Comparative investigation of three Bayesian p values

Goodness-of-fit testing for meta-analysis of rare binary events

Random-effects (RE) meta-analysis is a crucial approach for combining results from multiple independent studies that exhibit heterogeneity. Recently, two frequentist goodness-of-fit (GOF) tests were proposed to assess the fit of RE model. However, they tend to perform poorly when assessing rare binary events. Under a general binomial-normal framework, we propose a novel GOF test for the meta-analysis of rare events. Our method is based on pivotal quantities that play an important role in Bayesian model assessment. It further adopts the Cauchy combination idea proposed in a 2019 JASA paper, to combine dependent p-values computed using posterior samples from Markov Chain Monte Carlo. The advantages of our method include clear conception and interpretation, incorporation of all data including double zeros without the need for artificial correction, well-controlled Type I error, and generally improved ability in detecting model misfits compared to previous GOF methods. We illustrate the proposed method via simulation and three real data applications.

The risks of advancing parental age on neonatal morbidity and mortality are U- or J-shaped for both maternal and paternal ages

BACKGROUND

The biologic implications of delayed parenthood have been blamed for a major public health crisis in the United States, that includes high rates of neonatal morbidity and mortality (NMM). The objective of this study was to evaluate the risk of parent age on NMM and to provide results that can serve as a starting point for more specific mediation modeling.

METHODS

Data containing approximately 15,000,000 birth records were obtained from the United States Natality database for the years 2014 to 2018. A Bayesian modeling approach was used to estimate the both the total effect and the risk adjusted for confounding between parent ages and for mediation by chromosomal disorders including Down syndrome. Outcomes included intra-hospital death and nine measures of neonatal morbidity.

RESULTS

For paternal age, seven NMM (preterm birth, very preterm birth, low Apgar score, treatment with antibiotics, treatment with surfactant, prolonged ventilation, intra-hospital death) had U-shaped risk patterns, two NMM (small for gestational age, admission to neonatal intensive care) had J-shaped risk patterns, one NMM (seizures) was not significantly related to paternal age. For maternal age, three NMM (low Apgar score, treatment with antibiotics and intra-hospital death) had U-shaped risk patterns, four NMM (preterm delivery, very preterm delivery, admission to neonatal intensive care, treatment with surfactant) had J-shaped risk patterns, one NMM (small for gestational age) had a risk declining with age, one NMM (prolonged ventilation) had a risk increasing with age and one NMM (seizures) was not significantly related to maternal age.

CONCLUSIONS

Both advancing maternal and paternal ages had U- or J-shaped risk patterns for neonatal morbidity and mortality.

Estimating racial health disparities among adverse birth outcomes as deviations from the population rates

Background

Despite significant research, the reasons for racial health disparities among adverse birth outcomes (ABO) remain largely unknown. The bulk of research into racial health disparities among ABO in the United States has concentrated on the risk of race and ethnic groups relative to the specific sub-population of non-Hispanic white women and their children. The objective of this study was to estimate the racial and ethnic risks among a set of neonatal and maternal health disparities while minimizing bias attributable to how the baseline risk was established.

Methods

All birth records were obtained from the United States Natality database for the years 2014 to 2017. A Bayesian modeling approach was used to estimate the risk disparity for disorders by race. The estimation of the race-specific risks used a sum-to-zero constraint for the race regression coefficients.

Results

Estimating racial health disparities relative to the overall population rate yielded novel results and identified perinatal health disparities for all the race groups studied.

Conclusions

Unbiased risk estimates for racial disparities among ABO are now available for stimulating and initiating more complex causal modeling that can lead to understanding how racial health disparities for ABO are mediated and how they can be prevented.

Disentangling the roles of maternal and paternal age on birth prevalence of down syndrome and other chromosomal disorders using a Bayesian modeling approach

Background

Multiple neonatal and pediatric disorders have been linked to older paternal ages. Combining these findings with the evidence that many men are having children at much later ages generates considerable public health concern. The risk of paternal age has been difficult to estimate and interpret because children often have parents whose ages are similar and likely to be confounded. Epidemiologic studies often model the conditional effects of paternal age using regression models that typically treat maternal age as linear, curvilinear or as age-band categories. Each of these approaches has limitations. As an alternative, the current study measures age to the nearest year, and fits a Bayesian model in which each parent’s age is given a conditional autoregressive prior (CAR).

Methods

Data containing approximately 12,000,000 birth records were obtained from the United States Natality database for the years 2014 to 2016. Date were cross-tabulated for maternal ages 15–49 years and for paternal ages 15–65 years. A Bayesian logistic model was implemented using conditional autoregressive priors for both maternal and paternal ages modeled separately and jointly for both Down syndrome and chromosomal disorders other than Down syndrome.

Results

Models with maternal and paternal ages given CAR priors were judged to be better fitting than traditional models. For Down syndrome, the approach attributed a very large risk to advancing maternal age with the effect of advancing paternal age having a very small sparing effect on birth prevalence. Maternal age was also related to the birth prevalence of chromosomal disorders other than Down syndrome while paternal age was not.

Conclusions

Advancing paternal age was not associated with an increase in risk for either Down syndrome or chromosomal disorders other than Down syndrome.

Electronic supplementary material

The online version of this article (10.1186/s12874-019-0720-1) contains supplementary material, which is available to authorized users.

An evaluation of whether a gestational weight gain of 5 to 9 kg for obese women optimizes maternal and neonatal health risks

BACKGROUND

Maternal obesity has a wide range of health effects on both the pregnant woman and developing fetus. The clinical significance of these disorders, combined with a dramatically increasing prevalence of obesity among pregnant women has precipitated a major health crisis in the United States. The most commonly used recommendations for gestational weight gain were established by the Institute of Medicine (IOM) in 2009 and have become well known and often adopted. The authors of the IOM report acknowledged that the recommended gestational weight gain of 5 to 9 kg for obese women whose body mass index was greater than 30 kg/m2 was based on very little empirical evidence. The objective of this study was to evaluate whether a 5 to 9 kg weight gain, for obese women, optimized a set of maternal and neonatal health outcomes.

METHODS

Data containing approximately 12,000,000 birth records were obtained from the United States Natality database for the years 2014 to 2016. A Bayesian modeling approach was used to estimate the controlled direct effects of pre-pregnancy body mass index and gestational weight gain.

RESULTS

Obese women gaining less than 5 kg during pregnancy had reduced maternal risks for gestational hypertension, eclampsia, induction of labor and Caesarian section. In contrast, maternal gestational weight gain of less than 5 kg was associated with increased risks for multiple adverse neonatal outcomes with macrosomia the exception. Obese women who gained more than 9 kg during pregnancy had increased risk for multiple maternal and neonatal adverse outcomes.

CONCLUSIONS

Obese women who were observed to gain less than 5 kg during gestation had reduced odds of several peripartum disorders. However, this lower gestational weight gain was associated with an increase in multiple risks for the neonate.

Effect of intra-ovarian injection of mesenchymal stem cells in aged mares

PURPOSE

This study aims to determine if intra-ovarian injection of bone marrow-derived mesenchymal stem cells (MSCs) improves or restores ovarian function in aged females.

METHODS

Prospective randomized study of eight aged mares and six young mares receiving intra-ovarian injection of MSCs or vehicle. Main outcome measures were antral follicle count and serum anti-Müllerian hormone (AMH) (aged and young mares), and for aged mares, oocyte meiotic and developmental competence; gross and histological ovarian assessment; evaluation of presence of chimerism in recovered granulosa cells and in ovarian tissue samples; and gene expression in ovarian tissue as assessed by RNA sequencing.

RESULTS

Injection of MSCs was not associated with significant changes in follicle number, oocyte recovery rate on follicle aspiration, oocyte maturation rate, or blastocyst rate after ICSI in aged mares, or in changes in follicle number in young mares. There were no significant changes in peripheral AMH concentrations, indicating a lack of effect on growing follicles. MSC donor DNA was not recovered in granulosa cells or in ovarian tissue, indicating lack of persistence of injected MSC. RNA sequencing revealed significant differences in gene expression between MSC- and vehicle-injected ovaries.

CONCLUSIONS

Intra-ovarian injection of bone marrow-derived MSCs altered gene expression but did not improve ovarian function in aged mares.

Bayesian statistical approaches to evaluating cognitive models

Cognitive models aim to explain complex human behavior in terms of hypothesized mechanisms of the mind. These mechanisms can be formalized in terms of mathematical structures containing parameters that are theoretically meaningful. For example, in the case of perceptual decision making, model parameters might correspond to theoretical constructs like response bias, evidence quality, response caution, and the like. Formal cognitive models go beyond verbal models in that cognitive mechanisms are instantiated in terms of mathematics and they go beyond statistical models in that cognitive model parameters are psychologically interpretable. We explore three key elements used to formally evaluate cognitive models: parameter estimation, model prediction, and model selection. We compare and contrast traditional approaches with Bayesian statistical approaches to performing each of these three elements. Traditional approaches rely on an array of seemingly ad hoc techniques, whereas Bayesian statistical approaches rely on a single, principled, internally consistent system. We illustrate the Bayesian statistical approach to evaluating cognitive models using a running example of the Linear Ballistic Accumulator model of decision making (Brown SD, Heathcote A. The simplest complete model of choice response time: linear ballistic accumulation. Cogn Psychol 2008, 57:153-178). WIREs Cogn Sci 2018, 9:e1458. doi: 10.1002/wcs.1458 This article is categorized under: Neuroscience > Computation Psychology > Reasoning and Decision Making Psychology > Theory and Methods.

Metronidazole for the treatment of Tritrichomonas foetus in bulls

BACKGROUND

Tritrichomonas foetus is a sexually transmitted protozoon that causes reproductive failure, among cattle, so disruptive that many western US states have initiated control programs. Current control programs are based on the testing and exclusion of individual bulls. Unfortunately, these programs are utilizing screening tests that are lacking in sensitivity. Blanket treatment of all the exposed bulls and adequate sexual rest for the exposed cows could provide a more viable disease control option. The objectives of this study were twofold. The first objective was to demonstrate effectiveness for metronidazole treatment of a bull under ideal conditions and with an optimized treatment regime. This type of study with a single subject is often referred to as an n-of-1 or single subject clinical trial. The second objective of the current study was to review the scientific basis for the banning of metronidazole for use in Food Animals by the Animal Medicinal Drug Use Clarification Act of 1994 (AMDUCA).

RESULTS

Results from an antimicrobial assay indicated that metronidazole at a concentration of 0.5 μg/mL successfully eliminated in vitro protozoal growth of bovine Tritrichomonas foetus. The estimated effective intravenous dose was two treatments with 60 mg/kg metronidazole, 24 h apart. A bull that had tested positive for Tritrichomonas foetus culture at weekly intervals for 5 weeks prior to treatment was negative for Tritrichomonas foetus culture at weekly intervals for five consecutive weeks following this treatment regimen. An objective evaluation of the published evidence on the potential public health significance of using metronidazole to treat Tritrichomonas foetus in bulls provides encouragement for veterinarians and regulators to consider approaches that might lead to permitting the legal use of metronidazole in bulls.

CONCLUSION

The study demonstrated successful inhibition of Tritrichomonas foetus both in vitro and in vivo with metronidazole. The current status of metronidazole is that the Animal Medicinal Drug Use Clarification Act of 1994 prohibits its extra-label use in food-producing animals. Veterinarians and regulators should consider approaches that might lead to permitting the legal use of metronidazole in bulls.

Bayesian hierarchical modelling of continuous non-negative longitudinal data with a spike at zero: An application to a study of birds visiting gardens in winter

The development of methods for dealing with continuous data with a spike at zero has lagged behind those for overdispersed or zero‐inflated count data. We consider longitudinal ecological data corresponding to an annual average of 26 weekly maximum counts of birds, and are hence effectively continuous, bounded below by zero but also with a discrete mass at zero. We develop a Bayesian hierarchical Tweedie regression model that can directly accommodate the excess number of zeros common to this type of data, whilst accounting for both spatial and temporal correlation. Implementation of the model is conducted in a Markov chain Monte Carlo (MCMC) framework, using reversible jump MCMC to explore uncertainty across both parameter and model spaces. This regression modelling framework is very flexible and removes the need to make strong assumptions about mean‐variance relationships a priori. It can also directly account for the spike at zero, whilst being easily applicable to other types of data and other model formulations. Whilst a correlative study such as this cannot prove causation, our results suggest that an increase in an avian predator may have led to an overall decrease in the number of one of its prey species visiting garden feeding stations in the United Kingdom. This may reflect a change in behaviour of house sparrows to avoid feeding stations frequented by sparrowhawks, or a reduction in house sparrow population size as a result of sparrowhawk increase.