Francisco José Vázquez-Polo

• Ph.D.
• Professor (Full) at University of Las Palmas de Gran Canaria

The Bayesian approach to data analysis is useful when the variables considered are already subjective or abstract, as is the case with online consumer reviews and ratings in tourism research. The Bayesian framework provides a method for combining observed data from prominent e-commerce platforms with other prior information, such as expert knowledg...

This paper describes an alternative approach to measuring score heterogeneity between online consumer review websites. This topic is important in tourism management and in the hospitality sector, where it is helpful to be aware of the ratings obtained by services, from information readily available on the website. We approach this issue by consider...

In this paper, we calculate premiums that are based on the Conditional Tail Expectation (CTE) and asymmetric loss functions to account for the risk of both underestimation and overestimation losses. After selecting an appropriate loss function, the premium is calculated as the quantity minimizing an objective function related to the conditional tai...

For a wide class of daily applications in industrial quality control, there may be interest in comparing several Poisson means. A large catalogue of frequentist procedures for this hypothesis testing problem is available. However, some common drawbacks of them are their low power, interpretation of the p$$ p $$‐values for multiple comparison, among...

The meta–analysis of two trials is valuable in many practical situations, such as studies of rare and/or orphan diseases focussed on a single intervention. In this context, additional concerns, like small sample size and/or heterogeneity in the results obtained, might make standard frequentist and Bayesian techniques inappropriate. In a meta–analys...

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 fa...

In this paper, reference analysis, the tool provided by Berger et al. (2009), is used to obtain reference Bayesian premiums, which can be helpful when the practitioner has insufficient information to elicit a prior distribution. The Bayesian premiums thus obtained are based exclusively on prior distributions built from the model generated and from...

Archivos de Bronconeumología 58 (2022) 228-236 w w w. a r c h b r o n c o n e u m o l. o r g

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 severit...

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 me...

In meta-analysis, the existence of between-sample heterogeneity introduces model uncertainty, which must be incorporated into the inference. We argue that an alternative way to measure this heterogeneity is by clustering the samples and then determining the posterior probability of the cluster models. The meta-inference is obtained as a mixture of...

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 effective...

Selecting a statistical model from a set of competing models is a central issue in the scientific task, and the Bayesian approach to model selection is based on the posterior model distribution, a quantification of the updated uncertainty on the entertained models. We present a Bayesian procedure for choosing a family between the Poisson and the ge...

Background Noninvasive ventilation (NIV) is an effective form of treatment in obesity hypoventilation syndrome (OHS) with severe obstructive sleep apnea (OSA). However, there is paucity of evidence in OHS patients without severe OSA phenotype. Research questions Is NIV effective in OHS without severe OSA phenotype? Study design and methods In thi...

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 effectiv...

This paper presents a three-parameter family of distributions which includes the common exponential and the Marshall–Olkin exponential as special cases. This distribution exhibits a monotone failure rate function, which makes it appealing for practitioners interested in reliability, and means it can be included in the catalogue of appropriate non-s...

Rationale: Despite a significant association between obesity hypoventilation syndrome (OHS) and cardiac dysfunction, no randomized trials have assessed the impact of long-term noninvasive ventilation (NIV) or CPAP on cardiac structure and function assessed by echocardiography. Objectives: We performed a pre-specified secondary analysis of the la...

Introduction Obstructive sleep apnea (OSA) is a prevalent disease associated with significant morbidity and high healthcare costs. Information and communication technology could offer cost-effective management options. Objectives To evaluate an out-of-hospital Virtual Sleep Unit (VSU) based on telemedicine to manage all patients with suspected OSA...

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...

In cost–effectiveness analysis (CEA) of medical treatments the optimal treatment is chosen using an statistical model of the cost and effectiveness of the treatments, and data from patients under the treatments. Sometimes these data also include values of certain deterministic covariates of the patients which usually have valuable clinical informat...

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...

This paper describes a complementary tool for fitting probabilistic distributions in data analysis. First, we examine the well known bivariate index of skewness and the aggregate skewness function, and then introduce orderings of the skewness of probability distributions. Using an example, we highlight the advantages of this approach and then prese...

Cost–effectiveness analysis of medical treatments is a statistical decision problem whose aim is to choose an optimal treatment among a finite set of alternative treatments. It is assumed that the treatment selection is to be based on their cost and effectiveness. In this paper we revise this statistical decision problem, discuss two utility functi...

The Bayesian structural time series model, used in conjunction with a state–space model, is a novel means of exploring the causal impact of a policy intervention. It extends the widely used difference–in–differences approach to the time series setting and enables several control series to be used to construct the counterfactual. This paper highligh...

A new one-parameter family of discrete distributions is presented. It has some advantages against the Poisson distribution as a suitable model for modelling data with a high frequencies of zeros and showing over-dispersion (variance larger than the mean). The distribution is obtained from a simple modification of the Borel-Tanner distribution, whic...

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....

Presentamos una nueva distribución lognormal con colas pesadas que se adapta bien a muchas situaciones prácticas en el campo de los seguros. Utilizamos el procedimiento de Marshall y Olkin para generar tal distribución y estudiamos sus propiedades básicas. Se presenta una aplicación de la misma para datos de seguros dentales que es analizada en pro...

El objetivo de este trabajo es construir un procedimiento bayesiano, fácil de implementar en la práctica, que soslaye los problemas encontrados en los métodos de meta-análisis para el caso de datos binarios con alta presencia de ceros. Para ello, consideraremos el problema dentro de uno general de selección bayesiana de modelos identificando de for...

The sampling information for the cost-effectiveness analysis typically comes from different health care centers, and, as far as we know, it is taken for granted that the distribution of the cost and the effectiveness does not vary across centers. We argue that this assumption is unrealistic, and prove that to not consider the sample heterogeneity w...

Statistical meta-analysis is mostly carried out with the help of the random effect normal model, including the case of discrete random variables. We argue that the normal approximation is not always able to adequately capture the underlying uncertainty of the original discrete data. Furthermore, when we examine the influence of the prior distributi...

We briefly present the advantages and opportunities available to umbrella reviews from the use of Bayesian techniques while taking into account that the concerns commonly arising in Bayesian meta-analysis procedures are also present in umbrella reviews. This is the case, for example, of sparse data, for which the hierarchical logit-normal model can...

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 vid...

This paper introduces some new elements to measure the skewness of a probability distribution, suggesting that a given distribution can have both positive and negative skewness, depending on the centred sub-interval of the support set being observed. A skewness function for positive reals is defined, from which a bivariate index of positive–negativ...

To evaluate whether follow-up of patients with obstructive sleep apnoea (OSA) undergoing CPAP treatment could be performed in primary care (PC) settings. Non-inferiority, randomised, prospective controlled study. Sleep unit (SU) at the University Hospital and in 8 PC units in Lleida, Spain. Patients with OSA were randomised to be followed up at the...

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 approxima...

The propose of this paper is to develop a Bayesian procedure that adequately account for studies with zero observations in meta-analysis and then we focus the problem in the context of the Bayesian selection models. Also, attention is focused to the link distribution between effectiveness in each study/center and the meta-effectiveness. We present...

This paper presents a Bayesian model for meta‐analysis of sparse discrete binomial data, which are out of the scope of the usual hierarchical normal random‐effect models. Treatment effectiveness data are often of this type. The crucial linking distribution between the effectiveness conditional on the healthcare center and the unconditional effectiv...

A new discrete distribution depending on two parameters $\alpha >-1$ and $\sigma >0$ is obtained by discretizing the generalized normal distribution proposed in García et al. (Comput Stat and Data Anal 54:2021–2034, 2010), which was derived from the normal distribution by using the Marshall and Olkin (Biometrika 84(3):641–652, 1997) scheme. The...

In this paper, a new heavy-tailed distribution is used to model data with a strong right tail, as often occurs in practical situations. The distribution proposed is derived from the lognormal distribution, by using the Marshall and Olkin procedure. Some basic properties of this new distribution are obtained and we present situations where this new...

A new class of heavy–tailed distribution functions, containing the lognormal distribution as a particular case, is introduced. The class thus obtained depends on a set of three parameters, incorporating an additional distribution to the classical lognormal one. This new class of heavy-tailed distribution is presented as an alternative to other usef...

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. To determine the efficacy and cost of OSA management (diagnosi...

These are the written discussions of the paper "Bayesian measures of model complexity and fit" by D. Spiegelhalter et al. (2002), following the discussions given at the Annual Meeting of the Royal Statistical Society in Newcastle-upon-Tyne on September 3rd, 2013.

In the presence of covariates, the cost-effectiveness analysis of medical treatments shows that the optimal treatment varies across the patient population subgroups, and hence to accurately define the subgroups is a crucial step in the analysis. A patient subgroup definition using only influential covariates within the potential set of patients cov...

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 o...

The Bayes premium is a quantity of interest in the actuarial collective risk model, under which certain hypotheses are assumed. The usual assumption of independence among risk profiles is very convenient from a computational point of view but is not always realistic. Recently, several authors in the field of actuarial and operational risks have exa...

This paper deals with the decision problem of choosing an optimal medical treatment, among M possible candidates, when the states of nature are the net benefit of the treatments, and regression models for the treatment cost and effectiveness are assumed. In this setting a crucial step in the analysis is the construction of the population subgroups...

This paper examines a compound collective risk model in which the primary distribution comprised the Poisson–Lindley distribution with a λ parameter, and where the secondary distribution is an exponential one with a θ parameter. We consider the case of dependence between risk profiles (i.e., the parameters λ and θ), where the dependence is modelled...

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. To determine both the diagnostic effica...

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 o...

A new class of distribution functions with not-necessarily symmetric densities, which contains the normal one as a particular case, is introduced. The class thus obtained depends on a set of three parameters, with an additional one to the classical normal distribution being inserted. This new class of skewed distributions is presented as an alterna...

This paper deals with medical treatments comparison from the cost-effectiveness viewpoint. A decision theory scheme is considered, where the decision space is the set of treatments involved, the space of states of nature consists of the respective net benefits of the treatments, and the utility function is one of two possible candidates. A first ca...

Cost-effectiveness analysis of a treatment is typically based on specific functions of the expectation of the effectiveness and cost of the treatment, and treatment comparisons are made in the same vein. The mathematical expectation has been the cornerstone for defining the incremental cost-effectiveness ratio and the incremental net benefit, the m...

Linear regression models are often used to represent the cost and effectiveness of medical treatment. The covariates used may include sociodemographic variables, such as age, gender or race; clinical variables, such as initial health status, years of treatment or the existence of concomitant illnesses; and a binary variable indicating the treatment...

The economic literature on cost-effectiveness analysis in the context of decisions by health technology assessment agencies assumes as the quantity of interest a linear combination of the mean of the sampling distribution of the effectiveness and the cost. We argue that this is not always reasonable. Our reasons for this assertion are that (i) trea...

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...

The Bayesian approach to statistics has been growing rapidly in popularity as an alternative to the classical approach in the economic evaluation of health technologies, due to the significant benefits it affords. One of the most important advantages of Bayesian methods is their incorporation of prior information. Thus, use is made of a greater amo...

The conditional specification technique introduced by Arnold et al. (Conditional specification of statistical models. Springer series in statistics. Springer, New York, 1999) was used in Sarabia et al. (Astin Bull 34(1):85–98, 2004) to obtain bonus-malus premiums. The Poisson distribution for which the parameter is a function of the classical struc...

The present study aims to estimate the cost-effectiveness of interventions for reducing the burden of depression and schizophrenia in Spain and evaluate their population level impact. The study examines the cost-effectiveness of different types of clinical interventions at the level of the Spanish population. For depression, the interventions consi...

In this article, we consider Bayesian statistical models in which prior distribution of the risk parameter is to be specified in a hierarchical fashion. The model obtained is shown to be over-dispersed and competitive with other models in the literature for fitting automobile claim frequency data. We obtain analytical forms of the distribution, whi...

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 c...

Standard binary models have been developed to describe the behavior of consumers when they are faced with two choices. The classical logit model presents the feature of the symmetric link function. However, symmetric links do not provide good fits for data where one response is much more frequent than the other (as it happens in the insurance fraud...

The Bayesian approach to statistics has been growing rapidly in popularity as an alterna- tive to the classical approach in the economic evaluation of health technologies, due to the significant benefits it affords. One of the most important advantages of Bayesian meth- ods is their incorporation of prior information. Thus, use is made of a greater...

Objective: To study the learning curve associated with independent practice in coronary artery surgery. Participants: 123 patients undergoing coronary artery surgery for the first time between January 2001 and April 2002, who were operated on by 6 surgeons. Methods: Stochastic frontier cost funtion and an inefficiency model. The analysis of the dat...

Computing premiums in a Bayesian context requires the use of a prior distribution that the unknown risk parameter follows in the heterogeneous portfolio. Following the methodology that an actuary only has vague information about this parameter and therefore is unable to specify a simple prior, we choose a class Gamma of priors and compute posterior...

In a standard Bayesian model, a prior distribution is elicited for the structure parameter in order to obtain an estimate of this unknown parameter. The hierarchical model is a two way Bayesian one which incorporates a hyperprior distribution for some of the hyperparameters of the prior. In this way and under the Poisson-Gamma-Gamma model, a new di...

Cost-effectiveness analysis (CEA) compares the costs and outcomes of two or more technologies. However, there is no consensus about which measure of effectiveness should be used in each analysis. Clinical researchers have to select an appropriate outcome for their purpose, and this choice can have dramatic consequences on the conclusions of their a...

In this paper we consider statistical problems arising from applications concerning insurance-premium calculation. We describe an integrated set of Bayesian tools for modelling bonus-malus systems (BMS) for insurance premiums. This paper describes a bonus-malus system (BMS) applicable to insurance claims procedures, constructed using a hierarchical...

This report explores the use of regression models for estimating health status of schizophrenic patients from a Bayesian perspective. The aims are: to obtain a set of values of health states of the EQ-5D based on self-assessed health from a sample of schizophrenic patients; and to analyze the differences in the health status and in patients' percep...

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. To com...

In this article, a new methodology for obtaining a premium based on a broad class of conjugate prior distributions, assuming lognormal claims, is presented. The new class of prior distributions arise in a natural way, using the conditional specification technique introduced by Arnold, Castillo, and Sarabia (1998, 1999). The new family of prior dist...

When Bayesian models are implemented for a Bonus–Malus System (BMS), a parametric structure, π0 (λ), is normally included in the insurer's portfolio. Following Bayesian sensitivity analysis, it is possible to model the structure function by specifying a class Γ of priors instead of a single prior. This paper examines the ranges of the relativities...

  Populations where items are error free are found in many areas of applied statistics, such as auditing and actuarial science. Decisions are then made by inferring the total error in a population. This parameter is usually modelled by two parametric structures under the assumption of prior independence. This paper explores the usefulness of robust...

As part of their practice, policymakers have to make economic evaluations using clinical trial data. Recent interest has been expressed in determining how cost-effectiveness analysis can be undertaken in a regression framework. In this respect, published research basically provides a general method for prognostic factor adjustment in the presence o...

Recent studies have shown how cost-effectiveness analysis can be undertaken in a regression framework. This contribution explores the use of practical regression models for estimating cost-effectiveness from a Bayesian perspective. Two different Bayesian models are described. The first considers the outcome measure to be a quantitative variable. In...

A Benefit Function Transfer obtains estimates of Willingness-to-Pay (WTP) for the evaluation of a given policy at a site by combining existing information from different study sites. This has the advantage that more efficient estimates are obtained, but it relies on the assumption that the heterogeneity between sites is appropriately captured in th...

In this paper a new methodology using the conditional specification technique intoduced by Arnold et al. (1999) is used to obtain bonus-malus premiums. A Poisson distribution for which the parameter is a function of the classical structure parameter is used and a new class of prior distribution arises in a natural way. This model contains, as a par...