A new flexible regression model with application to recovery probability Covid-19 patients.

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.

The re-parameterized inverse Gaussian regression to model length of stay of COVID-19 patients in the public health care system of Piracicaba, Brazil.

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.

A random effect regression based on the odd log-logistic generalized inverse Gaussian distribution.

In recent decades, the use of regression models with random effects has made great progress. Among these models' attractions is the flexibility to analyze correlated data. In various situations, the distribution of the response variable presents asymmetry or bimodality. In these cases, it is possible to use the normal regression with random effect at the intercept. In light of these contexts, i.e. the desire to analyze correlated data in the presence of bimodality or asymmetry, in this paper we propose a regression model with random effect at the intercept based onthe generalized inverse Gaussian distribution model with correlated data. The maximum likelihood is adopted to estimate the parameters and various simulations are performed for correlated data. A type of residuals for the new regression is proposed whose empirical distribution is close to normal. The versatility of the new regression is demonstrated by estimating the average price per hectare of bare land in 10 municipalities in the state of São Paulo (Brazil). In this context, various databases are constantly emerging, requiring flexible modeling. Thus, it is likely to be of interest to data analysts, and can make a good contribution to the statistical literature.

Log-mean distribution: applications to medical data, survival regression, Bayesian and non-Bayesian discussion with MCMC algorithm.

We introduce a new family via the log mean of an underlying distribution and as baseline the proportional hazards model and derive some important properties. A special model is proposed by taking the Weibull for the baseline. We derive several properties of the sub-model such as moments, order statistics, hazard function, survival regression and certain characterization results. We estimate the parameters using frequentist and Bayesian approaches. Further, Bayes estimators, posterior risks, credible intervals and highest posterior density intervals are obtained under different symmetric and asymmetric loss functions. A Monte Carlo simulation study examines the biases and mean square errors of the maximum likelihood estimators. For the illustrative purposes, we consider heart transplant and bladder cancer data sets and investigate the efficiency of proposed model.

A new regression model for rates and proportions data with applications.

We propose a new continuous distribution in the interval ( 0 , 1 ) based on the generalized odd log-logistic-G family, whose density function can be symmetrical, asymmetric, unimodal and bimodal. The new model is implemented using the gamlss packages in R. We propose an extended regression based on this distribution which includes as sub-models some important regressions. We employ a frequentist and Bayesian analysis to estimate the parameters and adopt the non-parametric and parametric bootstrap methods to obtain better efficiency of the estimators. Some simulations are conducted to verify the empirical distribution of the maximum likelihood estimators. We compare the empirical distribution of the quantile residuals with the standard normal distribution. The extended regression can give more realistic fits than other regressions in the analysis of proportional data.

A new heteroscedastic regression to analyze mass loss of wood in civil construction in Brazil.

A heteroscedastic regression based on the odd log-logistic Marshall-Olkin normal (OLLMON) distribution is defined by extending previous models. Some structural properties of this distribution are presented. The estimation of the parameters is addressed by maximum likelihood. For different parameter settings, sample sizes and some scenarios, various simulations investigate the performance of the heteroscedastic OLLMON regression. We use residual analysis to detect influential observations and to check the model assumptions. The new regression explains the mass loss of different wood species in civil construction in Brazil.

The semiparametric regression model for bimodal data with different penalized smoothers applied to climatology, ethanol and air quality data.

Semiparametric regressions can be used to model data when covariables and the response variable have a nonlinear relationship. In this work, we propose three flexible regression models for bimodal data called the additive, additive partial and semiparametric regressions, basing on the odd log-logistic generalized inverse Gaussian distribution under three types of penalized smoothers, where the main idea is not to confront the three forms of smoothings but to show the versatility of the distribution with three types of penalized smoothers. We present several Monte Carlo simulations carried out for different configurations of the parameters and some sample sizes to verify the precision of the penalized maximum-likelihood estimators. The usefulness of the proposed regressions is proved empirically through three applications to climatology, ethanol and air quality data.

Joint regression modeling of location and scale parameters of the skew t distribution with application in soil chemistry data.

In regression model applications, the errors may frequently present a symmetric shape. In such cases, the normal and Student t distributions are commonly used. In this paper, we shall be concerned only to model heavy-tailed, skewed errors and absence of variance homogeneity with two regression structures based on the skew t distribution. We consider a classic analysis for the parameters of the proposed model. We perform a diagnostic analysis based on global influence and quantile residuals. For different parameter settings and sample sizes, various simulation results are obtained and compared to evaluate the performance of the skew t regression. Further, we illustrate the usefulness of the new regression by means of a real data set (amount of potassium in different soil areas) from a study carried out at the Department of Soil Science of the Luiz de Queiroz School of Agriculture, University of São Paulo.

The multinomial logistic regression model for predicting the discharge status after liver transplantation: estimation and diagnostics analysis.

The multinomial logistic regression model (MLRM) can be interpreted as a natural extension of the binomial model with logit link function to situations where the response variable can have three or more possible outcomes. In addition, when the categories of the response variable are nominal, the MLRM can be expressed in terms of two or more logistic models and analyzed in both frequentist and Bayesian approaches. However, few discussions about post modeling in categorical data models are found in the literature, and they mainly use Bayesian inference. The objective of this work is to present classic and Bayesian diagnostic measures for categorical data models. These measures are applied to a dataset (status) of patients undergoing kidney transplantation.

Microsatellite markers from sugarcane (Saccharum spp.) ESTs cross transferable to erianthus and sorghum.

Analysis of a sugarcane (Saccharum spp.) EST (expressed sequence tag) library of 8678 sequences revealed approximately 250 microsatellite or simple sequence repeats (SSRs) sequences. A diversity of dinucleotide and trinucleotide SSR repeat motifs were present although most were of the (CGG)(n) trinucleotide motif. Primer sets were designed for 35 sequences and tested on five sugarcane genotypes. Twenty-one primer pairs produced a PCR product and 17 pairs were polymorphic. Primer pairs that produced polymorphisms were mainly located in the coding sequence with only a single pair located within the 5' untranslated region. No primer pairs producing a polymorphic product were found in the 3' untranslated region. The level of polymorphism (PIC value) in cultivars detected by these SSRs was low in sugarcane (0.23). However, a subset of these markers showed a significantly higher level of polymorphism when applied to progenitor and related genera (Erianthus sp. and Sorghum sp.). By contrast, SSRs isolated from sugarcane genomic libraries amplify more readily, show high levels of polymorphism within sugarcane with a higher PIC value (0.72) but do not transfer to related species or genera well.