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.

Effectiveness of CPAP vs. Noninvasive Ventilation Based on Disease Severity in Obesity Hypoventilation Syndrome and Concomitant Severe Obstructive Sleep Apnea.

RATIONALE: Obesity hypoventilation syndrome (OHS) with concomitant severe obstructive sleep apnea (OSA) is treated with CPAP or noninvasive ventilation (NIV) during sleep. NIV is costlier, but may be advantageous because it provides ventilatory support. However, there are no long-term trials comparing these treatment modalities based on OHS severity. OBJECTIVE: To determine if CPAP have similar effectiveness when compared to NIV according to OHS severity subgroups. METHODS: Post hoc analysis of the Pickwick randomized clinical trial in which 215 ambulatory patients with untreated OHS and concomitant severe OSA, defined as apnoea-hypopnea index (AHI)≥30events/h, were allocated to NIV or CPAP. In the present analysis, the Pickwick cohort was divided in severity subgroups based on the degree of baseline daytime hypercapnia (PaCO2 of 45-49.9 or ≥50mmHg). Repeated measures of PaCO2 and PaO2 during the subsequent 3 years were compared between CPAP and NIV in the two severity subgroups. Statistical analysis was performed using linear mixed-effects model. RESULTS: 204 patients, 97 in the NIV group and 107 in the CPAP group were analyzed. The longitudinal improvements of PaCO2 and PaO2 were similar between CPAP and NIV based on the PaCO2 severity subgroups. CONCLUSION: In ambulatory patients with OHS and concomitant severe OSA who were treated with NIV or CPAP, long-term NIV therapy was similar to CPAP in improving awake hypercapnia, regardless of the severity of baseline hypercapnia. Therefore, in this patient population, the decision to prescribe CPAP or NIV cannot be solely based on the presenting level of PaCO2.

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.

Long-term Noninvasive Ventilation in Obesity Hypoventilation Syndrome Without Severe OSA: The Pickwick Randomized Controlled Trial.

BACKGROUND: Noninvasive ventilation (NIV) is an effective form of treatment in obesity hypoventilation syndrome (OHS) with severe OSA. However, there is paucity of evidence in patients with OHS without severe OSA phenotype. RESEARCH QUESTION: Is NIV effective in OHS without severe OSA phenotype? STUDY DESIGN AND METHODS: In this multicenter, open-label parallel group clinical trial performed at 16 sites in Spain, we randomly assigned 98 stable ambulatory patients with untreated OHS and apnea-hypopnea index < 30 events/h (ie, no severe OSA) to NIV or lifestyle modification (control group) using simple randomization through an electronic database. The primary end point was hospitalization days per year. Secondary end points included other hospital resource utilization, incident cardiovascular events, mortality, respiratory functional tests, BP, quality of life, sleepiness, and other clinical symptoms. Both investigators and patients were aware of the treatment allocation; however, treating physicians from the routine care team were not aware of patients' enrollment in the clinical trial. The study was stopped early in its eighth year because of difficulty identifying patients with OHS without severe OSA. The analysis was performed according to intention-to-treat and per-protocol principles and by adherence subgroups. RESULTS: Forty-nine patients in the NIV group and 49 in the control group were randomized, and 48 patients in each group were analyzed. During a median follow-up of 4.98 years (interquartile range, 2.98-6.62), the mean hospitalization days per year ± SD was 2.60 ± 5.31 in the control group and 2.71 ± 4.52 in the NIV group (adjusted rate ratio, 1.07; 95% CI, 0.44-2.59; P = .882). NIV therapy, in contrast with the control group, produced significant longitudinal improvement in Paco2, pH, bicarbonate, quality of life (Medical Outcome Survey Short Form 36 physical component), and daytime sleepiness. Moreover, per-protocol analysis showed a statistically significant difference for the time until the first ED visit favoring NIV. In the subgroup with high NIV adherence, the time until the first event of hospital admission, ED visit, and mortality was longer than in the low adherence subgroup. Adverse events were similar between arms. INTERPRETATION: In stable ambulatory patients with OHS without severe OSA, NIV and lifestyle modification had similar long-term hospitalization days per year. A more intensive program aimed at improving NIV adherence may lead to better outcomes. Larger studies are necessary to better determine the long-term benefit of NIV in this subgroup of OHS. TRIAL REGISTRY: ClinicalTrials.gov; No.: NCT01405976; URL: www.clinicaltrials.gov.

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.

A Bayesian cost-effectiveness analysis of a telemedicine-based strategy for the management of sleep apnoea: a multicentre randomised controlled trial.

BACKGROUND: Compliance with continuous positive airway pressure (CPAP) therapy is essential in patients with obstructive sleep apnoea (OSA), but adequate control is not always possible. This is clinically important because CPAP can reverse the morbidity and mortality associated with OSA. Telemedicine, with support provided via a web platform and video conferences, could represent a cost-effective alternative to standard care management. AIM: To assess the telemedicine impact on treatment compliance, cost-effectiveness and improvement in quality of life (QoL) when compared with traditional face-to-face follow-up. METHODS: A randomised controlled trial was performed to compare a telemedicine-based CPAP follow-up strategy with standard face-to-face management. Consecutive OSA patients requiring CPAP treatment, with sufficient internet skills and who agreed to participate, were enrolled. They were followed-up at 1, 3 and 6 months and answered surveys about sleep, CPAP side effects and lifestyle. We compared CPAP compliance, cost-effectiveness and QoL between the beginning and the end of the study. A Bayesian cost-effectiveness analysis with non-informative priors was performed. RESULTS: We randomised 139 patients. At 6 months, we found similar levels of CPAP compliance, and improved daytime sleepiness, QoL, side effects and degree of satisfaction in both groups. Despite requiring more visits, the telemedicine group was more cost-effective: costs were lower and differences in effectiveness were not relevant. CONCLUSIONS: A telemedicine-based strategy for the follow-up of CPAP treatment in patients with OSA was as effective as standard hospital-based care in terms of CPAP compliance and symptom improvement, with comparable side effects and satisfaction rates. The telemedicine-based strategy had lower total costs due to savings on transport and less lost productivity (indirect costs). TRIAL REGISTER NUMBER: NCT01716676.