Contagious statistical distributions: k-connections and applications in infectious disease environments.

Contagious statistical distributions are a valuable resource for managing contagion by means of k-connected chains of distributions. Binomial, hypergeometric, Pólya, uniform distributions with the same values for all parameters except sample size n are known to be strongly associated. This paper describes how the relationship can be obtained via factorial moments, simplifying the process by including novel elements. We describe the properties of these distributions and provide examples of their real-world application, and then define a chain of k-connected distributions, which generalises the relationship among samples of any size for a given population and the Pólya urn model.

Bayesian Meta-Analysis for Binary Data and Prior Distribution on Models.

In meta-analysis, the structure of the between-sample heterogeneity plays a crucial role in estimating the meta-parameter. A Bayesian meta-analysis for binary data has recently been proposed that measures this heterogeneity by clustering the samples and then determining the posterior probability of the cluster models through model selection. The meta-parameter is then estimated using Bayesian model averaging techniques. Although an objective Bayesian meta-analysis is proposed for each type of heterogeneity, we concentrate the attention of this paper on priors over the models. We consider four alternative priors which are motivated by reasonable but different assumptions. A frequentist validation with simulated data has been carried out to analyze the properties of each prior distribution for a set of different number of studies and sample sizes. The results show the importance of choosing an adequate model prior as the posterior probabilities for the models are very sensitive to it. The hierarchical Poisson prior and the hierarchical uniform prior show a good performance when the real model is the homogeneity, or when the sample sizes are high enough. However, the uniform prior can detect the true model when it is an intermediate model (neither homogeneity nor heterogeneity) even for small sample sizes and few studies. An illustrative example with real data is also given, showing the sensitivity of the estimation of the meta-parameter to the model prior.

Cost-effectiveness of positive airway pressure modalities in obesity hypoventilation syndrome with severe obstructive sleep apnoea.

BACKGROUND: Obesity hypoventilation syndrome (OHS) is treated with either non-invasive ventilation (NIV) or CPAP, but there are no long-term cost-effectiveness studies comparing the two treatment modalities. OBJECTIVES: We performed a large, multicentre, randomised, open-label controlled study to determine the comparative long-term cost and effectiveness of NIV versus CPAP in patients with OHS with severe obstructive sleep apnoea (OSA) using hospitalisation days as the primary outcome measure. METHODS: Hospital resource utilisation and within trial costs were evaluated against the difference in effectiveness based on the primary outcome (hospitalisation days/year, transformed and non-transformed in monetary term). Costs and effectiveness were estimated from a log-normal distribution using a Bayesian approach. A secondary analysis by adherence subgroups was performed. RESULTS: In total, 363 patients were selected, 215 were randomised and 202 were available for the analysis. The median (IQR) follow-up was 3.01 (2.91-3.14) years for NIV group and 3.00 (2.92-3.17) years for CPAP. The mean (SD) Bayesian estimated hospital days was 2.13 (0.73) for CPAP and 1.89 (0.78) for NIV. The mean (SD) Bayesian estimated cost per patient/year in the NIV arm, excluding hospitalisation costs, was €2075.98 (91.6), which was higher than the cost in the CPAP arm of €1219.06 (52.3); mean difference €857.6 (105.5). CPAP was more cost-effective than NIV (99.5% probability) because longer hospital stay in the CPAP arm was compensated for by its lower costs. Similar findings were observed in the high and low adherence subgroups. CONCLUSION: CPAP is more cost-effective than NIV; therefore, CPAP should be the preferred treatment for patients with OHS with severe OSA. TRIAL REGISTRATION NUMBER: NCT01405976.

Echocardiographic Changes with Positive Airway Pressure Therapy in Obesity Hypoventilation Syndrome. Long-Term Pickwick Randomized Controlled Clinical Trial.

Rationale: Obesity hypoventilation syndrome (OHS) has been associated with cardiac dysfunction. However, randomized trials assessing the impact of long-term noninvasive ventilation (NIV) or continuous positive airway pressure (CPAP) on cardiac structure and function assessed by echocardiography are lacking.Objectives: In a prespecified secondary analysis of the largest multicenter randomized controlled trial of OHS (Pickwick Project; N = 221 patients with OHS and coexistent severe obstructive sleep apnea), we compared the effectiveness of three years of NIV and CPAP on structural and functional echocardiographic changes.Methods: At baseline and annually during three sequential years, patients underwent transthoracic two-dimensional and Doppler echocardiography. Echocardiographers at each site were blinded to the treatment allocation. Statistical analysis was performed using a linear mixed-effects model with a treatment group and repeated measures interaction to determine the differential effect between CPAP and NIV.Measurements and Main Results: A total of 196 patients were analyzed: 102 were treated with CPAP and 94 were treated with NIV. Systolic pulmonary artery pressure decreased from 40.5 ± 1.47 mm Hg at baseline to 35.3 ± 1.33 mm Hg at three years with CPAP, and from 41.5 ± 1.56 mm Hg to 35.5 ± 1.42 with NIV (P < 0.0001 for longitudinal intragroup changes for both treatment arms). However, there were no significant differences between groups. NIV and CPAP therapies similarly improved left ventricular diastolic dysfunction and reduced left atrial diameter. Both NIV and CPAP improved respiratory function and dyspnea.Conclusions: In patients with OHS who have concomitant severe obstructive sleep apnea, long-term treatment with NIV and CPAP led to similar degrees of improvement in pulmonary hypertension and left ventricular diastolic dysfunction.Clinical trial registered with www.clinicaltrials.gov (NCT01405976).

Long-term clinical effectiveness of continuous positive airway pressure therapy versus non-invasive ventilation therapy in patients with obesity hypoventilation syndrome: a multicentre, open-label, randomised controlled trial.

BACKGROUND: Obesity hypoventilation syndrome is commonly treated with continuous positive airway pressure or non-invasive ventilation during sleep. Non-invasive ventilation is more complex and costly than continuous positive airway pressure but might be advantageous because it provides ventilatory support. To date there have been no long-term trials comparing these treatment modalities. We therefore aimed to determine the long-term comparative effectiveness of both treatment modalities. METHODS: We did a multicentre, open-label, randomised controlled trial at 16 clinical sites in Spain. We included patients aged 15-80 years with untreated obesity hypoventilation syndrome and an apnoea-hypopnoea index of 30 or more events per h. We randomly assigned patients, using simple randomisation through an electronic database, to receive treatment with either non-invasive ventilation or continuous positive airway pressure. Both investigators and patients were aware of the treatment allocation. The research team was not involved in deciding hospital treatment, duration of treatment in the hospital, and adjustment of medications, as well as adjudicating cardiovascular events or cause of mortality. Treating clinicians from the routine care team were not aware of the treatment allocation. The primary outcome was the number of hospitalisation days per year. The analysis was done according to the intention-to-treat principle. This study is registered with ClinicalTrials.gov, number NCT01405976. FINDINGS: From May 4, 2009, to March 25, 2013, 100 patients were randomly assigned to the non-invasive ventilation group and 115 to the continuous positive airway pressure group, of which 97 patients in the non-invasive ventilation group and 107 in the continuous positive airway pressure group were included in the analysis. The median follow-up was 5·44 years (IQR 4·45-6·37) for all patients, 5·37 years (4·36-6·32) in the continuous positive airway pressure group, and 5·55 years (4·53-6·50) in the non-invasive ventilation group. The mean hospitalisation days per patient-year were 1·63 (SD 3·74) in the continuous positive airway pressure group and 1·44 (3·07) in the non-invasive ventilation group (adjusted rate ratio 0·78, 95% CI 0·34-1·77; p=0·561). Adverse events were similar between both groups. INTERPRETATION: In stable patients with obesity hypoventilation syndrome and severe obstructive sleep apnoea, non-invasive ventilation and continuous positive airway pressure have similar long-term effectiveness. Given that continuous positive airway pressure has lower complexity and cost, continuous positive airway pressure might be the preferred first-line positive airway pressure treatment modality until more studies become available. FUNDING: Instituto de Salud Carlos III, Spanish Respiratory Foundation, and Air Liquide Spain.

Bayesian Inference in Auditing with Partial Prior Information Using Maximum Entropy Priors.

Problems in statistical auditing are usually one-sided. In fact, the main interest for auditors is to determine the quantiles of the total amount of error, and then to compare these quantiles with a given materiality fixed by the auditor, so that the accounting statement can be accepted or rejected. Dollar unit sampling (DUS) is a useful procedure to collect sample information, whereby items are chosen with a probability proportional to book amounts and in which the relevant error amount distribution is the distribution of the taints weighted by the book value. The likelihood induced by DUS refers to a 201-variate parameter p but the prior information is in a subparameter θ linear function of p , representing the total amount of error. This means that partial prior information must be processed. In this paper, two main proposals are made: (1) to modify the likelihood, to make it compatible with prior information and thus obtain a Bayesian analysis for hypotheses to be tested; (2) to use a maximum entropy prior to incorporate limited auditor information. To achieve these goals, we obtain a modified likelihood function inspired by the induced likelihood described by Zehna (1966) and then adapt the Bayes' theorem to this likelihood in order to derive a posterior distribution for θ . This approach shows that the DUS methodology can be justified as a natural method of processing partial prior information in auditing and that a Bayesian analysis can be performed even when prior information is only available for a subparameter of the model. Finally, some numerical examples are presented.

Bayesian meta-analysis: The role of the between-sample heterogeneity.

The random effect approach for meta-analysis was motivated by a lack of consistent assessment of homogeneity of treatment effect before pooling. The random effect model assumes that the distribution of the treatment effect is fully heterogenous across the experiments. However, other models arising by grouping some of the experiments are plausible. We illustrate on simulated binary experiments that the fully heterogenous model gives a poor meta-inference when fully heterogeneity is not the true model and that the knowledge of the true cluster model considerably improves the inference. We propose the use of a Bayesian model selection procedure for estimating the true cluster model, and Bayesian model averaging to incorporate into the meta-analysis the clustering estimation. A well-known meta-analysis for six major multicentre trials to assess the efficacy of a given dose of aspirin in post-myocardial infarction patients is reanalysed.

A Bayesian sensitivity study of risk difference in the meta-analysis of binary outcomes from sparse data.

In most cases, including those of discrete random variables, statistical meta-analysis is carried out using the normal random effect model. The authors argue that normal approximation does not always properly reflect the underlying uncertainty of the original discrete data. Furthermore, in the presence of rare events the results from this approximation can be very poor. This review proposes a Bayesian meta-analysis to address binary outcomes from sparse data and also introduces a simple way to examine the sensitivity of the quantities of interest in the meta-analysis with respect to the structure dependence selected. The findings suggest that for binary outcomes data it is possible to develop a Bayesian procedure, which can be directly applied to sparse data without ad hoc corrections. By choosing a suitable class of linking distributions, the authors found that a Bayesian robustness study can be easily implemented. For illustrative purposes, an example with real data is analyzed using the proposed Bayesian meta-analysis for binomial sparse data.

Effectiveness of three sleep apnea management alternatives.

RATIONALE: Home respiratory polygraphy (HRP) may be a cost-effective alternative to polysomnography (PSG) for diagnosis and treatment election in patients with high clinical probability of obstructive sleep apnea (OSA), but there is conflicting evidence on its use for a wider spectrum of patients. OBJECTIVES: To determine the efficacy and cost of OSA management (diagnosis and therapeutic decision making) using (1) PSG for all patients (PSG arm); (2) HRP for all patients (HRP arm); and (3) HRP for a subsample of patients with high clinical probability of being treated with continuous positive airway pressure (CPAP) and PSG for the remainder (elective HRP arm). METHODS: Multicentric study of 366 patients with intermediate-high clinical probability of OSA, randomly subjected to HRP and PSG. We explored the diagnostic and therapeutic decision agreements between the PSG and both HRP arms for several HRP cutoff points and calculated costs for equal diagnostic and/or therapeutic decision efficacy. RESULTS: For equal diagnostic and therapeutic decision efficacy, PSG arm costs were 18% higher than HRP arm costs and 20% higher than elective HRP arm costs. HRP arm costs tended to be lower than elective HRP arm costs, and both tended to be lower than PSG arm costs if patient costs were omitted. CONCLUSION: Home respiratory polygraphy is a less costly alternative than polysomnography for the diagnosis and therapeutic decision making for patients with suspected obstructive sleep apnea. We found no advantage in cost terms, however, in using home respiratory polygraphy for all patients or home respiratory polygraphy for the most symptomatic patients and polysomnography for the rest.

Effectiveness of sequential automatic-manual home respiratory polygraphy scoring.

Automatic home respiratory polygraphy (HRP) scoring functions can potentially confirm the diagnosis of sleep apnoea-hypopnoea syndrome (SAHS) (obviating technician scoring) in a substantial number of patients. The result would have important management and cost implications. The aim of this study was to determine the diagnostic cost-effectiveness of a sequential HRP scoring protocol (automatic and then manual for residual cases) compared with manual HRP scoring, and with in-hospital polysomnography. We included suspected SAHS patients in a multicentre study and assigned them to home and hospital protocols at random. We constructed receiver operating characteristic (ROC) curves for manual and automatic scoring. Diagnostic agreement for several cut-off points was explored and costs for two equally effective alternatives were calculated. Of 366 randomised patients, 348 completed the protocol. Manual scoring produced better ROC curves than automatic scoring. There was no sensitive automatic or subsequent manual HRP apnoea-hypopnoea index (AHI) cut-off point. The specific cut-off points for automatic and subsequent manual HRP scorings (AHI >25 and >20, respectively) had a specificity of 93% for automatic and 94% for manual scorings. The costs of manual protocol were 9% higher than sequential HRP protocol; these were 69% and 64%, respectively, of the cost of the polysomnography. A sequential HRP scoring protocol is a cost-effective alternative to polysomnography, although with limited cost savings compared to HRP manual scoring.

Comparing meta-analyses for chronic obstructive pulmonary disease.

Evaluation of: Oppe M, Al M, Rutten-van Mölken M. Comparing methods of data synthesis. Re-estimating parameters of an existing probabilistic cost-effectiveness model. Pharmacoeconomics 29(3), 239-250 (2011). In the paper by Oppe et al., a cost-effectiveness analysis of alternative treatments for chronic obstructive pulmonary disease (COPD), based on data from four different trials, is considered. The goal is to compare the usual (frequentist and Bayesian) fixed-effects (FE) and random-effects (RE) normal model for carrying out meta-analysis. Under RE and FE models, the meta-estimation of some quantities of interest for the disease are also carried out using three out of the four trials, and afterwards data from the fourth are incorporated into the meta-estimation. From these sequential estimators, some conclusions on the FE and RE procedures are drawn. Furthermore, as far as the cost-effectiveness is concerned, the main conclusion of the paper is that the Bayesian RE procedure overrides the Bayesian FE and frequentist methods for cost-effectiveness meta-analysis.

Effectiveness of home respiratory polygraphy for the diagnosis of sleep apnoea and hypopnoea syndrome.

INTRODUCTION: Home respiratory polygraphy (HRP) may be a cost-effective alternative to polysomnography for the diagnosis of sleep apnoea-hypopnoea syndrome (SAHS), but stronger evidence is needed. Normally, patients transport HRP equipment from the hospital to home and back, which may create difficulties for some patients. OBJECTIVES: To determine both the diagnostic efficacy and cost of HRP (with and without a transportation service moving the device and telematic transmission of data) in a large sample compared with in-hospital polysomnography. METHODS: Patients suspected of having SAHS were included in a multicentre study (eight hospitals). They were assigned to home and hospital protocols in random order. Receiver operating characteristic curves were constructed for manual respiratory polygraphy scoring protocol and different polysomnographic cut-off points. Diagnostic efficacies for several polysomnographic cut-off points were explored and costs for two equally effective alternatives were calculated. RESULTS: Of 366 randomised patients, 348 completed the protocol. The best receiver operating characteristic curve was obtained with a polysomnographic cut-off of the apnoea-hypopnoea index (AHI)≥5. The sensitive HRP AHI cut-off point (<5) had a sensitivity of 96%, a specificity of 57% and a negative likelihood ratio (LR) of 0.07; the specific cut-off (>10) had a sensitivity of 87%, a specificity of 86% and a positive LR of 6.25. The cost of HRP was half that of polysomnography. Telematic transmission costs were similar if the patients' costs were taken in to account. CONCLUSION: HRP is an alternative to polysomnography in patients with suspected SAHS. Telematic procedures may help patients with limited mobility and those who live a long way from the sleep centre.

Complementing the net benefit approach: a new framework for Bayesian cost-effectiveness analysis.

OBJECTIVES: The aim of cost-effectiveness analysis is to maximize health benefits from a given budget, taking a societal perspective. Consequently, the comparison of alternative treatments or technologies is solely based on their expected effectiveness and cost. However, the expectation, or mean, poses important limitations as it might be a poor summary of the underlying distribution, for instance when the effectiveness is a categorical variable, or when the distributions of either effectiveness or cost present a high degree of asymmetry. Clinical variables often present these characteristics. METHODS: In this study, we present a framework for cost-effectiveness analysis based on the whole posterior distribution of effectiveness and cost. RESULTS: An application with real data is included to illustrate the analysis. Decision-making measures such as the incremental cost-effectiveness ratio, incremental net-benefit, and cost-effectiveness acceptability curves, can also be defined under the new framework. CONCLUSIONS: This framework overcomes limitations of the mean and offers complementary information for the decision maker.

Incorporating model uncertainty in cost-effectiveness analysis: a Bayesian model averaging approach.

Recently, several authors have proposed the use of linear regression models in cost-effectiveness analysis. In this paper, by modelling costs and outcomes using patient and Health Centre covariates, we seek to identify the part of the cost or outcome difference that is not attributable to the treatment itself, but to the patients' condition or to characteristics of the Centres. Selection of the covariates to be included as predictors of effectiveness and cost is usually assumed by the researcher. This behaviour ignores the uncertainty associated with model selection and leads to underestimation of the uncertainty about quantities of interest. We propose the use of Bayesian model averaging as a mechanism to account for such uncertainty about the model. Data from a clinical trial are used to analyze the effect of incorporating model uncertainty, by comparing two highly active antiretroviral treatments applied to asymptomatic HIV patients. The joint posterior density of incremental effectiveness and cost and cost-effectiveness acceptability curves are proposed as decision-making measures.

An analysis of the costs of treating schizophrenia in Spain: a hierarchical Bayesian approach.

BACKGROUND: Health care decisions should incorporate cost of illness and treatment data, particularly for disorders such as schizophrenia with a high morbidity rate and a disproportionately low allocation of resources. Previous cost of illness analyses may have disregarded geographical aspects relevant for resource consumption and unit cost calculation. AIMS: To compare the utilisation of resources and the care costs of schizophrenic patients in four mental-health districts in Spain (in Madrid, Catalonia, Navarra and Andalusia), and to analyse factors that determine the costs and the differences between areas. METHODS: A treated prevalence bottom-up three year follow-up design was used for obtaining data concerning socio-demography, clinical evolution and the utilisation of services. 1997 reference prices were updated for years 1998-2000 in euros. We propose two different scenarios, varying in the prices applied. In the first (Scenario 0) the reference prices are those obtained for a single geographic area, and so the cost variations are only due to differences in the use of resources. In the second situation (Scenario 1), we analyse the variations in resource utilisation at different levels, using the prices applicable to each healthcare area. Bayesian hierarchical models are used to discuss the factors that determine such costs and the differences between geographic areas. RESULTS: In scenario 0, the estimated mean cost was 4918.948 euros for the first year. In scenario 1 the highest cost was in Gava (Catalonia) and the lowest in Loja (Andalusia). Mean costs were respectively 4547.24 and 2473.98 euros. With respect to the evolution of costs over time, we observed an increase during the second year and a reduction during the third year. Geographical differences appeared in follow-up costs. The variables related to lower treatment costs were: residence in the family household, higher patient age and being in work. On the contrary, the number of relapses is directly related to higher treatment costs. No differences were observed between health areas concerning resource utilisation. DISCUSSION: Calculating the costs of a given disease involves two principal factors: the resource utilisation and the prices. In most studies, emphasis is placed on the analysis of resource utilisation. Other evaluations, however, have recognized the implications of incorporating different prices into the final results. In this study we show both scenarios. The factors that determine the cost of schizophrenia for the Spanish case are similar to the factors encountered in studies carried out in other countries. IMPLICATIONS FOR HEALTH POLICIES: Treatment costs may be reduced by the prevention of psychotic symptoms and relapse. IMPLICATIONS FOR FUTURE RESEARCH: The use of the same price data in multicentre studies may not be realistic. More effort should be made to obtain price data from all the centres or countries participating in a study. In the present study, only direct healthcare and social costs have been included. Future research should consider informal and indirect costs.

Herramientas para la investigación biomédica: la perspectiva bayesiana (I)* / Biomedical research tools: Bayesian perspective (I)

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Herramientas para la investigación biomédica: la perspectiva bayesiana (y II)* / Biomedical research tools: Bayesian perspective (and II)

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