Vague Priors Research Articles

Accurately estimating correlations between demographic parameters: A comment on Deane etal. (2023).

Estimating correlations among demographic parameters is an important method in population ecology. A recent paper by Deane etal. (Ecology and Evolution 13:e9847, 2023) attempted to explore the effects of different priors for covariance matrices on inference when using mark-recovery data. Unfortunately, Deane etal. (2023) made a mistake when parameterizing some of their models. Rather than exploring the effects of different priors, they examined the effects of the use of incorrect equations on inference. In this manuscript, we clearly describe the mistake in Deane etal. (2023). We then demonstrate the use of an alternative and appropriate method and reach different conclusions regarding the effects of priors on inference. Consistent with other recent literature, informative inverse Wishart priors can lead to flawed inference, while vague priors on covariance matrix components have little impact when sample sizes are adequate.

Extracorporeal cardiopulmonary resuscitation versus standard treatment for refractory out-of-hospital cardiac arrest: a Bayesian meta-analysis

BackgroundThe outcomes of several randomized trials on extracorporeal cardiopulmonary resuscitation (ECPR) in patients with refractory out-of-hospital cardiac arrest were examined using frequentist methods, resulting in a dichotomous interpretation of results based on p-values rather than in the probability of clinically relevant treatment effects. To determine such a probability of a clinically relevant ECPR-based treatment effect on neurological outcomes, the authors of these trials performed a Bayesian meta-analysis of the totality of randomized ECPR evidence.MethodsA systematic search was applied to three electronic databases. Randomized trials that compared ECPR-based treatment with conventional CPR for refractory out-of-hospital cardiac arrest were included. The study was preregistered in INPLASY (INPLASY2023120060). The primary Bayesian hierarchical meta-analysis estimated the difference in 6-month neurologically favorable survival in patients with all rhythms, and a secondary analysis assessed this difference in patients with shockable rhythms (Bayesian hierarchical random-effects model). Primary Bayesian analyses were performed under vague priors. Outcomes were formulated as estimated median relative risks, mean absolute risk differences, and numbers needed to treat with corresponding 95% credible intervals (CrIs). The posterior probabilities of various clinically relevant absolute risk difference thresholds were estimated.ResultsThree randomized trials were included in the analysis (ECPR, n = 209 patients; conventional CPR, n = 211 patients). The estimated median relative risk of ECPR for 6-month neurologically favorable survival was 1.47 (95%CrI 0.73–3.32) with a mean absolute risk difference of 8.7% (− 5.0; 42.7%) in patients with all rhythms, and the median relative risk was 1.54 (95%CrI 0.79–3.71) with a mean absolute risk difference of 10.8% (95%CrI − 4.2; 73.9%) in patients with shockable rhythms. The posterior probabilities of an absolute risk difference > 0% and > 5% were 91.0% and 71.1% in patients with all rhythms and 92.4% and 75.8% in patients with shockable rhythms, respectively.ConclusionThe current Bayesian meta-analysis found a 71.1% and 75.8% posterior probability of a clinically relevant ECPR-based treatment effect on 6-month neurologically favorable survival in patients with all rhythms and shockable rhythms. These results must be interpreted within the context of the reported credible intervals and varying designs of the randomized trials.RegistrationINPLASY (INPLASY2023120060, December 14th, 2023, https://doi.org/10.37766/inplasy2023.12.0060).

Using generalized structured additive regression models to determine factors associated with and clusters for COVID-19 hospital deaths in South Africa

BackgroundThe first case of COVID-19 in South Africa was reported in March 2020 and the country has since recorded over 3.6 million laboratory-confirmed cases and 100 000 deaths as of March 2022. Transmission and infection of SARS-CoV-2 virus and deaths in general due to COVID-19 have been shown to be spatially associated but spatial patterns in in-hospital deaths have not fully been investigated in South Africa. This study uses national COVID-19 hospitalization data to investigate the spatial effects on hospital deaths after adjusting for known mortality risk factors.MethodsCOVID-19 hospitalization data and deaths were obtained from the National Institute for Communicable Diseases (NICD). Generalized structured additive logistic regression model was used to assess spatial effects on COVID-19 in-hospital deaths adjusting for demographic and clinical covariates. Continuous covariates were modelled by assuming second-order random walk priors, while spatial autocorrelation was specified with Markov random field prior and fixed effects with vague priors respectively. The inference was fully Bayesian.ResultsThe risk of COVID-19 in-hospital mortality increased with patient age, with admission to intensive care unit (ICU) (aOR = 4.16; 95% Credible Interval: 4.05–4.27), being on oxygen (aOR = 1.49; 95% Credible Interval: 1.46–1.51) and on invasive mechanical ventilation (aOR = 3.74; 95% Credible Interval: 3.61–3.87). Being admitted in a public hospital (aOR = 3.16; 95% Credible Interval: 3.10–3.21) was also significantly associated with mortality. Risk of in-hospital deaths increased in months following a surge in infections and dropped after months of successive low infections highlighting crest and troughs lagging the epidemic curve. After controlling for these factors, districts such as Vhembe, Capricorn and Mopani in Limpopo province, and Buffalo City, O.R. Tambo, Joe Gqabi and Chris Hani in Eastern Cape province remained with significantly higher odds of COVID-19 hospital deaths suggesting possible health systems challenges in those districts.ConclusionThe results show substantial COVID-19 in-hospital mortality variation across the 52 districts. Our analysis provides information that can be important for strengthening health policies and the public health system for the benefit of the whole South African population. Understanding differences in in-hospital COVID-19 mortality across space could guide interventions to achieve better health outcomes in affected districts.

A Bayes Analysis of a Dependent Competing Risk Model Based on Marshall–Olkin Bivariate Weibull Distribution

This paper considers a competing risk model defined on the basis of minimum of two dependent failures where the two failures are assumed to jointly follow Marshall–Olkin bivariate Weibull distribution. This paper explores some important features of corresponding likelihood functions and performs a full Bayesian analysis of the model for data resulting from normal as well as accelerated life tests. The accelerated model is described by regressing the scale parameters of the model through inverse power-law relationship. Posterior-based inferences are drawn using the Gibbs sampler algorithm after specifying proper but vague priors for the model parameters. The numerical illustration is provided using real datasets. The performance of the model is assured by Bayesian tools of model compatibility and then the entertained model is compared with the competing risk model based on Marshall–Olkin bivariate exponential assumption.

The Effect of Mobilization at 6 Months after Critical Illness — Meta-Analysis

BackgroundThe comparative efficacy and safety of early active mobilization compared with usual care regarding long-term outcomes for adult critically ill survivors remain uncertain.MethodsWe systematically reviewed randomized clinical trials comparing early active mobilization versus usual care in critically ill adults. The primary outcome was days alive and out of hospital to day 180 after pooling data using random effects modeling. We also performed a Bayesian meta-analysis to describe the treatment effect in probability terms. Secondary outcomes were mortality, physical function, strength, health-related quality of life at 6 months, and adverse events.ResultsFifteen trials from 11 countries were included with data from 2703 participants. From six trials (1121 participants) reporting the primary outcome, the pooled mean difference was an increase of 4.28 days alive and out of hospital to day 180 in those patients who received early active mobilization (95% confidence interval, −4.46 to 13.03; I2=41%). Using Bayesian analyses with vague priors, the probability that the intervention increased days alive and out of hospital was 75.1%. In survivors, there was a 95.1% probability that the intervention improved physical function measured through a patient-reported outcome measure at 6 months (standardized mean difference, 0.2; 95% confidence interval, 0.09 to 0.32; I2=0%). Although no treatment effect was identified on any other secondary outcome, there was a 66.4% possibility of increased adverse events with the implementation of early active mobilization and a 72.2% chance it increased 6-month mortality.ConclusionsUse of early active mobilization for critically ill adults did not significantly affect days alive and out of hospital to day 180. Early active mobilization was associated with improved physical function in survivors at 6 months; however, the possibility that it might increase mortality and adverse events needs to be considered when interpreting this finding. (PROSPERO number, CRD42022309650.)

What is the Best Evidence to Guide Management of Acute Achilles Tendon Ruptures? A Systematic Review and Network Meta-Analysis of Randomized Controlled Trials

Category: Sports; Trauma Introduction/Purpose: Uncertainty exists regarding the best treatment for acute Achilles tendon ruptures. Simultaneous comparison of the multiple treatment options using traditional study designs is problematic; multiarm clinical trials often are logistically constrained to small sample sizes, and traditional meta-analyses are limited to comparisons of only two treatments that have been compared in head-to-head trials. Network meta-analyses allow for simultaneous comparison of all existing treatments utilizing both direct and indirect evidence. We performed a network meta-analysis of randomized controlled trials to answer the following questions: Considering open repair, minimally invasive surgery repair, functional rehabilitation, or primary immobilization for acute Achilles tendon ruptures, (1) which intervention is associated with the lowest risk of rerupture? (2) Which intervention is associated with the lowest risk of complications resulting in surgery? Methods: Five databases and grey literature sources were searched from inception to September 30, 2019. Included studies were RCTs comparing treatment of acute Achilles tendon ruptures using two or more of the following interventions: primary immobilization, functional rehabilitation, open surgical repair, or MIS repair. We excluded studies enrolling patients with chronic ruptures, reruptures, and preexisting Achilles tendinopathy as well as studies with more than 20% loss to follow-up or less than 6 months of follow-up. Nineteen RCTs (1316 patients) were included in the final analysis. The mean number of patients per study treatment arm was 35 +- 16, mean age was 41 +- 5 years, mean sex composition was 80% +- 10% males, and mean follow-up was 22 +- 12 months. The four treatment groups were compared for the main outcomes of rerupture and complications resulting in operation. The analysis was conducted using random-effects Bayesian network meta-analysis with vague priors. Results: Treatment with primary immobilization had a greater risk of rerupture than open surgery (odds ratio 4.06 [95% credible interval {CrI} 1.47 to 11.88]; p < 0.05). There were no other differences between treatments for risk of rerupture. Minimally invasive surgery was ranked first for fewest complications resulting in surgery and was associated with a lower risk of complications resulting in surgery than functional rehabilitation (OR 0.16 [95% CrI 0.02 to 0.90]; p < 0.05), open surgery (OR 0.22 [95% CrI 0.04 to 0.93]; p < 0.05), and primary immobilization (OR < 0.01 [95% CrI < 0.01 to 0.01]; p < 0.05). Risk of complications resulting in surgery was no different between primary immobilization and open surgery (OR 1.46 [95% CrI 0.35 to 5.36]). Data for patient-reported outcome scores and return to activity were inappropriate for pooling secondary to considerable clinical heterogeneity and imprecision associated with small sample sizes. Conclusion: Faced with acute Achilles tendon rupture, patients should be counseled that the risk of rerupture likely is no different across contemporary treatments. Considering the possibly lower risk of complications resulting in surgery associated with MIS repair, patients and surgeons must balance any benefit with the potential risks of MIS techniques. As treatments continue to evolve, consistent reporting of validated patient-reported outcome measures is critically important to facilitate analysis with existing RCT evidence. Infrequent but serious complications such as rerupture and deep infection should be further explored to determine whether meaningful differences exist in specific patient populations.

Priors in Bayesian Deep Learning: A Review

SummaryWhile the choice of prior is one of the most critical parts of the Bayesian inference workflow, recent Bayesian deep learning models have often fallen back on vague priors, such as standard Gaussians. In this review, we highlight the importance of prior choices for Bayesian deep learning and present an overview of different priors that have been proposed for (deep) Gaussian processes, variational autoencoders and Bayesian neural networks. We also outline different methods of learning priors for these models from data. We hope to motivate practitioners in Bayesian deep learning to think more carefully about the prior specification for their models and to provide them with some inspiration in this regard.

Mortality Rates Among Hospitalized Patients With COVID-19 Infection Treated With Tocilizumab and Corticosteroids

A World Health Organization (WHO) meta-analysis found that tocilizumab was associated with reduced mortality in hospitalized patients with COVID-19. However, uncertainty remains concerning the magnitude of tocilizumab's benefits and whether its association with mortality benefit is similar across respiratory subgroups. To use bayesian methods to assess the magnitude of mortality benefit associated with tocilizumab and the differences between respiratory support subgroups in hospitalized patients with COVID-19. A bayesian hierarchical reanalysis of the WHO meta-analysis of tocilizumab studies published in 2020 and 2021 was performed. Main results were estimated using weakly informative priors to exert little influence on the observed data. The robustness of these results was evaluated using vague and informative priors. The studies featured in the meta-analysis were randomized clinical tocilizumab trials of hospitalized patients with COVID-19. Only patients receiving corticosteroids were included. Usual care plus tocilizumab in comparison with usual care or placebo. All-cause mortality at 28 days after randomization. Among the 5339 patients included in this analysis, most were men, with mean ages between 56 and 66 years. There were 2117 patients receiving simple oxygen only, 2505 receiving noninvasive ventilation (NIV), and 717 receiving invasive mechanical ventilation (IMV) in 15 studies from multiple countries and continents. Assuming weakly informative priors, the overall odds ratios (ORs) for survival were 0.70 (95% credible interval [CrI], 0.50-0.91) for patients receiving simple oxygen only, 0.81 (95% CrI, 0.63-1.03) for patients receiving NIV, and 0.89 (95% CrI, 0.61-1.22) for patients receiving IMV, respectively. The posterior probabilities of any benefit (OR <1) were notably different between patients receiving simple oxygen only (98.9%), NIV (95.5%), and IMV (75.4%). The posterior probabilities of a clinically meaningful association (absolute mortality risk difference >1%) were greater than 95% in patients receiving simple oxygen only and greater than 90% in patients receiving NIV. In contrast, the posterior probability of this clinically meaningful association was only approximately 67% in patients receiving IMV. The probabilities of tocilizumab superiority in the simple oxygen only subgroup compared with the NIV and IMV subgroups were 85% and 90%, respectively. Predictive intervals highlighted that only 72.1% of future tocilizumab IMV studies would show benefit. The conclusions did not change with different prior distributions. In this bayesian reanalysis of a previous meta-analysis of 15 studies of hospitalized patients with COVID-19 treated with tocilizumab and corticosteroids, use of simple oxygen only and NIV was associated with a probability of a clinically meaningful mortality benefit from tocilizumab. Future research should clarify whether patients receiving IMV also benefit from tocilizumab.

A Bayes Analysis and Comparison of Arrhenius Weibull and Arrhenius Lognormal Models under Competing Risk

The paper considers constant stress accelerated life test situations under a competing risk scenario. The different groups of experimental units are operated at different accelerated levels of stress and, at each level, the units are exposed to fail from two competing causes of failures. For modeling the failure times resulting from such a test, the paper considers two competing risk models. The first model is based on the minimum of two Weibull failure times whereas the second one is based on the minimum of two lognormal failure times. In order to study the effect of covariates on failure times, the scale parameter of component models in each modeling framework has been regressed using the Arrhenius relationship. The paper performs a complete Bayes analysis of both the considered models for a real dataset arising from a temperature accelerated life test experiment and compares the two models using a few standard Bayesian tools. Bayes analysis is done using vague but proper priors for the parameters. Moreover, the considered models result in to intractable posterior distributions and, therefore, the paper uses the Metropolis algorithm to draw the desired posterior based inferences. For censored data situations, however, the intermediate Gibbs steps are used as updating mechanism by defining full conditionals corresponding to unknown censored data. The plausibility of both the models for entertained dataset has also been checked before performing their comparison. A numerical example based on a real dataset is provided for illustration.

Balanced Crystalloids versus Saline in Critically Ill Adults — A Systematic Review with Meta-Analysis

BackgroundThe comparative efficacy and safety of balanced crystalloid solutions and saline for fluid therapy in critically ill adults remain uncertain.MethodsWe systematically reviewed randomized clinical trials (RCTs) comparing the use of balanced crystalloids with saline in critically ill adults. The primary outcome was 90-day mortality after pooling data from low-risk-of-bias trials using a random-effects model. We also performed a Bayesian meta-analysis to describe the primary treatment effect in probability terms. Secondary outcomes included the incidence of acute kidney injury (AKI), new treatment with renal replacement therapy (RRT), and ventilator-free and vasopressor-free days to day 28.ResultsWe identified 13 RCTs, comprising 35,884 participants. From six trials (34,450 participants) with a low risk of bias, the risk ratio (RR) for 90-day mortality with balanced crystalloids versus saline was 0.96 (95% confidence interval [CI], 0.91 to 1.01; I2 = 12.1%); using vague priors, the posterior probability that balanced crystalloids reduce mortality was 89.5%. The RRs of developing AKI and of being treated with RRT with balanced crystalloids versus saline were 0.96 (95% CI, 0.89 to 1.02) and 0.95 (95% CI, 0.81 to 1.11), respectively. Ventilator-free days (mean difference, 0.18 days; 95% CI, −0.45 to 0.81) and vasopressor-free days (mean difference, 0.19 days; 95% CI, −0.14 to 0.51) were similar between groups.ConclusionsThe estimated effect of using balanced crystalloids versus saline in critically ill adults ranges from a 9% relative reduction to a 1% relative increase in the risk of death, with a high probability that the average effect of using balanced crystalloids is to reduce mortality. (PROSPERO number, CRD42021243399.)

Correction to 'Bayesian inference reveals positive but subtle effects of experimental fishery closures on marine predator demographics'.

Correction to 'Bayesian inference reveals positive but subtle effects of experimental fishery closures on marine predator demographics'.

Choosing priors in Bayesian ecological models by simulating from the prior predictive distribution

AbstractBayesian data analysis is increasingly used in ecology, but prior specification remains focused on choosing non‐informative priors (e.g., flat or vague priors). One barrier to choosing more informative priors is that priors must be specified on model parameters (e.g., intercepts, slopes, and sigmas), but prior knowledge often exists on the level of the response variable. This is particularly true for common models in ecology, like generalized linear mixed models that have a link function and potentially dozens of parameters, each of which needs a prior distribution. We suggest that this difficulty can be overcome by simulating from the prior predictive distribution and visualizing the results on the scale of the response variable. In doing so, some common choices for non‐informative priors on parameters can easily be seen to produce biologically impossible values of response variables. Such implications of prior choices are difficult to foresee without visualization. We demonstrate a workflow for prior selection using simulation and visualization with two ecological examples (predator–prey body sizes and spider responses to food competition). This approach is not new, but its adoption by ecologists will help to better incorporate prior information in ecological models, thereby maximizing one of the benefits of Bayesian data analysis.

Determination of Quantile Range of Optimal Hyperparameters Using Bayesian Estimation

Bayesian estimations have the advantages of taking into account the uncertainty of all parameter estimates which allows virtually the use of vague priors. This study focused on determining the quantile range at which optimal hyperparameter of normally distributed data with vague information could be obtained in Bayesian estimation of linear regression models. A Monte Carlo simulation approach was used to generate a sample size of 200 data-set. Observation precisions and posterior precisions were estimated from the regression output to determine the posterior means estimate for each model to derive the new dependent variables. The variances were divided into 10 equal parts to obtain the hyperparameters of the prior distribution. Average absolute deviation for model selection was used to validate the adequacy of each model. The study revealed the optimal hyperparameters located at 5th and 7th deciles. The research simplified the process of selecting the hyperparameters of prior distribution from the data with vague information in empirical Bayesian inferences.&#x0D; Keywords: Optimal Hyperparameters; Quantile Ranges; Bayesian Estimation; Vague prior

What Is the Best Evidence to Guide Management of Acute Achilles Tendon Ruptures? A Systematic Review and Network Meta-Analysis of Randomized Controlled Trials.

Uncertainty exists regarding the best treatment for acute Achilles tendon ruptures. Simultaneous comparison of the multiple treatment options using traditional study designs is problematic; multiarm clinical trials often are logistically constrained to small sample sizes, and traditional meta-analyses are limited to comparisons of only two treatments that have been compared in head-to-head trials. Network meta-analyses allow for simultaneous comparison of all existing treatments utilizing both direct (head-to-head comparison) and indirect (not previously compared head-to-head) evidence. We performed a network meta-analysis of randomized controlled trials (RCTs) to answer the following questions: Considering open repair, minimally invasive surgery (MIS) repair, functional rehabilitation, or primary immobilization for acute Achilles tendon ruptures, (1) which intervention is associated with the lowest risk of rerupture? (2) Which intervention is associated with the lowest risk of complications resulting in surgery? This study was conducted with methods guided by the Cochrane Handbook for Systematic Reviews of Interventions and is reported in adherence with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension statement for incorporating network meta-analysis. Five databases and grey literature sources (such as major orthopaedic meeting presentation lists) were searched from inception to September 30, 2019. Included studies were RCTs comparing treatment of acute Achilles tendon ruptures using two or more of the following interventions: primary immobilization, functional rehabilitation, open surgical repair, or MIS repair. We excluded studies enrolling patients with chronic ruptures, reruptures, and preexisting Achilles tendinopathy as well as studies with more than 20% loss to follow-up or less than 6 months of follow-up. Nineteen RCTs (1316 patients) were included in the final analysis. The mean number of patients per study treatment arm was 35 ± 16, mean age was 41 ± 5 years, mean sex composition was 80% ± 10% males, and mean follow-up was 22 ± 12 months. The four treatment groups were compared for the main outcomes of rerupture and complications resulting in operation. The analysis was conducted using random-effects Bayesian network meta-analysis with vague priors. Evidence quality was evaluated using Grades of Recommendation, Assessment, Development, and Evaluation methodology. We found risk of selection, attrition, and reporting bias to be low across treatments, and we found the risk of performance and detection bias to be high. Overall risk of bias between treatments appeared similar. We found that treatment with primary immobilization had a greater risk of rerupture than open surgery (odds ratio 4.06 [95% credible interval {CrI} 1.47 to 11.88]; p < 0.05). There were no other differences between treatments for risk of rerupture. Minimally invasive surgery was ranked first for fewest complications resulting in surgery and was associated with a lower risk of complications resulting in surgery than functional rehabilitation (OR 0.16 [95% CrI 0.02 to 0.90]; p < 0.05), open surgery (OR 0.22 [95% CrI 0.04 to 0.93]; p < 0.05), and primary immobilization (OR < 0.01 [95% CrI < 0.01 to 0.01]; p < 0.05). Risk of complications resulting in surgery was no different between primary immobilization and open surgery (OR 1.46 [95% CrI 0.35 to 5.36]). Data for patient-reported outcome scores and return to activity were inappropriate for pooling secondary to considerable clinical heterogeneity and imprecision associated with small sample sizes. Faced with acute Achilles tendon rupture, patients should be counseled that, based on the best-available evidence, the risk of rerupture likely is no different across contemporary treatments. Considering the possibly lower risk of complications resulting in surgery associated with MIS repair, patients and surgeons must balance any benefit with the potential risks of MIS techniques. As treatments continue to evolve, consistent reporting of validated patient-reported outcome measures is critically important to facilitate analysis with existing RCT evidence. Infrequent but serious complications such as rerupture and deep infection should be further explored to determine whether meaningful differences exist in specific patient populations. Level I, therapeutic study.

THE ASSOCIATION OF ADENOMYOSIS WITH UTEROPLACENTAL INSUFFICIENCY AND PREECLAMPSIA IN WOMEN UNDERGOING ICSI CYCLE

To explore the association of adenomyosis with maternal and perinatal outcomes in women undergoing ICSI. Prospective cohort study over a 2-year period between 2018 and 2020. Women with ongoing pregnancy (>20 weeks) after ICSI were included. Exclusion criteria were oocyte donation cycles, high-order pregnancies and women with uterine fibroids, hydrosalpinx, or stage 3-4 endometriosis according to revised AFS criteria. Adenomyosis was diagnosed according to MUSA group consensus statement. The analysis groups were divided into women with and without adenomyosis. The primary outcomes were prevalence of preeclampsia and composite adverse perinatal outcomes (small-for-gestational age at birth, neonatal care unit admission, asphyxia, preeclampsia, preterm delivery). Secondary outcome was the difference of uterine artery Doppler pulsatility index between two groups. Group comparison of primary and secondary outcomes were performed using Bayesian inference methods (Metropolis Hastings MCMC) with vague priors due to limited sample size. The results were reported as mean difference between the groups, 95% credible intervals (CrI) and the probability of significant difference. Additional results were reported via frequentist statistical methods. There were 486 ongoing ICSI cycles during the study period and 101 (20.8%) ongoing pregnancies were eligible for inclusion. The adenomyosis prevalence was 18.8% (19/101). The prevalence of preeclampsia (21.1 vs. 13.4%) and composite adverse perinatal outcomes (63.1 vs. 42.7%) were higher in women with adenomyosis. Bayesian analysis showed the probability of preeclampsia (probability 84.1%, mean difference: 7.7%, 95% CrI: -11.7%-27.2%) and composite adverse perinatal outcomes (probability 99.5%, mean difference: 29.6% 95% CrI: 7.3%-51.8%) could be higher in women with adenomyosis compared to those without. First trimester mean uterine artery pulsatility index was higher in women with adenomyosis compared to those without (probability: 99.5%, mean difference: 0.32, 95% CrI: 0.07 to 0.57). Results of additional adverse pregnancy and neonatal outcomes are available in Table 1. Women with adenomyosis show signs of uteroplacental malperfusion during the first trimester and possibly have an increased risk of preeclampsia and composite adverse perinatal outcomes.Tabled 1Adverse OutcomeAdenomyosis (number, percentage)Control (number, percentage)Preeclampsia4 (21.1)4 (13.4)SGA at birth7 (36.8)9 (10.9)Preterm Delivery8 (42.3)15 (18.3)NICU admission7 (36.8)7 (8.5)Asphyxia2 (10.5)2 (2.4) Open table in a new tab

Using informative prior based on expert opinion in Bayesian estimation of the transition probability matrix in Markov modelling\u2014an example from the cost-effectiveness analysis of the treatment of patients with predominantly negative symptoms of schizophrenia with cariprazine

BackgroundWhen patient health state transition evidence is missing from clinical literature, analysts are inclined to make simple assumptions to complete the transition matrices within a health economic model. Our aim was to provide a solution for estimating transition matrices by the Bayesian statistical method within a health economic model when empirical evidence is lacking.MethodsWe used a previously published cost-effectiveness analysis of the use of cariprazine compared to that of risperidone in patients with predominantly negative symptoms of schizophrenia. We generated the treatment-specific state transition probability matrices in three different ways: (1) based only on the observed clinical trial data; (2) based on Bayesian estimation where prior transition probabilities came from experts’ opinions; and (3) based on Bayesian estimation with vague prior transition probabilities (i.e., assigning equal prior probabilities to the missing transitions from one state to the others). For the second approach, we elicited Dirichlet prior distributions by three clinical experts. We compared the transition probability matrices and the incremental quality-adjusted life years (QALYs) across the three approaches.ResultsThe estimates of the prior transition probabilities from the experts were feasible to obtain and showed considerable consistency with the clinical trial data. As expected, the estimated health benefit of the treatments was different when only the clinical trial data were considered (QALY difference 0.0260), its combination with the experts’ beliefs were used in the economic model (QALY difference 0.0253), and when vague prior distributions were used (QALY difference 0.0243).ConclusionsImputing zeros to missing transition probabilities in Markov models might be untenable from the clinical perspective and may result in inappropriate estimates. Bayesian statistics provides an appropriate framework for imputing missing values without making overly simple assumptions. Informative priors based on expert opinions might be more appropriate than vague priors.

Bayesian methods for pilot studies.

The use of pilot studies to help inform the design of randomized controlled trials has increased significantly over the last couple of decades. A pilot study can provide estimates of feasibility parameters, such as the recruitment, compliance and follow-up probabilities. The use of frequentist confidence intervals of these estimates fails to provide a meaningful measure of the uncertainty as it pertains to the design of the associated randomized controlled trial. The objective of this article is to introduce Bayesian methods for the analysis of pilot studies for determining the feasibility of an associated randomized controlled trial. An example from the literature is used to illustrate the advantages of a Bayesian approach for accounting for the uncertainty in pilot study results when assessing the feasibility of an associated randomized controlled trial. Vague beta distribution priors for the feasibility parameters are used. Based on the results from a feasibility study, simulation methods are used to determine the expected power of specified recruitment strategies for an associated randomized controlled trial. The vague priors used for the feasibility parameters are demonstrated to be considerably robust. Beta distribution posteriors for the feasibility parameters lead to beta-binomial predictive distributions for an associated randomized controlled trial regarding the number of patients randomized, the number of patients who are compliant and the number of patients who complete follow-up. Ignoring the uncertainty in pilot study results can lead to inadequate power for an associated randomized controlled trial. Applying Bayesian methods to pilot studies' results provides direct inference about the feasibility parameters and quantifies the uncertainty regarding the feasibility of an associated randomized controlled trial in an intuitive and meaningful way. Furthermore, Bayesian methods can identify recruitment strategies that yield the desired power for an associated randomized controlled trial.

Consequences of Lack of Parameterization Invariance of Non-informative Bayesian Analysis for Wildlife Management: Survival of San Joaquin Kit Fox and Declines in Amphibian Populations

Computational convenience has led to widespread use of Bayesian inference with vague or flat priors to analyze statistical models in ecology. Vague priors are claimed to be objective and to `let the data speak'. However, statisticians have long disputed these claims and have criticized the use of vague priors from philosophical to computational to pragmatic reasons. One of the major criticisms is that the inferences based on non-informative priors are generally dependent on the parameterization of the models. Ecologists, unfortunately, often dismiss such criticisms as having no practical implications. One argument is that for large sample sizes, the priors do not matter. The problem with this argument is that, in practice, one does not know whether or not the observed sample size is sufficiently large for the effect of the prior to vanish. It intricately depends on the complexity of the model and the strength of the prior. We study the consequences of parameterization dependence of the non-informative Bayesian analysis in the context of population viability analysis and occupancy models and at the commonly obtained sample sizes. We show that they can have significant impact on the analysis, in particular on prediction, and can lead to strikingly different managerial decisions. In general terms, the consequences are: (1) All subjective Bayesian inferences can be masqueraded as objective (flat prior) Bayesian inferences, (2) Induced priors on functions of parameters are not flat, thus leading to cryptic biases in scientific inferences, (3) Unrealistic independent priors for multiparameter models lead to unrealistic priors on induced parameters, (4) Bayesian prediction intervals may not have correct coverage, thus leading to errors in decision making, (5) Reparameterization to facilitate MCMC convergence may influence scientific inference. Given the wide spread applicability of the hierarchical models and uncritical use of non-informative Bayesian analysis in ecology, researchers should be cautious about using vague priors as a default choice in practical situations.

Model selection for Bayesian linear mixed models with longitudinal data: Sensitivity to the choice of priors

We explore the performance of three popular Bayesian model-selection criteria when vague priors are used for the covariance parameters of the random effects in a linear mixed-effects model (LMM) using an extensive simulation study. In a previous paper, we have shown that the conditional selection criteria perform worse than their marginal counterparts. It is known that for some “vague” priors, their impact on the estimated model parameters can be non-negligible, e.g., for the priors of the covariance matrix of the random effects in a longitudinal LMM. We evaluate here the impact of vague priors for the covariance matrix of the random effects on selecting the correct LMM using classical Bayesian selection criteria. We consider marginal and conditional criteria. For the random intercept case, we assign different vague priors to the variance parameters. With two or more random effects, we considered five different specifications of inverse-Wishart (IW) prior, five different separation priors and a joint prior. The results show again the better performance of the marginal over the conditional criteria and the superiority of joint and separation priors over IW in all settings. We also illustrate the performance of the selection criteria on a practical dataset.

First-line antihypertensive treatment for severe hypertension in pregnancy: A systematic review and network meta-analysis.

Hydralazine, labetalol, and nifedipine are the recommended first-line treatments for severe hypertension in pregnancy. While all three are effective, there is a lack of sufficient evidence regarding their comparative safety and efficacy. To determine the comparative safety and efficacy of the first-line treatment options for severe hypertension in pregnancy. A systematic search of Medline, Embase, and Cochrane Central Register of Controlled Trials up to May 31, 2018 was conducted. RCTs in pregnancy comparing a first-line antihypertensive agent to another first-line agent for the treatment of severe hypertension in pregnancy. Screening, data abstraction, and quality assessment were done by two independent reviewers. To estimate relative effects from all available evidence, a Bayesian network meta-analysis with vague priors was conducted. Of the 1330 publications identified, 17 RCTs comprised of a total of 1591 women met our selection criteria. For successful treatment of severe hypertension, nifedipine was found to be superior to hydralazine (OR 4.13 [95% CrI 1.01-20.75]) but not labetalol (OR 3.43 [95% CrI 0.94-19.95]). This was not associated with an increased risk for caesarean delivery or maternal side effects. There was no significant difference between labetalol and hydralazine. Given the results of this systematic review and network meta-analysis, maternity care providers should feel comfortable initiating management of severe hypertension in pregnancy using oral nifedipine.