transformed genotype matrix to detect genes containing rare and common variants associated with a binary phenotype

New horizons for plant translational research

In this issue, we launch a new article collection "The Promise of Plant Translational Research," featuring articles from leading plant researchers and call for additional plant translational research to be submitted to PLOS Biology for inclusion in this collection. We also discuss in this Editorial why this field has a vital role to play in meeting the challenges of sustainably feeding a growing world population

Simulation study for analysis of binary responses in the presence of extreme case problems

<p>Abstract</p> <p>Background</p> <p>Estimates of variance components for binary responses in presence of extreme case problems tend to be biased due to an under-identified likelihood. The bias persists even when a normal prior is used for the fixed effects.</p> <p>Methods</p> <p>A simulation study was carried out to investigate methods for the analysis of binary responses with extreme case problems. A linear mixed model that included a fixed effect and random effects of sire and residual on the liability scale was used to generate binary data. Five simulation scenarios were conducted based on varying percentages of extreme case problems, with true values of heritability equal to 0.07 and 0.17. Five replicates of each dataset were generated and analyzed with a generalized prior (<b>g-prior</b>) of varying weight.</p> <p>Results</p> <p>Point estimates of sire variance using a normal prior were severely biased when the percentage of extreme case problems was greater than 30%. Depending on the percentage of extreme case problems, the sire variance was overestimated when a normal prior was used by 36 to 102% and 25 to 105% for a heritability of 0.17 and 0.07, respectively. When a g-prior was used, the bias was reduced and even eliminated, depending on the percentage of extreme case problems and the weight assigned to the g-prior. The lowest Pearson correlations between true and estimated fixed effects were obtained when a normal prior was used. When a 15% g-prior was used instead of a normal prior with a heritability equal to 0.17, Pearson correlations between true and fixed effects increased by 11, 20, 23, 27, and 60% for 5, 10, 20, 30 and 75% of extreme case problems, respectively. Conversely, Pearson correlations between true and estimated fixed effects were similar, within datasets of varying percentages of extreme case problems, when a 5, 10, or 15% g-prior was included. Therefore this indicates that a model with a g-prior provides a more adequate estimation of fixed effects.</p> <p>Conclusions</p> <p>The results suggest that when analyzing binary data with extreme case problems, bias in the estimation of variance components could be eliminated, or at least significantly reduced by using a g-prior.</p

Design considerations and analysis planning of a phase 2a proof of concept study in rheumatoid arthritis in the presence of possible non-monotonicity

BACKGROUND: It is important to quantify the dose response for a drug in phase 2a clinical trials so the optimal doses can then be selected for subsequent late phase trials. In a phase 2a clinical trial of new lead drug being developed for the treatment of rheumatoid arthritis (RA), a U-shaped dose response curve was observed. In the light of this result further research was undertaken to design an efficient phase 2a proof of concept (PoC) trial for a follow-on compound using the lessons learnt from the lead compound. METHODS: The planned analysis for the Phase 2a trial for GSK123456 was a Bayesian Emax model which assumes the dose-response relationship follows a monotonic sigmoid "S" shaped curve. This model was found to be suboptimal to model the U-shaped dose response observed in the data from this trial and alternatives approaches were needed to be considered for the next compound for which a Normal dynamic linear model (NDLM) is proposed. This paper compares the statistical properties of the Bayesian Emax model and NDLM model and both models are evaluated using simulation in the context of adaptive Phase 2a PoC design under a variety of assumed dose response curves: linear, Emax model, U-shaped model, and flat response. RESULTS: It is shown that the NDLM method is flexible and can handle a wide variety of dose-responses, including monotonic and non-monotonic relationships. In comparison to the NDLM model the Emax model excelled with higher probability of selecting ED90 and smaller average sample size, when the true dose response followed Emax like curve. In addition, the type I error, probability of incorrectly concluding a drug may work when it does not, is inflated with the Bayesian NDLM model in all scenarios which would represent a development risk to pharmaceutical company. The bias, which is the difference between the estimated effect from the Emax and NDLM models and the simulated value, is comparable if the true dose response follows a placebo like curve, an Emax like curve, or log linear shape curve under fixed dose allocation, no adaptive allocation, half adaptive and adaptive scenarios. The bias though is significantly increased for the Emax model if the true dose response follows a U-shaped curve. CONCLUSIONS: In most cases the Bayesian Emax model works effectively and efficiently, with low bias and good probability of success in case of monotonic dose response. However, if there is a belief that the dose response could be non-monotonic then the NDLM is the superior model to assess the dose response

Use of linear mixed models for genetic evaluation of gestation length and birth weight allowing for heavy-tailed residual effects

<p>Abstract</p> <p>Background</p> <p>The distribution of residual effects in linear mixed models in animal breeding applications is typically assumed normal, which makes inferences vulnerable to outlier observations. In order to mute the impact of outliers, one option is to fit models with residuals having a heavy-tailed distribution. Here, a Student's-<it>t </it>model was considered for the distribution of the residuals with the degrees of freedom treated as unknown. Bayesian inference was used to investigate a bivariate Student's-<it>t </it>(BS<it>t</it>) model using Markov chain Monte Carlo methods in a simulation study and analysing field data for gestation length and birth weight permitted to study the practical implications of fitting heavy-tailed distributions for residuals in linear mixed models.</p> <p>Methods</p> <p>In the simulation study, bivariate residuals were generated using Student's-<it>t </it>distribution with 4 or 12 degrees of freedom, or a normal distribution. Sire models with bivariate Student's-<it>t </it>or normal residuals were fitted to each simulated dataset using a hierarchical Bayesian approach. For the field data, consisting of gestation length and birth weight records on 7,883 Italian Piemontese cattle, a sire-maternal grandsire model including fixed effects of sex-age of dam and uncorrelated random herd-year-season effects were fitted using a hierarchical Bayesian approach. Residuals were defined to follow bivariate normal or Student's-<it>t </it>distributions with unknown degrees of freedom.</p> <p>Results</p> <p>Posterior mean estimates of degrees of freedom parameters seemed to be accurate and unbiased in the simulation study. Estimates of sire and herd variances were similar, if not identical, across fitted models. In the field data, there was strong support based on predictive log-likelihood values for the Student's-<it>t </it>error model. Most of the posterior density for degrees of freedom was below 4. Posterior means of direct and maternal heritabilities for birth weight were smaller in the Student's-<it>t </it>model than those in the normal model. Re-rankings of sires were observed between heavy-tailed and normal models.</p> <p>Conclusions</p> <p>Reliable estimates of degrees of freedom were obtained in all simulated heavy-tailed and normal datasets. The predictive log-likelihood was able to distinguish the correct model among the models fitted to heavy-tailed datasets. There was no disadvantage of fitting a heavy-tailed model when the true model was normal. Predictive log-likelihood values indicated that heavy-tailed models with low degrees of freedom values fitted gestation length and birth weight data better than a model with normally distributed residuals.</p> <p>Heavy-tailed and normal models resulted in different estimates of direct and maternal heritabilities, and different sire rankings. Heavy-tailed models may be more appropriate for reliable estimation of genetic parameters from field data.</p