Bayesian Credible Interval Research Articles

Effectiveness of a community-based educational programme in reducing the cumulative incidence and prevalence of human Taenia solium cysticercosis in Burkina Faso in 2011–14 (EFECAB): a cluster-randomised controlled trial

SummaryBackgroundThe effectiveness of drug-free interventions in controlling human cysticercosis is not well known. We aimed to estimate the effectiveness of a community-based educational intervention in reducing the frequency of human cysticercosis in Burkina Faso.MethodsWe did a cluster-randomised controlled trial between 2011 and 2014. 60 eligible villages from three provinces (Boulkiemdé, Sanguié, and Nayala) were randomly allocated to the intervention or control group. Villages raising pigs, that were not a regional capital or located on a main road, that were more than 20 km from Ouagadougou or 5 km from one another, were eligible. In each village, 60 participants were asked for blood samples at baseline, 18 months later (before randomisation), and 18 months after randomisation. Villages were block randomised (1:1) by pig-raising department immediately after the pre-randomisation visit. The intervention aimed to improve knowledge of Taenia solium transmission and control through screening and structured discussion of a 52-min movie, and to increase community self-efficacy through a Self-esteem, Associative strengths, Resourcefulness, Action planning, Responsibility (SARAR) approach via the Participatory Hygiene and Sanitation Transformation (PHAST) model. The primary outcome was active cysticercosis, defined as the presence of circulating antigens detected by use of B158/B60 ELISA. Effectiveness measured at the village level was estimated by use of three Bayesian hierarchical models. This study is registered with ClinicalTrials.gov, number NCT0309339.FindingsTwo villages in the same randomisation block were excluded, resulting in a final sample size of 58 villages. Overall, the intervention tended towards a decrease in the cumulative incidence of active cysticercosis from baseline to after randomisation (adjusted cumulative incidence ratio 0·65, 95% Bayesian credible interval [95% CrI] 0·39–1·05) and a decrease in active cysticercosis prevalence from baseline to after randomisation (adjusted prevalence proportion ratio 0·84; 95% CrI 0·59–1·18). The intervention was shown to be effective in Nayala and Sanguié but not in Boulkiemdé.InterpretationCommunity-engaged participatory interventions can be effective at reducing the incidence and prevalence of cysticercosis in some low-resource settings.FundingUS National Institutes of Health (National Institute of Neurological Disorders and Stroke, Fogarty International Center, and National Institute of General Medical Sciences).

Latent class analysis to evaluate performance of point-of-care CCA for low-intensity Schistosoma mansoni infections in Burundi

BackgroundKato-Katz examination of stool smears is the field-standard method for detecting Schistosoma mansoni infection. However, Kato-Katz misses many active infections, especially of light intensity. Point-of-care circulating cathodic antigen (CCA) is an alternative field diagnostic that is more sensitive than Kato-Katz when intensity is low, but interpretation of CCA-trace results is unclear. To evaluate trace results, we tested urine and stool specimens from 398 pupils from eight schools in Burundi using four approaches: two in Burundi and two in a laboratory in Leiden, the Netherlands. In Burundi, we used Kato-Katz and point-of-care CCA (CCAB). In Leiden, we repeated the CCA (CCAL) and also used Up-Converting Phosphor Circulating Anodic Antigen (CAA).MethodsWe applied Bayesian latent class analyses (LCA), first considering CCA traces as negative and then as positive. We used the LCA output to estimate validity of the prevalence estimates of each test in comparison to the population-level infection prevalence and estimated the proportion of trace results that were likely true positives.ResultsKato-Katz yielded the lowest prevalence (6.8%), and CCAB with trace considered positive yielded the highest (53.5%). There were many more trace results recorded by CCA in Burundi (32.4%) than in Leiden (2.3%). Estimated prevalence with CAA was 46.5%. LCA indicated that Kato-Katz had the lowest sensitivity: 15.9% [Bayesian Credible Interval (BCI): 9.2–23.5%] with CCA-trace considered negative and 15.0% with trace as positive (BCI: 9.6–21.4%), implying that Kato-Katz missed approximately 85% of infections. CCAB underestimated disease prevalence when trace was considered negative and overestimated disease prevalence when trace was considered positive, by approximately 12 percentage points each way, and CAA overestimated prevalence in both models. Our results suggest that approximately 52.2% (BCI: 37.8–5.8%) of the CCAB trace readings were true infections.ConclusionsWhether measured in the laboratory or the field, CCA outperformed Kato-Katz at the low infection intensities in Burundi. CCA with trace as negative likely missed many infections, whereas CCA with trace as positive overestimated prevalence. In the absence of a field-friendly gold standard diagnostic, the use of a variety of diagnostics with differing properties will become increasingly important as programs move towards elimination of schistosomiasis. It is clear that CCA is a valuable tool for the detection and mapping of S. mansoni infection in the field and CAA may be a valuable field tool in the future.

Spatial analysis of macro-level bicycle crashes using the class of conditional autoregressive models

The objective of this study was to investigate the relationship between bicycle crash frequency and their contributing factors at the census block group level in Florida, USA. Crashes aggregated over the census block groups tend to be clustered (i.e., spatially dependent) rather than randomly distributed. To account for the effect of spatial dependence across the census block groups, the class of conditional autoregressive (CAR) models were employed within the hierarchical Bayesian framework. Based on four years (2011-2014) of crash data, total and fatal-and-severe injury bicycle crash frequencies were modeled as a function of a large number of variables representing demographic and socio-economic characteristics, roadway infrastructure and traffic characteristics, and bicycle activity characteristics. This study explored and compared the performance of two CAR models, namely the Besag’s model and the Leroux’s model, in crash prediction. The Besag’s models, which differ from the Leroux’s models by the structure of how spatial autocorrelation are specified in the models, were found to fit the data better. A 95% Bayesian credible interval was selected to identify the variables that had credible impact on bicycle crashes. A total of 21 variables were found to be credible in the total crash model, while 18 variables were found to be credible in the fatal-and-severe injury crash model. Population, daily vehicle miles traveled, age cohorts, household automobile ownership, density of urban roads by functional class, bicycle trip miles, and bicycle trip intensity had positive effects in both the total and fatal-and-severe crash models. Educational attainment variables, truck percentage, and density of rural roads by functional class were found to be negatively associated with both total and fatal-and-severe bicycle crash frequencies.

Counting bears in the Iranian Caucasus: Remarkable mismatch between scientifically-sound population estimates and perceptions

Lack of reliable information on the status of species often leads managers to exclusively rely on experiential knowledge, opinions or perceptions, usually derived from personnel associated with natural resource management agencies. Yet, the accuracy of these sources of information remains largely untested. We approached this challenge, which is particularly common for wildlife monitoring programs in developing countries, using a population of Asian brown bears (Ursus arctos) in the Iranian Caucasus as case study. We conducted a noninvasive, genetic, spatial capture-recapture (SCR) study to estimate bear density across a core protected area, Arasbaran Biosphere Reserve, and compared our estimate of bear abundance with rangers' perceptions as collated through interviews. The perceived abundance of bears by local rangers was between 3 and 5 times higher than our SCR estimate of 40 bears (2.5–97.5% Bayesian Credible Intervals = 27–70; density: 4.88 bears/100 km2). Our results suggest that basing management of the local bear population on perceptions of population status may result in overestimating the likelihood of population persistence. Our findings offer a scientific baseline for an evidence-based conservation policy for brown bears in Iran, and the broader Caucasus Ecoregion. The majority of threatened terrestrial megafauna occur in developing countries, where collecting and analyzing demographic data remain challenging. Delayed conservation responses due to the lack of, or erroneous knowledge of population status of such imperiled species may have serious consequences.

Direct Testing for Allele-Specific Expression Differences Between Conditions.

Allelic imbalance (AI) indicates the presence of functional variation in cis regulatory regions. Detecting cis regulatory differences using AI is widespread, yet there is no formal statistical methodology that tests whether AI differs between conditions. Here, we present a novel model and formally test differences in AI across conditions using Bayesian credible intervals. The approach tests AI by environment (G×E) interactions, and can be used to test AI between environments, genotypes, sex, and any other condition. We incorporate bias into the modeling process. Bias is allowed to vary between conditions, making the formulation of the model general. As gene expression affects power for detection of AI, and, as expression may vary between conditions, the model explicitly takes coverage into account. The proposed model has low type I and II error under several scenarios, and is robust to large differences in coverage between conditions. We reanalyze RNA-seq data from a Drosophila melanogaster population panel, with F1 genotypes, to compare levels of AI between mated and virgin female flies, and we show that AI × genotype interactions can also be tested. To demonstrate the use of the model to test genetic differences and interactions, a formal test between two F1s was performed, showing the expected 20% difference in AI. The proposed model allows a formal test of G×E and G×G, and reaffirms a previous finding that cis regulation is robust between environments.

Antiemetic Prophylaxis as a Marker of Health Care Disparities in the National Anesthesia Clinical Outcomes Registry.

US health care disparities persist despite repeated countermeasures. Research identified race, ethnicity, gender, and socioeconomic status as factors, mediated through individual provider and/or systemic biases; little research exists in anesthesiology. We investigated antiemetic prophylaxis as a surrogate marker for anesthesia quality by individual providers because antiemetics are universally available, indicated contingent on patient characteristics (gender, age, etc), but independent of comorbidities and not yet impacted by regulatory or financial constraints. We hypothesized that socioeconomic indicators (measured as insurance status or median income in the patients' home zip code area) are associated with the utilization of antiemetic prophylaxis (as a marker of anesthesia quality). We tested our hypothesis in several subsets of electronic anesthesia records from the National Anesthesia Clinical Outcomes Registry (NACOR), fitting frequentist and novel Bayesian multilevel logistic regression models. NACOR contained 12 million cases in 2013. Six institutions reported on antiemetic prophylaxis for 441,645 anesthesia cases. Only 173,133 cases included details on insurance information. Even fewer (n = 92,683) contained complete data on procedure codes and provider identifiers. Bivariate analysis, multivariable logistic regression, and our Bayesian hierarchical model all showed a large and statistically significant association between socioeconomic markers and antiemetic prophylaxis (ondansetron and dexamethasone). For Medicaid versus commercially insured patients, the odds ratio of receiving the antiemetic ondansetron is 0.85 in our Bayesian hierarchical mixed regression model, with a 95% Bayesian credible interval of 0.81-0.89 with similar inferences in classical (frequentist) regression models. Our analyses of NACOR anesthesia records raise concerns that patients with lower socioeconomic status may receive inferior anesthesia care provided by individual anesthesiologists, as indicated by less antiemetics administered. Effects persisted after we controlled for important patient characteristics and for procedure and provider influences. Findings were robust to sensitivity analyses. Our results challenge the notion that anesthesia providers do not contribute to health care disparities.

Relationship between antimicrobial-resistance programs and antibiotic dispensing for upper respiratory tract infection: An analysis of Australian data between 2004 and 2015.

ObjectiveNPS MedicineWise aims to ensure that medicines are prescribed and used in a manner consistent with current evidence-based best practice. A series of nationwide educational and advertising interventions for general practitioners and consumers were implemented in Australia between 2009 and 2015 with the aim of reducing antibiotic prescriptions for upper respiratory tract infections (URTIs). The work described in this paper quantifies the change in antibiotic dispensing following these interventions.MethodsAntibiotic dispensing data between 2004 and 2015 were obtained from a national claims database. A Bayesian structural time series model was used to forecast a series of antibiotic dispensing volumes expected to have occurred if the interventions had not taken place. These were compared with the volumes that were actually observed to estimate the intervention effect.ResultsOn average, 126,536 fewer antibiotics were dispensed each month since the intervention programs began in 2009 (95% Bayesian credible interval = 71,580–181,490). This change represents a 14% total reduction in dispensed scripts after the series of intervention programs began in 2009.ConclusionsContinual educational intervention programs that emphasise the judicious use of antibiotics may effectively reduce inappropriate prescribing of antibiotics for the treatment of URTIs at a national level.

Demography of a stable population of Crab Plovers wintering in Oman

The monotypic Crab Plover Dromas ardeola winters around the shores of the Indian Ocean and breeds in colonies on islands around the Arabian Peninsula. The IUCN lists the world population of Crab Plovers as stable, but long-term survey data or demographic estimates regarding the species status are lacking. Here, we use survey and demographic data collected from 2011 to 2015 to study the status of the population of Crab Plover at their most important wintering area: the Barr Al Hikman Peninsula in the Sultanate of Oman. Our survey data showed that the population of Crab Plovers initially increased and then stabilized. The overall observed finite rate of population change ( $$\bar{\lambda }_{\text{obs}}$$ ) was estimated at 1.004 (0.995–1.013 95% Bayesian credible interval [BCI]), indicating a stable population (7000–9000 birds), that is possibly at carrying capacity. Based on mark-recapture data, the mean annual apparent survival probability of Crab Plovers was estimated to be 0.90 (0.85–0.94 95% BCI). We used counts of adults and yearlings to estimate the mean annual fecundity rate at 0.06 young per pair. Using these demographic values, the overall mean expected finite rate of population change ( $$\bar{\lambda }_{ \exp }$$ ) was estimated to be 0.949 (0.899–0.996 95% BCI), so there is a low chance that $$\bar{\lambda }_{\text{obs}}$$ and $$\bar{\lambda }_{ \exp }$$ overlap. $$\bar{\lambda }_{\text{obs}}$$ and $$\bar{\lambda }_{ \exp }$$ would completely match if about 450 Crab Plovers immigrate to Barr Al Hikman each year. Regional surveys show that yearling densities are higher closer to the breeding areas, so immigrants could be birds that during their first winter stayed close to their natal area. Our study support the IUCN listing of Crab Plover as stable, but further population-wide monitoring is required. From a conservation point of view it is important to continue monitoring because Crab Plovers breed and winter in a region that is rapidly developing.

A Pragmatic Approach to Statistical Testing and Estimation (PASTE)

The p-value has dominated research in education and related fields and a statistically non-significant p-value is quite commonly interpreted as ‘confirming’ the null hypothesis (H0) of ‘equivalence’. This is unfortunate, because p-values are not fit for that purpose. This paper discusses three alternatives to the traditional p-value that unfortunately have remained underused but can provide evidence in favor of ‘equivalence’ relative to ‘non-equivalence’: two one-sided tests (TOST) equivalence testing, Bayesian hypothesis testing, and information criteria. TOST equivalence testing and p-values both rely on concepts of statistical significance testing and can both be done with confidence intervals, but treat H0 and the alternative hypothesis (H1) differently. Bayesian hypothesis testing and the Bayesian credible interval aka posterior interval provide Bayesian alternatives to traditional p-values, TOST equivalence testing, and confidence intervals. However, under conditions outlined in this paper, confidence intervals and posterior intervals may yield very similar interval estimates. Moreover, Bayesian hypothesis testing and information criteria provide fairly easy to use alternatives to statistical significance testing when multiple competing models can be compared. Based on these considerations, this paper outlines a pragmatic approach to statistical testing and estimation (PASTE) for research in education and related fields. In a nutshell, PASTE states that all of the alternatives to p-values discussed in this paper are better than p-values, that confidence intervals and posterior intervals may both provide useful interval estimates, and that Bayesian hypothesis testing and information criteria should be used when the comparison of multiple models is concerned.

Bayesian Approach to the Estimation of a Poisson Mean with Application to NBA Three Point Attempts

Bayesian Credible Intervals are proposed for a Poisson mean. These intervals are compared to five classical confidence intervals found in the literature. A simulation study is performed to compare the procedures using two different criteria and it is attempted to determine which of the procedures performs best for various values of the parameter and sample size. Estimation of the number of three-point shot attempts and three-point shot makes by the San Antonio Spurs is given as an example.

A matching prior for the product of normal means based on the modified profile likelihood

ABSTRACTIn this paper, we develop a matching prior for the product of means in several normal distributions with unrestricted means and unknown variances. For this problem, properly assigning priors for the product of normal means has been issued because of the presence of nuisance parameters. Matching priors, which are priors matching the posterior probabilities of certain regions with their frequentist coverage probabilities, are commonly used but difficult to derive in this problem. We developed the first order probability matching priors for this problem; however, the developed matching priors are unproper. Thus, we apply an alternative method and derive a matching prior based on a modification of the profile likelihood. Simulation studies show that the derived matching prior performs better than the uniform prior and Jeffreys’ prior in meeting the target coverage probabilities, and meets well the target coverage probabilities even for the small sample sizes. In addition, to evaluate the validity of the proposed matching prior, Bayesian credible interval for the product of normal means using the matching prior is compared to Bayesian credible intervals using the uniform prior and Jeffrey’s prior, and the confidence interval using the method of Yfantis and Flatman.

Malaria prevalence metrics in low- and middle-income countries: an assessment of precision in nationally-representative surveys

BackgroundOne pillar to monitoring progress towards the Sustainable Development Goals is the investment in high quality data to strengthen the scientific basis for decision-making. At present, nationally-representative surveys are the main source of data for establishing a scientific evidence base, monitoring, and evaluation of health metrics. However, little is known about the optimal precisions of various population-level health and development indicators that remains unquantified in nationally-representative household surveys. Here, a retrospective analysis of the precision of prevalence from these surveys was conducted.MethodsUsing malaria indicators, data were assembled in nine sub-Saharan African countries with at least two nationally-representative surveys. A Bayesian statistical model was used to estimate between- and within-cluster variability for fever and malaria prevalence, and insecticide-treated bed nets (ITNs) use in children under the age of 5 years. The intra-class correlation coefficient was estimated along with the optimal sample size for each indicator with associated uncertainty.FindingsResults suggest that the estimated sample sizes for the current nationally-representative surveys increases with declining malaria prevalence. Comparison between the actual sample size and the modelled estimate showed a requirement to increase the sample size for parasite prevalence by up to 77.7% (95% Bayesian credible intervals 74.7–79.4) for the 2015 Kenya MIS (estimated sample size of children 0–4 years 7218 [7099–7288]), and 54.1% [50.1–56.5] for the 2014–2015 Rwanda DHS (12,220 [11,950–12,410]).ConclusionThis study highlights the importance of defining indicator-relevant sample sizes to achieve the required precision in the current national surveys. While expanding the current surveys would need additional investment, the study highlights the need for improved approaches to cost effective sampling.

Maternal depression symptoms are highly prevalent among food-insecure households in Ethiopia.

We aimed to evaluate the association between household food insecurity and maternal depression in Ethiopia. Design/Setting/Subjects In 2014, we conducted a cross-sectional study in southern Ethiopia, including 591 food-secure and 2500 food-insecure households. We measured depression status of women using the Patient Health Questionnaire-9 validated for Ethiopia, with a cut-off of ≥5. We evaluated household-level food insecurity using a validated Household Food Insecurity Access Scale. We applied Bayesian modelling to evaluate the relationship between food insecurity and maternal depression accounting for other observed characteristics. Among the analytic sample, 80·8 (95 % CI 79·4, 82·2) % of women were living in food-insecure households. The overall prevalence of probable depression (mild and moderate forms) was 4·7 (95 % CI 4·1, 5·6) %. All individual depressive symptoms had a significantly higher prevalence in the food-insecure group, except for suicidal ideation (but small numbers; P<0·001). In the Bayesian model adjusting for paternal characteristics, there was a significant dose-response linear relationship (trend) between household food insecurity and maternal depression (P<0·01). The adjusted OR (95 % Bayesian credible interval) for depression for differing levels of food insecurity were: mild food insecurity, 3·29 (1·63, 6·18); moderate, 3·82 (1·91, 7·45); severe, 12·50 (3·38, 32·70). The study documented a high burden of depression among women who lived in food-insecure households. Given this finding, we recommend integrating mental health in the livelihood programmes in areas suffering from food insecurity.

Bayesian Credible Intervals for Maize Grain Yields of the Maintenance Varieties Evaluated in Sudan

Improved of maintenance crop varieties developed at agricultural research corporation, Wad median, Sudan is intended for seed foundation which is recently established. This study was undertaken to establish statistical investigation using Bayesian estimation for credible interval or posterior interval as a Bayesian strategy for a maintenance variety. Data on grain yield (kg/ha) on a maize crop variety were used. Bayesian posterior information can be annoying to investigate but are important in maintenance varieties that foundational claims are used to make general recommendations for practice. Half normal informative priors set were used. The heritability of yield (varieties)) was (h = 0.75). Predicted posterior means of varieties were shown with a Bayesian interval for scientific inference in the maintenance maize grain yield. Bayesian approach is useful for reducing uncertainty on decisions based on economic evaluation of new maize varieties in Sudan, the use of credible intervals for grain yield allow for early decisions.Int. J. Appl. Sci. Biotechnol. Vol 5(3): 390-396

Bayesian analysis of head and neck cancer data using generalized inverse Lindley stress–strength reliability model

ABSTRACTIn this article, we present the analysis of head and neck cancer data using generalized inverse Lindley stress–strength reliability model. We propose Bayes estimators for estimating P(X > Y), when X and Y represent survival times of two groups of cancer patients observed under different therapies. The X and Y are assumed to be independent generalized inverse Lindley random variables with common shape parameter. Bayes estimators are obtained under the considerations of symmetric and asymmetric loss functions assuming independent gamma priors. Since posterior becomes complex and does not possess closed form expressions for Bayes estimators, Lindley’s approximation and Markov Chain Monte Carlo techniques are utilized for Bayesian computation. An extensive simulation experiment is carried out to compare the performances of Bayes estimators with the maximum likelihood estimators on the basis of simulated risks. Asymptotic, bootstrap, and Bayesian credible intervals are also computed for the P(X > Y).

Direct STR typing from bullet casings

It is not uncommon for cartridges, bullets, and casings (CBCs) to be left at a crime scene involving shootings. During loading of guns, the handler touches the CBCs and hence they can be a valuable source of touch DNA. Previous studies on development of STR profiles from CBCs resulted in very low success rates. Direct PCR has shown increased success rates with low-level DNA but has not been applied to STR typing from casings. Here, we quantified the effect of firing on DNA quantity and also evaluated direct PCR as an alternative method to STR typing from bullet casings. Buffy coat was deposited on 9mm bullets and DNA was extracted from the casings of fired and unfired bullets (N=30 each). Firing the bullets decreased the amount of DNA recovered by around 30%. For comparison of STR typing protocols, ten volunteers touched three ammunition types (9mm, 5.56mm, and 7.62mm; N=60 bullets). Casings were swabbed with EO swab moistened with PBS. Total DNA obtained from fired casings were 207±523pg. In terms of the number of alleles typed, the direct PCR protocol did not differ statistically from the conventional extraction-STR typing protocol (95% Bayesian credible intervals of 3.0–7.8 and 3.9–10.3 alleles, respectively). This study showed that direct PCR can be used as an alternative method for STR typing from bullet casings. As the direct PCR protocol is quicker and cheaper than the conventional protocol, forensic DNA laboratories may benefit from using direct PCR for bullet casings.

Increases in the Number of American Black Ducks Wintering in Nova Scotia, 1970–2015

AbstractDespite extensive conservation and management efforts, American black duck (Anas rubripes) populations remain below desired population levels. Researchers have noted declines at a number of wintering areas, but indications are that wintering populations in the northern part of the range are increasing. Intermittently between 1970 and 1989, and annually since 1992, wildlife biologists have flown aerial surveys of the entire coast of Nova Scotia, Canada, to count wintering waterfowl. This survey counted the total number of ducks seen in predefined lengths of coastline. We analyzed those survey data using generalized linear mixed models, over the entire time period (1970–2015) and in the recent time period (1992–2015, when surveys were done every year), across five general regions of Nova Scotia. We fit models using Bayesian methods with uninformative priors; models with negative binomial response distributions performed well. Due to the large variation in mean numbers of black ducks across the predefined lengths of coastline, we treated these blocks of coastline as a fixed effect, while annual trend (slope) was modeled as a random effect to account for variation in annual trend across blocks of coastline. Results were similar between the entire time series (1970–2015) or the most recent and more complete time series (1992–2015). In general, numbers of wintering black ducks in Nova Scotia increased (1.0–16.0%/y) and increases were significant (Bayesian credible intervals did not bound 0) in four of five regions. Increasing numbers in Nova Scotia are consistent with other observations of increasing wintering numbers at the northern range of American black ducks and may indicate a shift in the wintering range that has been ongoing for decades. Future habitat management actions will benefit from consideration of regional trends and the distributional change of black duck.

Effectiveness of online tailored advice to prevent running-related injuries and promote preventive behaviour in Dutch trail runners: a pragmatic randomised controlled trial

BackgroundTrail running is popular worldwide, but there is no preventive intervention for running-related injury (RRI).AimTo evaluate the effectiveness of adding online tailored advice (TrailS6) to general advice on (1) the...

Statistical inferences with jointly type-II censored samples from two Pareto distributions

Abstract In the several fields of industries the product comes from more than one production line, which is required to work the comparative life tests. This problem requires sampling of the different production lines, then the joint censoring scheme is appeared. In this article we consider the life time Pareto distribution with jointly type-II censoring scheme. The maximum likelihood estimators (MLE) and the corresponding approximate confidence intervals as well as the bootstrap confidence intervals of the model parameters are obtained. Also Bayesian point and credible intervals of the model parameters are presented. The life time data set is analyzed for illustrative purposes. Monte Carlo results from simulation studies are presented to assess the performance of our proposed method.

State of the art: duration of dual antiplatelet therapy after percutaneous coronary intervention and coronary stent implantation - past, present and future perspectives.

Evidence from studies published more than 10 years ago suggested that patients receiving first-generation drug-eluting stents (DES) needed dual antiplatelet therapy (DAPT) for at least 12 months. Current evidence from randomised controlled trials (RCT) reported within the past five years suggests that patients with stable ischaemic heart disease who receive newer-generation DES need DAPT for a minimum of three to six months. Patients who undergo stenting for an acute coronary syndrome benefit from DAPT for at least 12 months, but a Bayesian network meta-analysis confirms that extending DAPT beyond 12 months confers a trade-off between reduced ischaemic events and increased bleeding. However, the network meta-analysis finds no credible increase in all-cause mortality if DAPT is lengthened from three to six months to 12 months (posterior median odds ratio [OR] 0.98; 95% Bayesian credible interval [BCI]: 0.73-1.43), from 12 months to 18-48 months (OR 0.87; 95% BCI: 0.64-1.17), or from three to six months to 18-48 months (OR 0.86; 95% BCI: 0.63-1.21). Future investigation should focus on identifying scoring systems that have excellent discrimination and calibration. Although predictive models should be incorporated into systems of care, most decisions about DAPT duration will be based on clinical judgement and patient preference.