Bayesian Synthesis Research Articles

Bayesian Synthesis of Astrometric Wobble and Total Light Curves in Close Binary Supermassive Black Holes

We test the potential of Bayesian synthesis of upcoming multi-instrument data to extract orbital parameters and individual light curves of close binary supermassive black holes (CB-SMBH) with subparsec separations. Next-generation interferometers, will make possible the observation of astrometric wobbles in CB-SMBH. Combining them with periodic variable time-domain data from surveys like the Vera C. Rubin Legacy Survey of Space and Time, allows for more information on CB-SMBH candidates compared to standalone observational methods. Our method reliably determines binary parameters and component fluxes from binary total flux across long-term, intermediate, and short-term binary dynamics and observational configurations, assuming 10 annual observations, even in short period “q-accrete” objects. Expected CB-SMBH astrometric wobbles constructed from binary dynamical parameters might serve in refining observational strategies for CB-SMBH. Combination of inferred mass ratio, light curves of binary components, and observed photocenter wobbles can be a proxy for the activity states of CB-SMBH components.

A Comparison of Methods for Synthesizing Results from Previous Research to Obtain Priors for Bayesian Structural Equation Modeling

Bayesian estimation of latent variable models provides some unique advantages to researchers working with small samples and complex models when compared with the more commonly used maximum likelihood approach. A key aspect of Bayesian modeling involves the selection of prior distributions for the parameters of interest. Prior research has demonstrated that using default priors, which are typically noninformative, may yield biased and inefficient estimates. Therefore, it is recommended that data analysts obtain useful, informative priors from prior research whenever possible. The goal of the current simulation study was to compare several methods designed to combine results from prior studies that will yield informative priors for regression coefficients in structural equation models. These methods include noninformative priors, Bayesian synthesis, pooled analysis, aggregated priors, standard meta-analysis, power priors, and the meta-analytic predictive methods. Results demonstrated that power priors and meta-analytic predictive priors, used in conjunction with Bayesian estimation, may yield the most accurate estimates of the latent structure coefficients. Implications for practice and suggestions for future research are discussed.

A Robust Estimate of Continental‐Scale Terrestrial Carbon Sinks Using GOSAT XCO2 Retrievals

AbstractSatellite XCO2 retrievals could improve the estimates of surface carbon fluxes, but it remains unknown on what scales these estimates are robust. Here, we use the time‐dependent Bayesian synthesis top‐down method and prior net ecosystem exchanges (NEEs) from 12 terrestrial biosphere models (TBMs) to infer the monthly carbon fluxes of 51 land regions with constraints by GOSAT XCO2 retrievals. We find that the uncertainty (standard deviation of 12 TBMs) reduction rates (uncertainty reduction rate (URR)) decrease significantly at decreasing spatial scales. On the continental‐scale, the mean URR is about 57%, and the annual and seasonal cycle estimates of NEE are rather robust. The evaluation shows that the posterior CO2 concentrations are significantly improved at the continental scale. Our study suggests that the GOSAT XCO2 can only promise a robust continental‐scale NEE estimate, and improving the XCO2 accuracy is an effective way to achieve robust estimates on smaller scales under current spatial coverage.

Bayesian historical borrowing with longitudinal large-scale assessments

The purpose of this paper is to extend and evaluate methods of Bayesian historical borrowing applied to longitudinal data with a focus on parameter recovery and predictive performance. Bayesian historical borrowing allows researchers to utilize information from previous data sources and to adjust the extent of borrowing based on the similarity of current data to historical data. We examine the utility of three static historical borrowing methods including complete pooling, Bayesian synthesis with aggregated data-dependent priors, traditional power priors, and two dynamic borrowing methods including Bayesian dynamic borrowing and commensurate priors. Using data from two administrations of the United States Early Childhood Longitudinal Study, we evaluate these methods in terms of in-sample simulation statistics, as well as pseudo out-of-sample measures of predictive performance. A case study examining growth in reading competency over time revealed that for one historical cycle, most methods of historical borrowing perform similarly with respect to predictive performance and parameter recovery. Pooling and power priors performed relatively poorly across the conditions in this study, particularly when the current data and the historical data were heterogeneous. Results from a comprehensive simulation study revealed that the advantages of different historical borrowing methods vary across different evaluation criteria. Overall, Bayesian dynamic borrowing and commensurate priors are no worse, and in some cases better, than other methods in terms of parameter recovery and predictive performance, and considering a previous paper by Kaplan et al. (Psychometrika, 10.1007/s11336-022-09869-3, 2022) found clear benefits of Bayesian dynamic borrowing over other methods of historical borrowing in the multilevel context using data from the Program for International Student Assessment (PISA) with five historical cycles, this paper argues that Bayesian dynamic borrowing or commensurate priors is a prudent choice for borrowing information from previous cycles of longitudinal data.

Population size estimation of transgender women and men in Bhutan.

IntroductionTransgender persons experience health disparities and are marginalized in many societies worldwide. Even their numbers are unknown in many countries. We conducted the first effort to estimate the population size of transgender women (TGW) and transgender men (TGM) in Bhutan from November 2019 to January 2020.MethodsCommunity-based surveys of TGW and TGM integrated several methods to estimate the size of hidden populations, including key informant mapping, wisdom-of-the-crowd, the service multiplier, and the unique object multiplier. Results of the several methods were synthesized using a Bayesian approach.ResultsSurveys included 34 TGW and 124 TGM. TGW was persons assigned to the male sex at birth and currently self-identified as “trans women” (91%), “women” (6%), or another gender (3%). TGM were persons assigned female sex at birth and self-identified as “trans men” (100%). Bayesian synthesis of the multiple methods estimated 84 TGW (credible interval 61–110) and 166 TGM (credible interval 124–211) in Bhutan.ConclusionsOur study documented that TGW and TGM are part of Bhutanese society, with TGW constituting 0.03% of adult women and TGM 0.06% of adult men. Estimates can help advocate for resources and programs to address the health and well-being of these communities.

The Impact of Sample Size on Exchangeability in the Bayesian Synthesis Approach to Data Fusion

Data fusion approaches have been adopted to facilitate more complex analyses and produce more accurate results. Bayesian Synthesis is a relatively new approach to data fusion where results from the analysis of one dataset are used as prior information for the analysis of the next dataset. Datasets of interest are sequentially analyzed until a final posterior distribution is created, incorporating information from all candidate datasets, rather than simply combining the datasets into one large dataset and analyzing them simultaneously. One concern with this approach lies in the sequence of datasets being fused. This study examines whether the order of datasets matters when the datasets being fused each have substantially different sample sizes. The performance of Bayesian Synthesis with varied sample sizes is evaluated by examining results from simulated data with known population values under a variety of conditions. Results suggest that the order in which the dataset are fused can have a significant impact on the obtained estimates.

Improving the joint estimation of CO2 and surface carbon fluxes using a constrained ensemble Kalman filter in COLA (v1.0)

Abstract. Atmospheric inversion of carbon dioxide (CO2) measurements to better understand carbon sources and sinks has made great progress over the last 2 decades. However, most of the studies, including a four-dimensional variational ensemble Kalman filter and Bayesian synthesis approaches, directly obtain only fluxes, while CO2 concentration is derived with the forward model as part of a post-analysis. Kang et al. (2012) used the local ensemble transform Kalman filter (LETKF), which updates the CO2, surface carbon flux (SCF), and meteorology fields simultaneously. Following this track, a system with a short assimilation window and a long observation window was developed (Liu et al., 2019). However, this data assimilation system faces the challenge of maintaining carbon mass conservation. To overcome this shortcoming, here we apply a constrained ensemble Kalman filter (CEnKF) approach to ensure the conservation of global CO2 mass. After a standard LETKF procedure, an additional assimilation is used to adjust CO2 at each model grid point and to ensure the consistency between the analysis and the first guess of the global CO2 mass. Compared to an observing system simulation experiment without mass conservation, the CEnKF significantly reduces the annual global SCF bias from ∼ 0.2 to less than 0.06 Gt and slightly improves the seasonal and annual performance over tropical and southern extratropical regions. We show that this system can accurately track the spatial distribution of annual mean SCF. And the system reduces the seasonal flux root mean square error from a priori to analysis by 48 %–90 %, depending on the continental region. Moreover, the 2015–2016 El Niño impact is well captured with anomalies mainly in the tropics.

Bayesian Dynamic Borrowing of Historical Information with Applications to the Analysis of Large-Scale Assessments.

The purpose of this paper is to demonstrate and evaluate the use of Bayesian dynamic borrowing (Viele et al, in Pharm Stat 13:41-54, 2014) as a means of systematically utilizing historical information with specific applications to large-scale educational assessments. Dynamic borrowing via Bayesian hierarchical models is a special case of a general framework of historical borrowing where the degree of borrowing depends on the heterogeneity among historical data and current data. A joint prior distribution over the historical and current data sets is specified with the degree of heterogeneity across the data sets controlled by the variance of the joint distribution. We apply Bayesian dynamic borrowing to both single-level and multilevel models and compare this approach to other historical borrowing methods such as complete pooling, Bayesian synthesis, and power priors. Two case studies using data from the Program for International Student Assessment reveal the utility of Bayesian dynamic borrowing in terms of predictive accuracy. This is followed by two simulation studies that reveal the utility of Bayesian dynamic borrowing over simple pooling and power priors in cases where the historical data is heterogeneous compared to the current data based on bias, mean squared error, and predictive accuracy. In cases of homogeneous historical data, Bayesian dynamic borrowing performs similarly to data pooling, Bayesian synthesis, and power priors. In contrast, for heterogeneous historical data, Bayesian dynamic borrowing performed at least as well, if not better, than other methods of borrowing with respect to mean squared error, percent bias, and leave-one-out cross-validation. Supplementary InformationThe online version contains supplementary material available at 10.1007/s11336-022-09869-3.

Data Privacy Protection and Utility Preservation through Bayesian Data Synthesis: A Case Study on Airbnb Listings

ABSTRACT When releasing record-level data containing sensitive information to the public, the data disseminator is responsible for protecting the privacy of every record in the dataset, simultaneously preserving important features of the data for users’ analyses. These goals can be achieved by data synthesis, where confidential data are replaced with synthetic data that are simulated based on statistical models estimated on the confidential data. In this article, we present a data synthesis case study, where synthetic values of price and the number of available days in a sample of the New York Airbnb Open Data are created for privacy protection. One sensitive variable, the number of available days of an Airbnb listing, has a large amount of zero-valued records and also truncated at the two ends. We propose a zero-inflated truncated Poisson regression model for its synthesis. We use a sequential synthesis approach to further synthesize the sensitive price variable. The resulting synthetic data are evaluated for its utility preservation and privacy protection, the latter in the form of disclosure risks. Furthermore, we propose methods to investigate how uncertainties in intruder’s knowledge would influence the identification disclosure risks of the synthetic data. In particular, we explore several realistic scenarios of uncertainties in intruder’s knowledge of available information and evaluate their impacts on the resulting identification disclosure risks.

WOMBAT v1.0: a fully Bayesian global flux-inversion framework

Abstract. WOMBAT (the WOllongong Methodology for Bayesian Assimilation of Trace-gases) is a fully Bayesian hierarchical statistical framework for flux inversion of trace gases from flask, in situ, and remotely sensed data. WOMBAT extends the conventional Bayesian synthesis framework through the consideration of a correlated error term, the capacity for online bias correction, and the provision of uncertainty quantification on all unknowns that appear in the Bayesian statistical model. We show, in an observing system simulation experiment (OSSE), that these extensions are crucial when the data are indeed biased and have errors that are spatio-temporally correlated. Using the GEOS-Chem atmospheric transport model, we show that WOMBAT is able to obtain posterior means and variances on non-fossil-fuel CO2 fluxes from Orbiting Carbon Observatory-2 (OCO-2) data that are comparable to those from the Model Intercomparison Project (MIP) reported in Crowell et al. (2019). We also find that WOMBAT's predictions of out-of-sample retrievals obtained from the Total Column Carbon Observing Network (TCCON) are, for the most part, more accurate than those made by the MIP participants.

Trends in undiagnosed HIV prevalence in England and implications for eliminating HIV transmission by 2030: an evidence synthesis model

SummaryBackgroundA target to eliminate HIV transmission in England by 2030 was set in early 2019. This study aimed to estimate trends from 2013 to 2019 in HIV prevalence, particularly the number of people living with undiagnosed HIV, by exposure group, ethnicity, gender, age group, and region. These estimates are essential to monitor progress towards elimination.MethodsA Bayesian synthesis of evidence from multiple surveillance, demographic, and survey datasets relevant to HIV in England was used to estimate trends in the number of people living with HIV, the proportion of people unaware of their HIV infection, and the corresponding prevalence of undiagnosed HIV. All estimates were stratified by exposure group, ethnicity, gender, age group (15–34, 35–44, 45–59, or 60–74 years), region (London, or outside of London) and year (2013–19).FindingsThe total number of people living with HIV aged 15–74 years in England increased from 83 500 (95% credible interval 80 200–89 600) in 2013 to 92 800 (91 000–95 600) in 2019. The proportion diagnosed steadily increased from 86% (80–90%) to 94% (91–95%) during the same time period, corresponding to a halving in the number of undiagnosed infections from 11 600 (8300–17 700) to 5900 (4400–8700) and in undiagnosed prevalence from 0·29 (0·21–0·44) to 0·14 (0·11–0·21) per 1000 population. Similar steep declines were estimated in all subgroups of gay, bisexual, and other men who have sex with men and in most subgroups of Black African heterosexuals. The pace of reduction was less pronounced for heterosexuals in other ethnic groups and people who inject drugs, particularly outside London; however, undiagnosed prevalence in these groups has remained very low.InterpretationThe UNAIDS target of diagnosing 90% of people living with HIV by 2020 was reached by 2016 in England, with the country on track to achieve the new target of 95% diagnosed by 2025. Reductions in transmission and undiagnosed prevalence have corresponded to large scale-up of testing in key populations and early diagnosis and treatment. Additional and intensified prevention measures are required to eliminate transmission of HIV among the communities that have experienced slower declines than other subgroups, despite having very low prevalences of HIV.FundingUK Medical Research Council and Public Health England.

Assessing efficacy of antiviral therapy for COVID-19 patients: A case study on remdesivir with bayesian synthesis design and multistate analysis

Background/purposeA synthesis design and multistate analysis is required for assessing the clinical efficacy of antiviral therapy on dynamics of multistate disease progression and in reducing the mortality and enhancing the recovery of patients with COVID-19. A case study on remdesivir was illustrated for the clinical application of such a novel design and analysis.MethodsA Bayesian synthesis design was applied to integrating the empirical evidence on the one-arm compassion study and the two-arm ACTT-1 trial for COVID-19 patients treated with remdesivir. A multistate model was developed to model the dynamics of hospitalized COVID-19 patients from three transient states of low, medium-, and high-risk until the two outcomes of recovery and death. The outcome measures for clinical efficacy comprised high-risk state, death, and discharge.ResultsThe efficacy of remdesivir in reducing the risk of death and enhancing the odds of recovery were estimated as 31% (95% CI, 18–44%) and 10% (95% CI, 1–18%), respectively. Remdesivir therapy for patients with low-risk state showed the efficacy in reducing subsequent progression to high-risk state and death by 26% (relative rate (RR), 0.74; 95% CI, 0.55–0.93) and 62% (RR, 0.38; 95% CI, 0.29–0.48), respectively. Less but still statistically significant efficacy in mortality reduction was noted for the medium- and high-risk patients. Remdesivir treated patients had a significantly shorter period of hospitalization (9.9 days) compared with standard care group (12.9 days).ConclusionThe clinical efficacy of remdesvir therapy in reducing mortality and accelerating discharge has been proved by the Bayesian synthesis design and multistate analysis.

Risk-Efficient Bayesian Data Synthesis for Privacy Protection

Abstract Statistical agencies utilize models to synthesize respondent-level data for release to the public for privacy protection. In this study, we efficiently induce privacy protection into any Bayesian synthesis model by employing a pseudo-likelihood that exponentiates each likelihood contribution by an observation record-indexed weight ∈[0,1], defined to be inversely proportional to the identification risk for that record. We start with the marginal probability of identification risk for a record, which is composed as the probability that the identity of the record may be disclosed. Our application to the Consumer Expenditure Surveys (CE) of the U.S. Bureau of Labor Statistics demonstrates that the marginally risk-weighted synthesizer provides an overall improved privacy protection. However, the identification risks actually increase for some moderate-risk records after risk-weighted pseudo-posterior estimation synthesis owing to increased isolation after weighting, a phenomenon we label “whack-a-mole.” We proceed to construct a weight for each record from a collection of pairwise identification risk probabilities with other records, where each pairwise probability measures the joint probability of reidentification of the pair of records, which mitigates the whack-a-mole issue and produces a more efficient set of synthetic data with lower risk and higher utility for the CE data.

The cost-effectiveness profile of sex-neutral HPV immunisation in European tender-based settings: a model-based assessment

In many European countries, human papillomavirus (HPV) vaccine uptake among girls has remained below target levels, supporting the scope for vaccination of boys. We aimed to investigate if sex-neutral HPV vaccination can be considered cost-effective compared with girls-only vaccination at uptake levels equal to those among girls and under tender-based vaccination costs achieved throughout Europe. We investigated the cost-effectiveness of sex-neutral HPV vaccination in European tender-based settings. We applied a Bayesian synthesis framework for health economic evaluation to 11 countries (Austria, Belgium, Croatia, Estonia, Italy, Latvia, the Netherlands, Poland, Slovenia, Spain, and Sweden), accommodating country-specific information on key epidemiological and economic parameters, and on current HPV vaccination programmes. We used projections from three independently developed HPV transmission models to tailor region-specific herd effects. The main outcome measures in the comparison of sex-neutral with girls-only vaccination were cancer cases prevented and incremental cost-effectiveness ratios (ICERs), defined as the cost in international dollars (I$) per life-year gained. The total number of cancer cases to be prevented by vaccinating girls at currently realised vaccine uptake varied from 318 (95% CI 197-405) per cohort of 200 000 preadolescents (100 000 girls plus 100 000 boys) in Croatia (under 20% uptake of the 9-valent vaccine) to 1904 (1741-2101) in Estonia (under 70% uptake of the 9-valent vaccine). Vaccinating boys at equal coverage increased these respective numbers by 168 (95% CI 121-213) in Croatia and 467 (391-587) in Estonia. Sex-neutral vaccination was likely to be cost-effective, with ICERs of sex-neutral compared with girls-only vaccination varying from I$4300 per life-year gained in Latvia (95% credibility interval 3450-5160; 40% uptake) to I$25 720 per life-year gained in Spain (21 380-30 330; 80% uptake). At uniform 80% uptake, a favourable cost-effectiveness profile was retained for most of the countries investigated (Austria, Belgium, Italy, Latvia, the Netherlands, Slovenia, Spain, and Sweden). Sex-neutral HPV vaccination is economically attractive in European tender-based settings. However, tendering mechanisms need to ensure that vaccination of boys will remain cost-effective at high vaccine uptake rates. European Commission 7th Framework Programme and WHO.

Vertical transmission of Zika virus and its outcomes: a Bayesian synthesis of prospective studies

SummaryBackgroundProspective studies of Zika virus in pregnancy have reported rates of congenital Zika syndrome and other adverse outcomes by trimester. However, Zika virus can infect and damage the fetus early in utero, but clear before delivery. The true vertical transmission rate is therefore unknown. We aimed to provide the first estimates of underlying vertical transmission rates and adverse outcomes due to congenital infection with Zika virus by trimester of exposure.MethodsThis was a Bayesian latent class analysis of data from seven prospective studies of Zika virus in pregnancy. We estimated vertical transmission rates, rates of Zika-virus-related and non-Zika-virus-related adverse outcomes, and the diagnostic sensitivity of markers of congenital infection. We allowed for variation between studies in these parameters and used information from women in comparison groups with no PCR-confirmed infection, where available.FindingsThe estimated mean risk of vertical transmission was 47% (95% credible interval 26 to 76) following maternal infection in the first trimester, 28% (15 to 46) in the second, and 25% (13 to 47) in the third. 9% (4 to 17) of deliveries following infections in the first trimester had symptoms consistent with congenital Zika syndrome, 3% (1 to 7) in the second, and 1% (0 to 3) in the third. We estimated that in infections during the first, second, and third trimester, respectively, 13% (2 to 27), 3% (−5 to 14), and 0% (−7 to 11) of pregnancies had adverse outcomes attributable to Zika virus infection. Diagnostic sensitivity of markers of congenital infection was lowest in the first trimester (42% [18 to 72]), but increased to 85% (51 to 99) in trimester two, and 80% (42 to 99) in trimester three. There was substantial between-study variation in the risks of vertical transmission and congenital Zika syndrome.InterpretationThis preliminary analysis recovers the causal effects of Zika virus from disparate study designs. Higher transmission in the first trimester is unusual with congenital infections but accords with laboratory evidence of decreasing susceptibility of placental cells to infection during pregnancy.FundingEuropean Union Horizon 2020 programme.

Vertical Transmission of Zika Virus and Its Outcomes: A Bayesian Synthesis of Prospective Studies

Background: Prospective studies of Zika virus (ZIKV) in pregnancy have reported rates of Congenital Zika Syndrome (CZS) and other adverse outcomes by trimester. However, ZIKV may infect and damage the fetus in utero, but clear before delivery. The true vertical transmission rate is therefore unknown. Methods: We applied Bayesian latent class analysis to data from 7 prospective studies, in order to simultaneously estimate: vertical transmission (VT) rates, rates of ZIKV-related and non-ZIKV related adverse outcomes, and the diagnostic sensitivity of markers of congenital infection. We allowed for variation between studies in these parameters, and utilised information from women in comparison groups with no PCR-confirmed infection, where available. Findings: Following maternal infection in the 1st, 2nd, and 3rd trimesters, the estimated average risks of VT were 46%, 28% and 25%; 8.5%, 2.9%, and 0.8% deliveries had symptoms consistent with Congenital Zika Syndrome (CZS). We estimated that in 1st, 2nd, and 3rd trimesters respectively 13.4%, 3.3% and 0.3% of pregnancies had adverse outcomes attributable to ZIKV in pregnancy. Diagnostic sensitivity of markers of congenital infection is lowest in the 1st trimester (42%) but about 80% subsequently. There was substantial between-study variation in the risks of VT and CZS. Interpretation: This preliminary analysis recovers the causal effects of ZIKV from disparate study designs. Higher transmission in the first trimester is unusual with congenital infections but accords with laboratory evidence of decreasing susceptibility of placental cells over pregnancy. Funding Statement: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 734857. Declaration of Interests: CT and CP report that this work was partly supported by the National Institute of Health Research Great Ormond Street Hospital Biomedical Research Centre. CT received funding from AbbVie and the Penta Foundation during the period of the study, outside the submitted work. All authors are members of the ZIKAction consortium. Ethics Approval Statement: Not required.

Bayesian synthesis of probabilistic programs for automatic data modeling

We present new techniques for automatically constructing probabilistic programs for data analysis, interpretation, and prediction. These techniques work with probabilistic domain-specific data modeling languages that capture key properties of a broad class of data generating processes, using Bayesian inference to synthesize probabilistic programs in these modeling languages given observed data. We provide a precise formulation of Bayesian synthesis for automatic data modeling that identifies sufficient conditions for the resulting synthesis procedure to be sound. We also derive a general class of synthesis algorithms for domain-specific languages specified by probabilistic context-free grammars and establish the soundness of our approach for these languages. We apply the techniques to automatically synthesize probabilistic programs for time series data and multivariate tabular data. We show how to analyze the structure of the synthesized programs to compute, for key qualitative properties of interest, the probability that the underlying data generating process exhibits each of these properties. Second, we translate probabilistic programs in the domain-specific language into probabilistic programs in Venture, a general-purpose probabilistic programming system. The translated Venture programs are then executed to obtain predictions of new time series data and new multivariate data records. Experimental results show that our techniques can accurately infer qualitative structure in multiple real-world data sets and outperform standard data analysis methods in forecasting and predicting new data.

Who Will Benefit From Expanding HPV Vaccination Programs to Boys?

Indications for human papillomavirus vaccination programs are expanding to boys. However, the rationale behind their inclusion is often not clear. Using a Bayesian synthesis framework and assuming equal vaccine coverage in both sexes, we assessed how the incremental number of cancer cases prevented and life-years gained from boys’ vaccination are distributed between women, heterosexual men, and men who have sex with men (MSM). Below 60% coverage, at least 50% of the gains from boys’ vaccination was attributable to cervical cancer prevention, whereas at 80% coverage, 50% of the gains was attributable to women, 15% to heterosexual men, and 35% to MSM. Above 90% coverage, 85–100% of the gains from boys’ vaccination was attributable to anal and oropharyngeal cancer prevention, mainly in MSM. Sex-neutral vaccination can be advocated on grounds of bolstering herd protection to women and directly protecting men, particularly MSM, with the clinical significance of either argument determined by the coverage.

Bayesian synthesis using prior information on fracture risk from randomized trials to analyze post-market data

ObjectiveTo conduct a Bayesian evidence synthesis using commonly available statistical procedures to estimate fracture risk for postmenopausal women undergoing hormonal therapy for breast cancer. Study Design and SettingUsing linked administrative data, we conducted a retrospective cohort study of women aged 66 years or older diagnosed with stage I to III breast cancer in Ontario, Canada, between April 1, 2003, and February 28, 2010. We used data augmentation to perform Bayesian Cox regression of the hazard of a hip, spine, or wrist/forearm fracture, adjusting for age, history of fragility fracture, corticosteroid use, osteoporosis, rheumatoid arthritis, dementia, or diabetes diagnoses. ResultsOf 10,259 included in the sample, 3,733 initiated on tamoxifen and 6,526 on an aromatase inhibitor. Posterior probabilities that the hazard ratio (HR) exceeded 1 for aromatase inhibitor compared with tamoxifen were 46% (HR = 0.99, 95% credible interval [CrI] 0.71, 1.25), 35% (HR = 0.94, 95% CrI 0.78, 1.26), and 76% (HR = 1.08, 95% CrI 0.88, 1.32) with an uninformative prior, and 63% (HR = 1.04, 95% CrI 0.83, 1.3), 84% (HR = 1.12, 95% CrI 0.89, 1.4), and 89% (HR = 1.13, 95% CrI 0.93, 1.36) with an informative prior, for hip, spine, and wrist/forearm fractures, respectively. ConclusionsPrior information resulted in higher posterior probabilities. The strength of evidence for increased risk varied by fracture site.

Bayesian synthesis for simulation-based generation of probability of detection (PoD) curves

This paper examines the feasibility of using Bayesian synthesis to reduce the number of experimental cases and trials required for generation of probability of detection (PoD) curves. A Bayesian framework is developed for the data-level combination of experimental and simulated datasets, in the context of the inspection of back-wall breaking notches in metallic samples by bulk ultrasonic shear waves. PoD curves generated using the proposed approach, where results from a reduced number of experimental defect cases and trials are used in combination with simulated datasets, are shown to compare well with those from the conventional approach using a large number of experiments. Finally, the framework is also shown to be versatile for generating PoD curves for complex defects (illustrated through the example of an inclined notch) using simulations for canonical defects (vertical notches).