Prior elicitation for Gaussian spatial process: An application to TMS brain mapping.

The power and commensurate prior distributions are informative prior distributions that incorporate historical data as prior knowledge in Bayesian analysis to improve inference about a phenomenon under study. Although these distributions have been developed for analyzing non-spatial data, little or no attention has been given to spatial geostatistical data. In this study, we extend these informative prior distributions to a Gaussian spatial process, which enables the elicitation of prior knowledge from historical geostatistical data for Bayesian analysis. Three informative prior distributions were developed for spatial modeling, and an efficient Markov Chain Monte Carlo algorithm was developed for performing Bayesian analysis. Simulation studies were used to assess the adequacy of the informative prior distributions. Hierarchical models combined with the developed informative prior distributions were applied to analyze transcranial magnetic stimulation (TMS) brain mapping data to gain insights into the spatial pattern of a patient's response to motor cortex stimulation. The study quantified the uncertainty in motor response and found that the primary motor cortex of the hand is responsible for most of the movement of the right first dorsal interosseous muscle. The findings provide a deeper understanding of the neural mechanisms underlying motor function and ultimately aid the improvement of treatment options for individuals with health issues.

New statistical process control charts for overdispersed count data based on the Bell distribution.

Poisson distribution is a popular discrete model used to describe counting information, from which traditional control charts involving count data, such as the c and u charts, have been established in the literature. However, several studies recognize the need for alternative control charts that allow for data overdispersion, which can be encountered in many fields, including ecology, healthcare, industry, and others. The Bell distribution, recently proposed by Castellares et al. (2018), is a particular solution of a multiple Poisson process able to accommodate overdispersed data. It can be used as an alternative to the usual Poisson (which, although not nested in the Bell family, is approached for small values of the Bell distribution) Poisson, negative binomial, and COM-Poisson distributions for modeling count data in several areas. In this paper, we consider the Bell distribution to introduce two new exciting, and useful statistical control charts for counting processes, which are capable of monitoring count data with overdispersion. The performance of the so-called Bell charts, namely Bell-c and Bell-u charts, is evaluated by the average run length in numerical simulation. Some artificial and real data sets are used to illustrate the applicability of the proposed control charts.

Under age five children survival times in Nigeria: a Bayesian spatial modeling approach.

BACKGROUND: Nigeria is among the top five countries in the world with the highest under-five mortality rates. In addition to the general leading causes of under-five mortality, studies have shown that disparity in sociocultural values and practices across ethnic groups in Nigeria influence child survival, thus there is a need for scientific validation. This study quantified the survival probabilities and the impact of socioeconomic and demographic factors, proximate and biological determinants, and environmental factors on the risk of under-five mortality in Nigeria. METHODS: The Kaplan-Meier survival curve, Nelson Aalen hazard curve, and components survival probabilities were estimated. The Exponential, Gamma, Log-normal, Weibull, and Cox hazard models in a Bayesian mixed effect hierarchical hazard modeling framework with spatial components were considered, and the Deviance and Watanabe Akaike information criteria were used to select the best model for inference. A [Formula: see text] level of significance was assumed throughout this work. The 2018 Nigeria Demographic and Health Survey dataset was used, and the outcome variable was the time between birth and death or birth and the date of interview for children who were alive on the day of the interview. RESULTS: Findings show that the probability of a child dying within the first two months is 0.04, and the probability of a boy child dying before attaining age five is 0.106, while a girl child is 0.094 probability. Gender, maternal education, household wealth status, source of water and toilet facility, residence, mass media, frequency of antenatal and postnatal visits, marital status, place of delivery, multiple births, who decide healthcare use, use of bednet are significant risk factors of child mortality in Nigeria. The mortality risk is high among the maternal age group below 24 and above 44years, and birth weight below 2.5Kg and above 4.5Kg. The under-five mortality risk is severe in Kebbi, Kaduna, Jigawa, Adamawa, Gombe, Kano, Kogi, Nasarawa, Plateau, and Sokoto states in Nigeria. CONCLUSION: This study accentuates the need for special attention for the first two months after childbirth as it is the age group with the highest expected mortality. A practicable way to minimize death in the early life of children is to improve maternal healthcare service, promote maternal education, encourage delivery in healthcare facilities, positive parental attitude to support multiple births, poverty alleviation programs for the less privileged, and a prioritized intervention to Northern Nigeria.

Nonproportional hazards model with a frailty term for modeling subgroups with evidence of long-term survivors: Application to a lung cancer dataset.

With advancements in medical treatments for cancer, an increase in the life expectancy of patients undergoing new treatments is expected. Consequently, the field of statistics has evolved to present increasingly flexible models to explain such results better. In this paper, we present a lung cancer dataset with some covariates that exhibit nonproportional hazards (NPHs). Besides, the presence of long-term survivors is observed in subgroups. The proposed modeling is based on the generalized time-dependent logistic model with each subgroup's effect time and a random term effect (frailty). In practice, essential covariates are not observed for several reasons. In this context, frailty models are useful in modeling to quantify the amount of unobservable heterogeneity. The frailty distribution adopted was the weighted Lindley distribution, which has several interesting properties, such as the Laplace transform function on closed form, flexibility in the probability density function, among others. The proposed model allows for NPHs and long-term survivors in subgroups. Parameter estimation was performed using the maximum likelihood method, and Monte Carlo simulation studies were conducted to evaluate the estimators' performance. We exemplify this model's use by applying data of patients diagnosed with lung cancer in the state of São Paulo, Brazil.

Safety-Stock: Predicting the demand for supplies in Brazilian hospitals during the COVID-19 pandemic.

Many challenges lie ahead when dealing with COVID-19, not only related to the acceleration of the pandemic, but also to the prediction of personal protective equipment sets consumption to accommodate the explosive demand. Due to this situation of uncertainty, hospital administration encourages the excess stock of these materials, over-stocking products in some hospitals, and provoking shortages in others. The number of available personal protective equipment sets is one of the three main factors that limit the number of patients at a hospital, as well as the number of available beds and the number of professionals per shift. In this scenario, we developed an easy-to-use expert system to predict the demand for personal protective equipment sets in hospitals during the COVID-19 pandemic, which can be updated in real-time for short term planning. For this system, we propose a naive statistical modeling which combines historical data of the consumption of personal protective equipment sets by hospitals, current protocols for their uses and epidemiological data related to the disease, to build predictive models for the demand for personal protective equipment in Brazilian hospitals during the pandemic. We then embed this modeling in the free Safety-Stock system, which provides useful information for the hospital, especially the safety-stock level and the prediction of consumption/demand for each personal protective equipment set over time. Considering our predictions, a hospital may have its needs related to specific personal protective equipment sets estimated, taking into account its historical stock levels and possible scheduled purchases. The tool allows for adopting strategies to control and keep the stock at safety levels to the demand, mitigating the risk of stock-out. As a direct consequence, it also enables the interchange and cooperation between hospitals, aiming to maximize the availability of equipment during the pandemic.

On Posterior Properties of the Two Parameter Gamma Family of Distributions.

The gamma distribution has been extensively used in many areas of applications. In this paper, considering a Bayesian analysis we provide necessary and sufficient conditions to check whether or not improper priors lead to proper posterior distributions. Further, we also discuss sufficient conditions to verify if the obtained posterior moments are finite. An interesting aspect of our findings are that one can check if the posterior is proper or improper and also if its posterior moments are finite by looking directly in the behavior of the proposed improper prior. To illustrate our proposed methodology these results are applied in different objective priors.

A new mixed-effects regression model for the analysis of zero-modified hierarchical count data.

Count data sets are traditionally analyzed using the ordinary Poisson distribution. However, such a model has its applicability limited as it can be somewhat restrictive to handle specific data structures. In this case, it arises the need for obtaining alternative models that accommodate, for example, (a) zero-modification (inflation or deflation at the frequency of zeros), (b) overdispersion, and (c) individual heterogeneity arising from clustering or repeated (correlated) measurements made on the same subject. Cases (a)-(b) and (b)-(c) are often treated together in the statistical literature with several practical applications, but models supporting all at once are less common. Hence, this paper's primary goal was to jointly address these issues by deriving a mixed-effects regression model based on the hurdle version of the Poisson-Lindley distribution. In this framework, the zero-modification is incorporated by assuming that a binary probability model determines which outcomes are zero-valued, and a zero-truncated process is responsible for generating positive observations. Approximate posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the Adaptive Metropolis algorithm. Intensive Monte Carlo simulation studies were performed to assess the empirical properties of the Bayesian estimators. The proposed model was considered for the analysis of a real data set, and its competitiveness regarding some well-established mixed-effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian p -value and the randomized quantile residuals were considered for model diagnostics.

Weighted Lindley frailty model: estimation and application to lung cancer data.

In this paper, we propose a novel frailty model for modeling unobserved heterogeneity present in survival data. Our model is derived by using a weighted Lindley distribution as the frailty distribution. The respective frailty distribution has a simple Laplace transform function which is useful to obtain marginal survival and hazard functions. We assume hazard functions of the Weibull and Gompertz distributions as the baseline hazard functions. A classical inference procedure based on the maximum likelihood method is presented. Extensive simulation studies are further performed to verify the behavior of maximum likelihood estimators under different proportions of right-censoring and to assess the performance of the likelihood ratio test to detect unobserved heterogeneity in different sample sizes. Finally, to demonstrate the applicability of the proposed model, we use it to analyze a medical dataset from a population-based study of incident cases of lung cancer diagnosed in the state of São Paulo, Brazil.

A New Regression Model for the Analysis of Overdispersed and Zero-Modified Count Data.

Count datasets are traditionally analyzed using the ordinary Poisson distribution. However, said model has its applicability limited, as it can be somewhat restrictive to handling specific data structures. In this case, the need arises for obtaining alternative models that accommodate, for example, overdispersion and zero modification (inflation/deflation at the frequency of zeros). In practical terms, these are the most prevalent structures ruling the nature of discrete phenomena nowadays. Hence, this paper's primary goal was to jointly address these issues by deriving a fixed-effects regression model based on the hurdle version of the Poisson-Sujatha distribution. In this framework, the zero modification is incorporated by considering that a binary probability model determines which outcomes are zero-valued, and a zero-truncated process is responsible for generating positive observations. Posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the g-prior method. Intensive Monte Carlo simulation studies were performed to assess the Bayesian estimators' empirical properties, and the obtained results have been discussed. The proposed model was considered for analyzing a real dataset, and its competitiveness regarding some well-established fixed-effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian p-value and the randomized quantile residuals were considered for the task of model validation.

A new long-term survival model with dispersion induced by discrete frailty.

Frailty models are generally used to model heterogeneity between the individuals. The distribution of the frailty variable is often assumed to be continuous. However, there are situations where a discretely-distributed frailty may be appropriate. In this paper, we propose extending the proportional hazards frailty models to allow a discrete distribution for the frailty variable. Having zero frailty can be interpreted as being immune or cured (long-term survivors). Thus, we develop a new survival model induced by discrete frailty with zero-inflated power series distribution, which can account for overdispersion. A numerical study is carried out under the scenario that the baseline distribution follows an exponential distribution, however this assumption can be easily relaxed and some other distributions can be considered. Moreover, this proposal allows for a more realistic description of the non-risk individuals, since individuals cured due to intrinsic factors (immune) are modeled by a deterministic fraction of zero-risk while those cured due to an intervention are modeled by a random fraction. Inference is developed by the maximum likelihood method for the estimation of the model parameters. A simulation study is performed in order to evaluate the performance of the proposed inferential method. Finally, the proposed model is applied to a data set on malignant cutaneous melanoma to illustrate the methodology.

Improved Bayes estimators and prediction for the Wilson-Hilferty distribution.

In this paper, we revisit the Wilson-Hilferty distribution and presented its mathematical properties such as the r-th moments and reliability properties. The parameters estimators are discussed using objective reference Bayesian analysis for both complete and censored data where the resulting marginal posterior intervals have accurate frequentist coverage. A simulation study is presented to compare the performance of the proposed estimators with the frequentist approach where it is observed a clear advantage for the Bayesian method. Finally, the proposed methodology is illustrated on three real datasets.

Defective regression models for cure rate modeling with interval-censored data.

Regression models in survival analysis are most commonly applied for right-censored survival data. In some situations, the time to the event is not exactly observed, although it is known that the event occurred between two observed times. In practice, the moment of observation is frequently taken as the event occurrence time, and the interval-censored mechanism is ignored. We present a cure rate defective model for interval-censored event-time data. The defective distribution is characterized by a density function whose integration assumes a value less than one when the parameter domain differs from the usual domain. We use the Gompertz and inverse Gaussian defective distributions to model data containing cured elements and estimate parameters using the maximum likelihood estimation procedure. We evaluate the performance of the proposed models using Monte Carlo simulation studies. Practical relevance of the models is illustrated by applying datasets on ovarian cancer recurrence and oral lesions in children after liver transplantation, both of which were derived from studies performed at A.C. Camargo Cancer Center in São Paulo, Brazil.

Two new defective distributions based on the Marshall-Olkin extension.

The presence of immune elements (generating a fraction of cure) in survival data is common. These cases are usually modeled by the standard mixture model. Here, we use an alternative approach based on defective distributions. Defective distributions are characterized by having density functions that integrate to values less than 1, when the domain of their parameters is different from the usual one. We use the Marshall-Olkin class of distributions to generalize two existing defective distributions, therefore generating two new defective distributions. We illustrate the distributions using three real data sets.

The exponential-Poisson model for recurrent event data: an application to a set of data on malaria in Brazil.

In this paper, we introduce a new model for recurrent event data characterized by a baseline rate function fully parametric, which is based on the exponential-Poisson distribution. The model arises from a latent competing risk scenario, in the sense that there is no information about which cause was responsible for the event occurrence. Then, the time of each recurrence is given by the minimum lifetime value among all latent causes. The new model has a particular case, which is the classical homogeneous Poisson process. The properties of the proposed model are discussed, including its hazard rate function, survival function, and ordinary moments. The inferential procedure is based on the maximum likelihood approach. We consider an important issue of model selection between the proposed model and its particular case by the likelihood ratio test and score test. Goodness of fit of the recurrent event models is assessed using Cox-Snell residuals. A simulation study evaluates the performance of the estimation procedure in the presence of a small and moderate sample sizes. Applications on two real data sets are provided to illustrate the proposed methodology. One of them, first analyzed by our team of researchers, considers the data concerning the recurrence of malaria, which is an infectious disease caused by a protozoan parasite that infects red blood cells.

Reducing delivery insurance costs through risk score model for food delivery company.

In this paper, we propose a novel pricing model for delivery insurance in a food delivery company in Latin America, with the aim of reducing the high costs associated with the premium paid to the insurer. To achieve this goal, a thorough analysis was conducted to estimate the probability of losses based on delivery routes, transportation modes, and delivery drivers' profiles. A large amount of data was collected and used as a database, and various statistical models and machine learning techniques were employed to construct a comprehensive risk profile and perform risk classification. Based on the risk classification and the estimated probability associated with it, a new pricing model for delivery insurance was developed using advanced mathematical algorithms and machine learning techniques. This new pricing model took into account the pattern of loss occurrence and high and low-risk behaviors, resulting in a significant reduction of insurance costs for both the contracting company and the insurer. The proposed pricing model also allowed for greater flexibility in insurance contracting, making it more accessible and appealing to delivery drivers. The use of estimated loss probabilities and a risk score for the pricing of delivery insurance proved to be a highly effective and efficient alternative for reducing the high costs associated with insurance, while also improving the profitability and competitiveness of the food delivery company in Latin America.

Conceptual framework for tinnitus: a cognitive model in practice.

Tinnitus is a conscious attended awareness perception of sourceless sound. Widespread theoretical and evidence-based neurofunctional and psychological models have tried to explain tinnitus-related distress considering the influence of psychological and cognitive factors. However, tinnitus models seem to be less focused on causality, thereby easily misleading interpretations. Also, they may be incapable of individualization. This study proposes a Conceptual Cognitive Framework (CCF) providing insight into cognitive mechanisms involved in the predisposition, precipitation, and perpetuation of tinnitus and consequent cognitive-emotional disturbances. The current CCF for tinnitus relies on evaluative conditional learning and appraisal, generating negative valence (emotional value) and arousal (cognitive value) to annoyance, distress, and distorted perception. The suggested methodology is well-defined, reproducible, and accessible, which can help foster future high-quality clinical databases. Perceived tinnitus through the perpetual-learning process can always lead to annoyance, but only in the clinical stage directly cause annoyance. In the clinical stage, tinnitus perception can lead indirectly to distress only with experiencing annoyance either with (" I n d - 1 C " = 1.87; 95% CI 1.18-2.72)["1st indirect path in the Clinical stage model": Tinnitus Loudness → Attention Bias → Cognitive-Emotional Value → Annoyance → Clinical Distress]or without (" I n d - 2 C "= 2.03; 95% CI 1.02-3.32)[ "2nd indirect path in the Clinical stage model": Tinnitus Loudness → Annoyance → Clinical Distress] the perpetual-learning process. Further real-life testing of the CCF is expected to express a meticulous, decision-supporting platform for cognitive rehabilitation and clinical interventions. Furthermore, the suggested methodology offers a reliable platform for CCF development in other cognitive impairments and supports the causal clinical data models. It may also enhance our knowledge of psychological disorders and complicated comorbidities by supporting the design of different rehabilitation interventions and comprehensive frameworks in line with the "preventive medicine" policy.

A mechanistic breast cancer survival modelling through the axillary lymph node chain.

In this paper, we proposed a mechanistic breast cancer survival model based on the axillary lymph node chain structure, considering lymph nodes as a potential dissemination arrangement. We assume a naive breast cancer treatment protocol consisting of exposing patients first to a chemotherapy treatment on r intervals at k-cycles separated by equal time intervals, and then they proceed to surgery. Our model, different from former ones, accommodates a quantity of contaminated lymph nodes, which is observed during surgery. We assume a generalised negative binomial survival distribution for the unknown number of contaminated lymph nodes after surgery, which, during an unknown period, may potentially propagate the disease. Estimation is based on a maximum likelihood approach. A simulation study assesses the coverage probability of asymptotic confidence intervals when small or moderate samples are considered. A Brazilian breast cancer data illustrate the applicability of our modelling.

The destructive negative binomial cure rate model with a latent activation scheme.

A new flexible cure rate survival model is developed where the initial number of competing causes of the event of interest (say lesions or altered cells) follow a compound negative binomial (NB) distribution. This model provides a realistic interpretation of the biological mechanism of the event of interest as it models a destructive process of the initial competing risk factors and records only the damaged portion of the original number of risk factors. Besides, it also accounts for the underlying mechanisms that leads to cure through various latent activation schemes. Our method of estimation exploits maximum likelihood (ML) tools. The methodology is illustrated on a real data set on malignant melanoma, and the finite sample behavior of parameter estimates are explored through simulation studies.

Zero-modified Poisson model: Bayesian approach, influence diagnostics, and an application to a Brazilian leptospirosis notification data.

In this paper, a Bayesian method for inference is developed for the zero-modified Poisson (ZMP) regression model. This model is very flexible for analyzing count data without requiring any information about inflation or deflation of zeros in the sample. A general class of prior densities based on an information matrix is considered for the model parameters. A sensitivity study to detect influential cases that can change the results is performed based on the Kullback-Leibler divergence. Simulation studies are presented in order to illustrate the performance of the developed methodology. Two real datasets on leptospirosis notification in Bahia State (Brazil) are analyzed using the proposed methodology for the ZMP model.

Unraveling water monitoring association towards weather attributes for response proportions data: A unit-Lindley learning.

Learning techniques involve unraveling regression structures, which aim to analyze in a probabilistic frame the associations across variables of interest. Thus, analyzing fraction and/or proportion data may not be adequate with standard regression procedures, since the linear regression models generally assume that the dependent (outcome) variable is normally distributed. In this manner, we propose a statistical model called unit-Lindley regression model, for the purpose of Statistical Process Control (SPC). As a result, a new control chart tool was proposed, which targets the water monitoring dynamic, as well as the monitoring of relative humidity, per minute, of Copiapó city, located in Atacama Desert (one of the driest non-polar places on Earth), north of Chile. Our results show that variables such as wind speed, 24-hour temperature variation, and solar radiation are useful to describe the amount of relative humidity in the air. Additionally, Information Visualization (InfoVis) tools help to understand the time seasonality of the water particle phenomenon of the region in near real-time analysis. The developed methodology also helps to label unusual events, such as Camanchaca, and other water monitoring-related events.