Bayesian Credible Interval Research Articles

Statistical inference via conditional Bayesian posteriors in high-dimensional linear regression

We propose a new method under the Bayesian framework to perform valid inference for low dimensional parameters in high dimensional linear models under sparsity constraints. Our approach is to use surrogate Bayesian posteriors based on partial regression models to remove the effect of high dimensional nuisance variables. We name the final distribution we used to conduct inference “conditional Bayesian posterior” as it is a surrogate posterior constructed conditional on quasi posterior distributions of other parameters and does not admit a fully Bayesian interpretation. Unlike existing Bayesian regularization methods, our method can be used to quantify the estimation uncertainty for arbitrarily small signals and therefore does not require variable selection consistency to guarantee its validity. Theoretically, we show that the resulting Bayesian credible intervals achieve desired coverage probabilities in the frequentist sense. Methodologically, our proposed Bayesian framework can easily incorporate popular Bayesian regularization procedures such as those based on spike and slab priors and horseshoe priors to facilitate high accuracy estimation and inference. Numerically, our proposed method rectifies the uncertainty underestimation of Bayesian shrinkage approaches and has a comparable empirical performance with state-of-the-art frequentist methods based on extensive simulation studies and a real data analysis.

Systematic review and network meta-analysis (NMA) for cladribine tablets in achieving sustained disability improvement (SDI) in multiple sclerosis.

This study was performed to compare probabilities of SDI on the Expanded Disability Status Scale (EDSS) in patients with relapsing-remitting multiple sclerosis (RRMS), treated with cladribine tablets (CT) or fingolimod (FTY), natalizumab (NAT), alemtuzumab (ALE) and ocrelizumab (OCR). Progression of neurological disability as measured by the EDSS has been a common endpoint in multiple sclerosis (MS) trials. Novel therapies can not only slow this process, but in some patients even reverse it. This effect can be measured by the sustained disability improvement (SDI) - an endpoint that seems to continuously gain importance in clinical practice. Despite that, SDI has rarely been explored as an outcome in MS clinical studies, mostly as post-hoc analyses from randomised trials or as retrospective analyses based on patient registry records. A systematic review was conducted in Medline, Embase and Cochrane to identify clinical trials (RCT or non-RCT) evaluating 6-month SDI. An indirect comparison via network meta-analysis (NMA) was performed. Bayesian inference with Markov chains Monte Carlo methods were applied. Eight trials presenting SDI results and applicable for NMA were included: six non-RCTs, with control groups selected by propensity score matching, and two RCTs. NMA results revealed that probability of achieving 6-month SDI with CT was significantly higher compared to all other high efficacy disease-modifying drugs with available data - HR (95% Crl - Bayesian Credibility Interval) vs. FTY: 4.98 (2.11-11.79); vs. NAT: 3.12 (1.31-7.27); vs. ALE: 9.29 (3.40-25.21). The main results were confirmed in the sensitivity analyses. Of all considered therapies, treatment with cladribine tablets was associated with a higher probability of sustained disability improvement in RRMS patients. As this conclusion is based on available clinical data of limited quality, future studies, as well as real-world data, would be valuable to provide further evidence regarding the comparative effectiveness of RRMS therapies.

Molnupiravir plus usual care versus usual care alone as early treatment for adults with COVID-19 at increased risk of adverse outcomes (PANORAMIC): an open-label, platform-adaptive randomised controlled trial

The safety, effectiveness, and cost-effectiveness of molnupiravir, an oral antiviral medication for SARS-CoV-2, has not been established in vaccinated patients in the community at increased risk of morbidity and mortality from COVID-19. We aimed to establish whether the addition of molnupiravir to usual care reduced hospital admissions and deaths associated with COVID-19 in this population. PANORAMIC was a UK-based, national, multicentre, open-label, multigroup, prospective, platform adaptive randomised controlled trial. Eligible participants were aged 50 years or older-or aged 18 years or older with relevant comorbidities-and had been unwell with confirmed COVID-19 for 5 days or fewer in the community. Participants were randomly assigned (1:1) to receive 800 mg molnupiravir twice daily for 5 days plus usual care or usual care only. A secure, web-based system (Spinnaker) was used for randomisation, which was stratified by age (<50 years vs ≥50 years) and vaccination status (yes vs no). COVID-19 outcomes were tracked via a self-completed online daily diary for 28 days after randomisation. The primary outcome was all-cause hospitalisation or death within 28 days of randomisation, which was analysed using Bayesian models in all eligible participants who were randomly assigned. This trial is registered with ISRCTN, number 30448031. Between Dec 8, 2021, and April 27, 2022, 26 411 participants were randomly assigned, 12 821 to molnupiravir plus usual care, 12 962 to usual care alone, and 628 to other treatment groups (which will be reported separately). 12 529 participants from the molnupiravir plus usual care group, and 12 525 from the usual care group were included in the primary analysis population. The mean age of the population was 56·6 years (SD 12·6), and 24 290 (94%) of 25 708 participants had had at least three doses of a SARS-CoV-2 vaccine. Hospitalisations or deaths were recorded in 105 (1%) of 12 529 participants in the molnupiravir plus usual care group versus 98 (1%) of 12 525 in the usual care group (adjusted odds ratio 1·06 [95% Bayesian credible interval 0·81-1·41]; probability of superiority 0·33). There was no evidence of treatment interaction between subgroups. Serious adverse events were recorded for 50 (0·4%) of 12 774 participants in the molnupiravir plus usual care group and for 45 (0·3%) of 12 934 in the usual care group. None of these events were judged to be related to molnupiravir. Molnupiravir did not reduce the frequency of COVID-19-associated hospitalisations or death among high-risk vaccinated adults in the community. UK National Institute for Health and Care Research.

Simultaneous Confidence Intervals for All Pairwise Differences between the Coefficients of Variation of Multiple Birnbaum–Saunders Distributions

In situations where several positive random variables cannot be described using symmetrical distributions, a positively asymmetric distribution which has garnered much attention for studying them is the Birnbaum-Saunders (BS) distribution. This distribution was originally proposed to study fatigue over time in materials and has become widely employed for reliability and fatigue studies. In statistics, the coefficient of variation (CV) is employed to measure relative variation. Furthermore, comparing the CVs of several samples from BS distributions is an important approach to assess the variation among them. Herein, we propose estimation methods for the simultaneous confidence intervals (SCIs) for all pairwise differences between the CVs of multiple BS distributions based on the percentile bootstrap, the generalized confidence interval (GCI), the method of variance estimates recovery (MOVER) based on the asymptotic confidence interval (ACI) and GCI, Bayesian credible interval, and the highest posterior density (HPD) interval. The coverage probabilities and average lengths of the proposed methods were examined via a simulation study to determine their performance. The results demonstrate that GCI and the MOVER based on the GCI method provided satisfactory performances in almost every case studied. Particulate matter ≤ 2.5 μm (PM2.5) concentration datasets from three areas in northern Thailand were used to illustrate the effectiveness of the proposed methods.

Statistical Inference of Stress-Strength Reliability of Gompertz Distribution under Type II Censoring

This paper develops the problem of estimating stress-strength reliability for Gompertz lifetime distribution. First, the maximum likelihood estimation (MLE) and exact and asymptotic confidence intervals for stress-strength reliability are obtained. Then, Bayes estimators under informative and noninformative prior distributions are obtained by using Lindley approximation, Monte Carlo integration, and MCMC. Bayesian credible intervals are constructed under these prior distributions. Also, simulation studies are used to illustrate these inference methods. Finally, a real dataset is analyzed to show the implementation of the proposed methodologies.

Non-Bayesian and Bayesian estimation of stress-strength reliability from Topp-Leone distribution under progressive first-failure censoring

ABSTRACT In this paper, the Bayesian and non-Bayesian estimation of based on the progressively first-failure censored data is considered. The and are strength and stress random variables and follow the Topp-Leone distributions, respectively. The maximum likelihood and Bayes estimators of are derived. The Bayes estimators under generalized entropy loss function are computed using Lindley’s approximation and Gibbs sampling methods. Different interval estimates like asymptotic, bootstrap confidence, Bayesian credible, and highest posterior density credible intervals of are constructed. Furthermore, a Monte Carlo numerical study is conducted to check the performance of various estimators developed. Finally, an application of algorithm real data is considered for illustrative purposes.

Confidence Intervals for the Ratio of Variances of Delta-Gamma Distributions with Applications

Since rainfall data often contain zero observations, the ratio of the variances of delta-gamma distributions can be used to compare the rainfall dispersion between two rainfall datasets. To this end, we constructed the confidence interval for the ratio of the variances of two delta-gamma distributions by using the fiducial quantity method, Bayesian credible intervals based on the Jeffreys, uniform, or normal-gamma-beta priors, and highest posterior density (HPD) intervals based on the Jeffreys, uniform, or normal-gamma-beta priors. The performances of the proposed confidence interval methods were evaluated in terms of their coverage probabilities and average lengths via Monte Carlo simulation. Our findings show that the HPD intervals based on Jeffreys prior and the normal-gamma-beta prior are both suitable for datasets with a small and large probability of containing zeros, respectively. Rainfall data from Phrae province, Thailand, are used to illustrate the practicability of the proposed methods with real data.

A test of spatial coincidence between CHIME FRBs and IceCube TeV energy neutrinos

We search for a spatial association between the Canadian Hydrogen Mapping Intensity Experiment (CHIME) FRBs and IceCube neutrinos detected in the TeV energy range, by counting the total number of neutrino-FRB pairs with angular separations of <3 degrees, as well as within the observed neutrino error circle. This number constitutes the total signal events, which is then compared to the total background, corresponding to the null hypothesis of no spatial association. The background was obtained from the total neutrino-FRB matches in off-source angular windows with the same solid angle as the signal window. We do not find any statistically significant excess compared to the background. Therefore, we conclude that there is no evidence for an angular correlation between the IceCube neutrinos in the TeV energy range and CHIME FRBs. For each of these searches, we report 90% Bayesian credible interval upper limits on the observed FRB-induced neutrinos.

Shared genetic risk factors and causal association between psoriasis and coronary artery disease

Psoriasis and coronary artery disease (CAD) are related comorbidities that are well established, but whether a genetic basis underlies this is not well studied. We apply trans-disease meta-analysis to 11,024 psoriasis and 60,801 CAD cases, along with their associated controls, identifying one opposing and three shared genetic loci, which are confirmed through colocalization analysis. Combining results from Bayesian credible interval analysis with independent information from genomic, epigenomic, and spatial chromatin organization, we prioritize genes (including IFIH1 and IL23A) that have implications for common molecular mechanisms involved in psoriasis and CAD inflammatory signaling. Chronic systemic inflammation has been associated with CAD and myocardial infarction, and Mendelian randomization analysis finds that CAD as an exposure can have a significant causal effect on psoriasis (OR = 1.11; p = 3×10−6) following adjustment for BMI and waist-hip ratio. Together, these findings suggest that systemic inflammation which causes CAD can increase the risk of psoriasis.

Bayesian accuracy estimates and fit for purpose thresholds of cytology and culture of endometrial swab samples for detecting endometritis in mares

The overall aim of this work was to identify the potential impact of misclassification errors associated with routine screening and diagnostic testing for endometritis in mares. Using Bayesian latent class models (BLCM), specific objectives were to: 1) estimate the diagnostic accuracy of cytology and culture of endometrial swab samples to detect endometritis in mares; 2) assess the impact of different cytology thresholds on test accuracy and misclassification costs; and 3) assess the sensitivity (Se) and specificity (Sp) of a diagnostic strategy including both tests interpreted in series and parallel. Diagnostic and pre-breeding endometrial swab samples collected from 3448 mares based at breeding premises located in the South East of England between 2014 and 2020 were retrospectively analysed. Culture results were classified as positive according to three different case definitions: (A) > 90% of the growth colonies were a monoculture; (B) pathogenic or pathogenic and non-pathogenic bacteria were identified; and (C) any growth was observed. Endometrial smears were graded based on the percent of polymorphonuclear cells (PMN) per high power field (HPF). A hierarchical BLCM was fitted using the cross-tabulated results of the three culture case definitions with a cytology threshold fixed at > 0.5% PMN. Fit for purpose cytology thresholds were proposed using a misclassification cost analysis in the context of good antimicrobial stewardship and for varying endometritis prevalence estimates. Median [95% Bayesian credible intervals (BCI)] cytology Se estimates were 6.5% (2.2–11.6), 6.4% (2.2–10.8) and 6.3% (2.2–10.8) for scenario A, B and C, respectively. Median (95% BCI) cytology Sp estimates were 88.8% (83.1–94.8), 88.9% (83.9–93.8) and 88.8% (84.0–93.8) for scenarios A, B and C, respectively. Median (95% BCI) culture Se estimates were 37.5% (29.9–46.0), 42.3% (33.8–51.1) and 46.4% (35.7–55.9) for scenarios A, B and C, respectively. Median (95% BCI) culture Sp estimates were 92.8% (84.3–99.0), 91.5% (82.5–98.0) and 90.8% (80.1–97.4) for scenarios A, B and C, respectively. Regardless of the culture case definition, Se and Sp of cytology (> 0.5% PMN) was lower than previously reported for swab samples in studies using histology as the reference standard test. The misclassification cost term decreased as the cytology threshold increased for all scenarios and all prevalence contexts, suggesting that, regardless of the endometritis prevalence in the population, increasing the cytology threshold would reduce the misclassification costs associated with false positive mares contributing to good antimicrobial stewardship.

Association of hematologic response and assay sensitivity on the prognostic impact of measurable residual disease in acute myeloid leukemia: a systematic review and meta-analysis.

Measurable residual disease (MRD) is associated with relapse and survival in acute myeloid leukemia (AML). We aimed to quantify the impact of MRD on outcomes across clinical contexts, including its association with hematologic response and MRD assay sensitivity. We performed systematic literature review and meta-analysis of 48 studies that reported the association between MRD and overall survival (OS) or disease-free survival (DFS) in AML and provided information on the MRD threshold used and the hematologic response of the study population. Among studies limited to patients in complete remission (CR), the estimated 5-year OS for the MRD-negative and MRD-positive groups was 67% (95% Bayesian credible interval [CrI], 53-77%) and 31% (95% CrI, 18-44%), respectively. Achievement of an MRD-negative response was associated with superior DFS and OS, regardless of MRD threshold or analytic sensitivity. Among patients in CR, the benefit of MRD negativity was highest in studies using an MRD cutoff less than 0.1%. The beneficial impact of MRD negativity was observed across MRD assays and timing of MRD assessment. In patients with AML in morphological remission, achievement of MRD negativity is associated with superior DFS and OS, irrespective of hematologic response or the MRD threshold used.

Confidence Intervals for Common Coefficient of Variation of Several Birnbaum–Saunders Distributions

The Birnbaum–Saunders (BS) distribution, also known as the fatigue life distribution, is right-skewed and used to model the failure times of industrial components. It has received much attention due to its attractive properties and its relationship to the normal distribution (which is symmetric). Furthermore, the coefficient of variation (CV) is commonly used to analyze variation within a dataset. In some situations, the independent samples are collected from different instruments or laboratories. Consequently, it is of importance to make inference for the common CV. To this end, confidence intervals based on the generalized confidence interval (GCI), method of variance estimates recovery (MOVER), large-sample (LS), Bayesian credible interval (BayCrI), and highest posterior density interval (HPDI) methods are proposed herein to estimate the common CV of several BS distributions. Their performances in terms of their coverage probabilities and average lengths were investigated by using Monte Carlo simulation. The simulation results indicate that the HPDI-based confidence interval outperformed the others in all of the investigated scenarios. Finally, the efficacies of the proposed confidence intervals are illustrated by applying them to real datasets of PM10 (particulate matter ≤ 10 μm) concentrations from three pollution monitoring stations in Chiang Mai, Thailand.

Comparing Dose Levels to Placebo using a Continuous Outcome in a Small n, Sequential, Multiple Assignment, Randomized trial (snSMART)

ABSTRACT Identifying optimal treatments for patients living with rare diseases is challenging due to the small numbers of individuals affected. One design used to address this challenge is known as the small n, sequential, multiple assignment, randomized trial (snSMART). To investigate the efficacy of an active drug measured by a continuous outcome tested at a low and high dose compared to placebo, we propose a new two-stage snSMART design. In stage 1, patients are randomized to an initial treatment. In stage 2, patients are re-randomized, depending on their stage 1 outcome, to either the same or a different dose of treatment. Data from both stages are used to determine the marginal efficacy of the dose levels of active treatment. We propose a Bayesian approach for borrowing information across stage 1 and stage 2 data. We compare the proposed approach to standard methods using only stage 1 data. We observe that the joint stage Bayesian method has smaller root-mean-square-error and 95% Bayesian credible interval widths than standard methods in several tested settings. We conclude that our approach using data from both stages is advantageous for efficacy inference and the proposed snSMART design is useful for the design of registration trials in rare diseases.

Modeling the effect of different drugs and treatment regimen for hookworm on cure and egg reduction rates taking into account diagnostic error.

BackgroundHookworm infections, caused by Ancylostoma duodenale and Necator americanus, are of considerable public health importance. The World Health Organization recommends preventive chemotherapy as the key strategy for morbidity control. Meta-analyses have been conducted to estimate treatment efficacy of available drugs and drug combinations. However, in most studies, the relation between the diagnostic error and infection intensity have not been considered, resulting in an overestimation of cure rates (CRs).MethodologyA Bayesian model was developed to compare the ‘true’ CR and egg reduction rate of different treatment regimens for hookworm infections taking into account the error of the recommended Kato-Katz thick smear diagnostic technique. It was fitted to the observed egg count data which was linked to the distribution of worms, considered the day-to-day variation of hookworm egg excretion and estimated the infection intensity-dependent sensitivity. The CR was obtained by defining the prevalence of infection at follow-up as the probability of having at least one fertilized female worm. The model was applied to individual-level egg count data available from 17 treatments and six clinical trials.Principal findingsTaking the diagnostic error into account resulted in considerably lower CRs than previously reported. Overall, of all treatments analyzed, mebendazole administered in six dosages of 100 mg each was the most efficacious treatment with a CR of 88% (95% Bayesian credible interval: 79-95%). Furthermore, diagnostic sensitivity varied with the infection intensity and sampling effort. For an infection intensity of 50 eggs per gram of stool, the sensitivity is close to 60%; for two Kato-Katz thick smears it increased to approximately 76%.Conclusions/significanceOur model-based estimates provide the true efficacy of different treatment regimens against hookworm infection taking into account the diagnostic error of the Kato-Katz method. Estimates of the diagnostic sensitivity for different number of stool samples and thick smears are obtained. To accurately assess efficacy in clinical trials with the Kato-Katz method, at least two stool samples on consecutive days should be collected.

Narrative Restrictions and Proxies

We compare two approaches to using information about the signs of structural shocks at specific dates within a structural vector autoregression (SVAR): imposing “narrative restrictions” (NR) on the shock signs in an otherwise set-identified SVAR; and casting the information about the shock signs as a discrete-valued “narrative proxy” (NP) to point-identify the impulse responses. The NP is likely to be “weak” given that the sign of the shock is typically known in a small number of periods, in which case the weak-proxy robust confidence intervals in Montiel Olea, Stock, and Watson are the natural approach to conducting inference. However, we show both theoretically and via Monte Carlo simulations that these confidence intervals have distorted coverage—which may be higher or lower than the nominal level—unless the sign of the shock is known in a large number of periods. Regarding the NR approach, we show that the prior-robust Bayesian credible intervals from Giacomini, Kitagawa, and Read deliver coverage exceeding the nominal level, but which converges toward the nominal level as the number of NR increases.

Cause and risk factors of early neonatal death in Ethiopia.

BackgroundGlobally, three fourth of neonatal deaths occur during the early neonatal period, this makes it a critical time to reduce the burden of neonatal death. The survival status of a newborn is determined by the individual (neonatal and maternal), and facility-level factors. Several studies were conducted in Ethiopia to assess early neonatal death; however, most of the studies had limited participants and did not well address the two main determinant factors covered in this study. In response to this gap, this study attempted to examine factors related to early neonatal death based on perinatal death surveillance data in consideration of all the possible determinants of early neonatal death.MethodsThe national perinatal death surveillance data were used for this study. A total of 3814 reviewed perinatal deaths were included in the study. Bayesian multilevel parametric survival analysis was employed to identify factors affecting the survival of newborns during the early neonatal period. Adjusted time ratio (ATR) with 95% Bayesian credible intervals (CrI) was reported and log-likelihood was used for model comparison. Statistical significance was declared based on the non-inclusion of 1.0 in the 95% CrI.ResultMore than half (52.4%) of early neonatal deaths occurred within the first two days of birth. Per the final model, as gestational age increases by a week the risk of dying during the early neonatal period is reduced by 6% [ATR = 0.94,95%CrI:(0.93–0.96)]. There was an increased risk of death during the early neonatal period among neonates deceased due to birth injury as compared to neonates who died due to infection [ATR = 2.05,95%CrI:(1.30–3.32)]; however, perinates who died due to complication of an intrapartum event had a lower risk of death than perinates who died due to infection [ATR = 0.87,95%CrI:(0.83–0.90)]. As the score of delay one and delay three increases by one unit, the newborn’s likelihood of surviving during the early neonatal period is reduced by 4% [ATR = 1.04,95%CrI:(1.01–1.07)] and 21% [ATR = 1.21,95%CrI:(1.15–1.27)] respectively. Neonates born from mothers living in a rural area had a higher risk of dying during the early neonatal period than their counterparts living in an urban area [ATR = 3.53,95%CrI:(3.34–3.69)]. As compared to neonates treated in a primary health facility, being treated in secondary [ATR = 1.14,95%CrI:(1.02–1.27)] and tertiary level of care [ATR = 1.15,95%CrI:(1.04–1.25)] results in a higher risk of death during the early neonatal period.ConclusionThe survival of a newborn during the early neonatal period is determined by both individual (gestational age, cause of death, and delay one) and facility (residence, type of health facility and delay three) level factors. Thus, to have a positive early neonatal outcome, a tailored intervention is needed for the three major causes of death (i.e Infection, birth injury, and complications of the intrapartum period). Furthermore, promoting maternal health, improving the health-seeking behaviour of mothers, strengthening facility readiness, and narrowing down inequalities in service provision are recommended to improve the newborn’s outcomes during the early neonatal period.

Bayesian estimation of rainfall dispersion in Thailand using gamma distribution with excess zeros.

The gamma distribution is commonly used to model environmental data. However, rainfall data often contain zero observations, which violates the assumption that all observations must be positive in a gamma distribution, and so a gamma model with excess zeros treated as a binary random variable is required. Rainfall dispersion is important and interesting, the confidence intervals for the variance of a gamma distribution with excess zeros help to examine rainfall intensity, which may be high or low risk. Herein, we propose confidence intervals for the variance of a gamma distribution with excess zeros by using fiducial quantities and parametric bootstrapping, as well as Bayesian credible intervals and highest posterior density intervals based on the Jeffreys’, uniform, or normal-gamma-beta prior. The performances of the proposed confidence interval were evaluated by establishing their coverage probabilities and average lengths via Monte Carlo simulations. The fiducial quantity confidence interval performed the best for a small probability of the sample containing zero observations (δ) whereas the Bayesian credible interval based on the normal-gamma-beta prior performed the best for large δ. Rainfall data from the Kiew Lom Dam in Lampang province, Thailand, are used to illustrate the efficacies of the proposed methods in practice.

Community-level prevalence of epilepsy and of neurocysticercosis among people with epilepsy in the Balaka district of Malawi: A cross-sectional study.

BackgroundEpilepsy and neurocysticercosis (NCC) prevalence estimates in sub-Saharan Africa are still scarce but show important variation due to the population studied and different screening and diagnosis strategies used. The aims of this study were to estimate the prevalence of epileptic seizures and epilepsy in the sampled population, and the proportion of NCC among people with epilepsy (PWE) in a large cross-sectional study in a rural district of southern Malawi.MethodsWe conducted a community-based door-to-door screening study for epileptic seizures in Balaka, Malawi between October and December 2012. Past epileptic seizures were reported through a 15-item questionnaire answered by at least one person per household generating five major criteria. People who screened positive were further examined by a neurologist to establish diagnosis. Patients diagnosed with epilepsy were examined and offered Taenia solium cyst antigen and antibody serological tests, and a CT scan for the diagnosis of NCC.ResultsIn total, screening information on 69,595 individuals was obtained for lifetime occurrence of epileptic seizures. 3,100 (4.5%) participants screened positive, of whom 1,913 (62%) could be followed-up and underwent further assessment. Lifetime prevalence was 3.0% (95% Bayesian credible interval [CI] 2.8 to 3.1%) and 1.2% (95%BCI 0.9 to 1.6%) for epileptic seizures and epilepsy, respectively. NCC prevalence among PWE was estimated to be 4.4% (95%BCI 0.8 to 8.5%). A diagnosis of epilepsy was ultimately reached for 455 participants.ConclusionThe results of this large community-based study contribute to the evaluation and understanding of the burden of epilepsy in the population and of NCC among PWE in sub-Saharan Africa.

Accommodating a Latent XM Interaction in Statistical Mediation Analysis

Statistical mediation analysis is used in the social sciences and public health to uncover potential mechanisms, known as mediators, by which a treatment led to a change in an outcome. Recently, the estimation of the treatment-by-mediator interaction (i.e., the XM interaction) has been shown to play a pivotal role in understanding the equivalence between the traditional mediation effects in linear models and the causal mediation effects in the potential outcomes framework. However, there is limited guidance on how to estimate the XM interaction when the mediator is latent. In this article, we discuss eight methods to accommodate latent XM interactions in statistical mediation analysis, which fall in two categories: using structural models (e.g., latent moderated structural equations, Bayesian mediation, unconstrained product indicator method, multiple-group models) or scoring the mediator prior to estimating the XM interaction (e.g., summed scores and factor scores, with and without attenuation correction). Simulation results suggest that finite-sample bias is low, type 1 error rates and coverage of percentile bootstrap confidence intervals and Bayesian credible intervals are close to the nominal values, and statistical power is similar across approaches. The methods are demonstrated with an applied example, syntax is provided for their implementation, and general considerations are discussed.

Bayesian Simultaneous Credible Intervals for Effect Measures from Multiple Markers

Inference from multiple markers is often encountered in biomedical research, especially when comparing treatments. Most common statistical methods rely on hypothesis testing with null hypothesis of no effect for each marker and methods based on closed testing for getting the combined p-value. This article proposes the use of simultaneous credible intervals obtained from the joint posterior distribution of effect measures of multiple markers for combined inference. The advantage of this method is that it finds the actual effect sizes and also allows different types of effect measures for various markers. We used equal tailed intervals and highest posterior density regions for effect measures of multiple markers. Simulation studies were carried out to examine frequentist properties of these simultaneous credible regions. These studies revealed that the inference based on simultaneous intervals can be different than the inference based on individual marker. The method is demonstrated through two case studies: (a) an observational study of wet age-related macular degeneration (wet-AMD); and (b) reanalysis of a randomized controlled trial for treatment of migraine. The wet-AMD observational study was the motivation for the present research.