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This paper presents a novel approach for analyzing bivariate positive data, taking into account a covariate vector and left-censored observations, by introducing a hierarchical Bayesian analysis. The proposed method assumes marginal Weibull distributions and employs either a usual Weibull likelihood or Weibull-Tobit likelihood approaches. A latent variable or frailty is included in the model to capture the possible correlation between the bivariate responses for the same sampling unit. The posterior summaries of interest are obtained through Markov Chain Monte Carlo methods. To demonstrate the effectiveness of the proposed methodology, we apply it to a bivariate data set from stellar astronomy that includes left-censored observations and covariates. Our results indicate that the new bivariate model approach, which incorporates the latent factor to capture the potential dependence between the two responses of interest, produces accurate inference results. We also compare the two models using the different likelihood approaches (Weibull or Weibull-Tobit likelihoods) in the application. Overall, our findings suggest that the proposed hierarchical Bayesian analysis is a promising approach for analyzing bivariate positive data with left-censored observations and covariate information.

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The article proposes a new regression based on the generalized odd log-logistic family for interval-censored data. The survival times are not observed for this type of data, and the event of interest occurs at some random interval. This family can be used in interval modeling since it generalizes some popular lifetime distributions in addition to its ability to present various forms of the risk function. The estimation of the parameters is addressed by the classical and Bayesian methods. We examine the behavior of the estimates for some sample sizes and censorship percentages. Selection criteria, likelihood ratio tests, residual analysis, and graphical techniques assess the goodness of fit of the fitted models. The usefulness of the proposed models is red shown by means of two real data sets.

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The aim of this study is to propose a generalized odd log-logistic Maxwell mixture model to analyze the effect of gender and age groups on lifetimes and on the recovery probabilities of Chinese individuals with COVID-19. We add new properties of the generalized Maxwell model. The coefficients of the regression and the recovered fraction are estimated by maximum likelihood and Bayesian methods. Further, some simulation studies are done to compare the regressions for different scenarios. Model-checking techniques based on the quantile residuals are addressed. The estimated survival functions for the patients are reported by age range and sex. The simulation study showed that mean squared errors decay toward zero and the average estimates converge to the true parameters when sample size increases. According to the fitted model, there is a significant difference only in the age group on the lifetime of individuals with COVID-19. Women have higher probability of recovering than men and individuals aged ≥60 years have lower recovered probabilities than those who aged <60 years. The findings suggest that the proposed model could be a good alternative to analyze censored lifetime of individuals with COVID-19.

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Analysing data from educational tests allows governments to make decisions for improving the quality of life of individuals in a society. One of the key responsibilities of statisticians is to develop models that provide decision-makers with pertinent information about the latent process that educational tests seek to represent. Mixtures of t $$ t $$ factor analysers (MtFA) have emerged as a powerful device for model-based clustering and classification of high-dimensional data containing one or several groups of observations with fatter tails or anomalous outliers. This paper considers an extension of MtFA for robust clustering of censored data, referred to as the MtFAC model, by incorporating external covariates. The enhanced flexibility of including covariates in MtFAC enables cluster-specific multivariate regression analysis of dependent variables with censored responses arising from upper and/or lower detection limits of experimental equipment. An alternating expectation conditional maximization (AECM) algorithm is developed for maximum likelihood estimation of the proposed model. Two simulation experiments are conducted to examine the effectiveness of the techniques presented. Furthermore, the proposed methodology is applied to Peruvian data from the 2007 Early Grade Reading Assessment, and the results obtained from the analysis provide new insights regarding the reading skills of Peruvian students.

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Among the models applied to analyze survival data, a standout is the inverse Gaussian distribution, which belongs to the class of models to analyze positive asymmetric data. However, the variance of this distribution depends on two parameters, which prevents establishing a functional relation with a linear predictor when the assumption of constant variance does not hold. In this context, the aim of this paper is to re-parameterize the inverse Gaussian distribution to enable establishing an association between a linear predictor and the variance. We propose deviance residuals to verify the model assumptions. Some simulations indicate that the distribution of these residuals approaches the standard normal distribution and the mean squared errors of the estimators are small for large samples. Further, we fit the new model to hospitalization times of COVID-19 patients in Piracicaba (Brazil) which indicates that men spend more time hospitalized than women, and this pattern is more pronounced for individuals older than 60 years. The re-parameterized inverse Gaussian model proved to be a good alternative to analyze censored data with non-constant variance.

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The discriminative and predictive power of a continuous-valued marker for survival outcomes can be summarized using the receiver operating characteristic and predictiveness curves, respectively. In this paper, fully parametric and semi-parametric copula-based constructions of the joint model of the marker and the survival time are developed for characterizing, plotting, and analyzing both curves along with other underlying performance measures. The formulations require a copula function, a parametric specification for the margin of the marker, and either a parametric distribution or a non-parametric estimator for the margin of the time to event, to respectively characterize the fully parametric and semi-parametric joint models. Estimation is carried out using maximum likelihood and a two-stage procedure for the parametric and semi-parametric models, respectively. Resampling-based methods are used for computing standard errors and confidence bounds for the various parameters, curves, and associated measures. Graphical inspection of residuals from each conditional distribution is employed as a guide for choosing a copula from a set of candidates. The performance of the estimators of various classification and predictiveness measures is assessed in simulation studies, assuming different copula and censoring scenarios. The methods are illustrated with the analysis of two markers using the familiar primary biliary cirrhosis data set.

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Polycyclic aromatic hydrocarbons (PAHs) are considered potentially toxic, even carcinogenic, because of their affection to public health and the environment. It is necessary to know their ambient levels and the origin of these pollutants in order to mitigate them. A concerning scenario is the one in which commercial/administrative, industrial, and residential activities coexist. In this context, Gran La Plata (Argentina) presents such characteristics, in addition to the presence of one of the most important petrochemical complexes in the country and intense vehicular traffic. The source apportionment of PAH emission in the region, associated to 10-µm and 2.5-µm particulate matter fractions, was studied. First, different missing value imputation methods were evaluated for PAH databases. GSimp presented a better performance, with mean concentrations of ∑PAHs of 65.8 ± 40.2 ng m-3 in PM10 and 39.5 ± 18.0 ng m-3 in PM2.5. For both fractions, it was found that the highest contribution was associated with low molecular weight PAHs (3 rings), with higher concentrations of anthracene. Emission sources were identified by using principal component analysis (PCA) together with multiple linear regression (MLR) and diagnostic ratios of PAHs. The results showed that the main emission source is associated with vehicular traffic in both fractions. Classification by discriminant analysis showed that emissions can be identified by region and that fluoranthene, benzo(a)anthracene, and anthracene in PM10 and anthracene and phenanthrene in PM2.5 are a characteristic of emissions from the petrochemical complex.

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This article extends the semiparametric mixed model for longitudinal censored data with Gaussian errors by considering the Student's t $$ t $$ -distribution. This model allows us to consider a flexible, functional dependence of an outcome variable over the covariates using nonparametric regression. Moreover, the proposed model takes into account the correlation between observations by using random effects. Penalized likelihood equations are applied to derive the maximum likelihood estimates that appear to be robust against outlying observations with respect to the Mahalanobis distance. We estimate nonparametric functions using smoothing splines under an EM-type algorithm framework. Finally, the proposed approach's performance is evaluated through extensive simulation studies and an application to two datasets from acquired immunodeficiency syndrome clinical trials.

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In longitudinal studies involving laboratory-based outcomes, repeated measurements can be censored due to assay detection limits. Linear mixed-effects (LMEs) models are a powerful tool to model the relationship between a response variable and covariates in longitudinal studies. However, the linear parametric form of linear mixed-effect models is often too restrictive to characterize the complex relationship between a response variable and covariates. More general and robust modeling tools, such as nonparametric and semiparametric regression models, have become increasingly popular in the last decade. In this article, we use semiparametric mixed models to analyze censored longitudinal data with irregularly observed repeated measures. The proposed model extends the censored linear mixed-effect model and provides more flexible modeling schemes by allowing the time effect to vary nonparametrically over time. We develop an Expectation-Maximization (EM) algorithm for maximum penalized likelihood estimation of model parameters and the nonparametric component. Further, as a byproduct of the EM algorithm, the smoothing parameter is estimated using a modified linear mixed-effects model, which is faster than alternative methods such as the restricted maximum likelihood approach. Finally, the performance of the proposed approaches is evaluated through extensive simulation studies as well as applications to data sets from acquired immune deficiency syndrome studies.

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Survival data involving silent events are often subject to interval censoring (the event is known to occur within a time interval) and classification errors if a test with no perfect sensitivity and specificity is applied. Considering the nature of this data plays an important role in estimating the time distribution until the occurrence of the event. In this context, we incorporate validation subsets into the parametric proportional hazard model, and show that this additional data, combined with Bayesian inference, compensate the lack of knowledge about test sensitivity and specificity improving the parameter estimates. The proposed model is evaluated through simulation studies, and Bayesian analysis is conducted within a Gibbs sampling procedure. The posterior estimates obtained under validation subset models present lower bias and standard deviation compared to the scenario with no validation subset or the model that assumes perfect sensitivity and specificity. Finally, we illustrate the usefulness of the new methodology with an analysis of real data about HIV acquisition in female sex workers that have been discussed in the literature.

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Mixed-effects models, with modifications to accommodate censored observations (LMEC/NLMEC), are routinely used to analyze measurements, collected irregularly over time, which are often subject to some upper and lower detection limits. This paper presents a likelihood-based approach for fitting LMEC/NLMEC models with autoregressive of order p dependence of the error term. An EM-type algorithm is developed for computing the maximum likelihood estimates, obtaining as a byproduct the standard errors of the fixed effects and the likelihood value. Moreover, the constraints on the parameter space that arise from the stationarity conditions for the autoregressive parameters in the EM algorithm are handled by a reparameterization scheme, as discussed in Lin and Lee (2007). To examine the performance of the proposed method, we present some simulation studies and analyze a real AIDS case study. The proposed algorithm and methods are implemented in the new R package ARpLMEC.

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We propose a new extended regression model based on the logarithm of the generalized odd log-logistic Weibull distribution with four systematic components for the analysis of survival data. This regression model can be very useful and could give more realistic fits than other special regression models. We obtain the maximum likelihood estimates of the model parameters for censored data and address influence diagnostics and residual analysis. We prove empirically the importance of the proposed regression by means of a real data set (survival times of the captive snakes) from a study carried out at the Herpetology Laboratory of the Butantan Institute in São Paulo, Brazil.

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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.

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Recreational waters are a source of many diseases caused by human viral pathogens, including norovirus genogroup II (NoV GII) and enterovirus (EV). Water samples from the Arenales river in Salta, Argentina, were concentrated by ultrafiltration and analyzed for the concentrations of NoV GII and EV by quantitative PCR. Out of 65 samples, 61 and 59 were non-detects (below the Sample Limit of Detection limit, SLOD) for EV and NoV GII, respectively. We hypothesized that a finite number of environmental samples would lead to different conclusions regarding human health risks based on how data were treated and fitted to existing distribution functions. A quantitative microbial risk assessment (QMRA) was performed and the risk of infection was calculated using: (a) two methodological approaches to find the distributions that best fit the data sets (methods H and R), (b) four different exposure scenarios (primary contact for children and adults and secondary contact by spray inhalation/ingestion and hand-to-mouth contact), and (c) five alternatives for treating censored data. The risk of infection for NoV GII was much higher (and exceeded in most cases the acceptable value established by the USEPA) than for EV (in almost all the scenarios within the recommended limit), mainly due to the low infectious dose of NoV. The type of methodology used to fit the monitoring data was critical for these datasets with numerous non-detects, leading to very different estimates of risk. Method R resulted in higher projected risks than Method H. Regarding the alternatives for treating censored data, replacing non-detects by a unique value like the average or median SLOD to simplify the calculations led to the loss of information about the particular characteristics of each sample. In addition, the average SLOD was highly impacted by extreme values (due to events such as precipitations or point source contamination). Instead, using the SLOD or half- SLOD captured the uniqueness of each sample since they account for the history of the sample including the concentration procedure and the detection method used. Finally, substitution of non-detects by Zero is not realistic since a negative result would be associated with a SLOD that can change by developing more efficient and sensitive methodology; hence this approach would lead to an underestimation of the health risk. Our findings suggest that in most cases the use of the half-SLOD approach is appropriate for QMRA modeling.

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Cure rate models have been widely studied to analyze time-to-event data with a cured fraction of patients. Our proposal consists of incorporating frailty into a cure rate model, as an alternative to the existing models to describe this type of data, based on the Birnbaum-Saunders distribution. Such a distribution has theoretical arguments to model medical data and has shown empirically to be a good option for their analysis. An advantage of the proposed model is the possibility to jointly consider the heterogeneity among patients by their frailties and the presence of a cured fraction of them. In addition, the number of competing causes is described by the negative binomial distribution, which absorbs several particular cases. We consider likelihood-based methods to estimate the model parameters and to derive influence diagnostics for this model. We assess local influence on the parameter estimates under different perturbation schemes. Deriving diagnostic tools is needed in all statistical modeling, which is another novel aspect of our proposal. Numerical evaluation of the considered model is performed by Monte Carlo simulations and by an illustration with melanoma data, both of which show its good performance and its potential applications. Particularly, the illustration confirms the importance of statistical diagnostics in the modeling.

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Knowledge of spatial variation in pollutant profiles among sea turtle nesting locations is limited. This poses challenges in identifying processes shaping this variability and sets constraints to the conservation management of sea turtles and their use as biomonitoring tools for environmental pollutants. We aimed to increase understanding of the spatial variation in polycyclic aromatic hydrocarbon (PAH), organochlorine pesticide (OCP) and polychlorinated biphenyl (PCB) compounds among nesting beaches. We link the spatial variation to turtle migration patterns and the persistence of these pollutants. Specifically, using gas chromatography, we confirmed maternal transfer of a large number of compounds (n = 68 out of 69) among 104 eggs collected from 21 nests across three nesting beaches within the Yucatán Peninsula, one of the world's most important rookeries for hawksbill turtles (Eretmochelys imbricata). High variation in PAH profiles was observed among beaches, using multivariate correspondence analysis and univariate Peto-Prentice tests, reflecting local acquisition during recent migration movements. Diagnostic PAH ratios reflected petrogenic origins in Celestún, the beach closest to petroleum industries in the Gulf of Mexico. By contrast, pollution profiles of OCPs and PCBs showed high similarity among beaches, reflecting the long-term accumulation of these pollutants at regional scales. Therefore, spatial planning of protected areas and the use of turtle eggs in biomonitoring needs to account for the spatial variation in pollution profiles among nesting beaches.

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After undergoing liver transplantation, children are susceptible to oral lesions due to immunosuppressant drugs that are needed to maintain the transplant. In this context, it is important to understand how disease characteristics and age at transplantation influence the development of these lesions. Monitoring of lesions begins after transplantation and children are usually observed by a specialist in stomatology at periodic visits. Consequently, lesion development is estimated to occur between two observed times, and this is characterized as interval-censored data. However, in clinical practice, it is common to assume the moment of observation as the time of event occurrence, thereby excluding interval-censored data. Here, we discuss the impact of excluding interval-censored mechanisms in statistical analyses by using simulation studies to consider differences in sample sizes and amplitudes between observed intervals. Then, application studies are presented which use a data set from a prospective study that was conducted to investigate oral lesions in patients after liver transplantation at the A.C.Camargo Cancer Center in Brazil between 2013 and 2016 and a data set involving recurrent ovarian cancer in patients diagnosed with high-grade serous carcinoma at the A.C.Camargo Cancer Center between 2003 and 2016 (AU)

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In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum-Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum-likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real-world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.

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In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.

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A survey of 210Pb activity concentration, one of the major internal natural radiation sources to man, has been carried in the most common species of beans (Phaseolus vulgaris L.) grown and consumed in Brazil. The representative bean types chosen, Carioca beans and black type sown in the Brazilian Midwestern and Southern regions, have been collected in this study and 210Pb determined by liquid scintillation spectrometry after separation with chromatographic extraction using Sr-resin. Available values in data set of radioactivity in Brazil (GEORAD) on the 210Pb activity concentration in black beans grown in Southeastern region have been added to the results of this study with the purpose of to amplify the population considered. Concerning the multiple detection limits and due to the high level of censored observations, a robust semi-parametric statistical method called regression on order statistics (ROS) has been employed to provide a reference value of the 210Pb in Brazilian beans, which amounted to 41 mBq kg-1 fresh wt. The results suggest that the 210Pb activity concentration in carioca beans is lower than in black beans. Also evaluated was the 210Pb activity concentration in vegetable component of a typical diet, which displays lower values than those shown in the literature for food consumed in Europe.

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