This paper presents a comprehensive investigation of statistical inference and predictive analysis for two Poisson-exponential distributions using a joint type-II censored sample. The Poisson-exponential distribution is widely used in reliability and survival analysis where failure times follow an exponential distribution within each groups. Parameter estimation is performed using the expectation-maximization algorithm, with approximate confidence intervals derived from the observed Fisher information matrix. Bayesian estimators are obtained via importance sampling under squared error, linear-exponential, and generalized entropy loss functions, along with corresponding credible intervals. A shrinkage pretest estimator combining Bayesian and maximum likelihood approaches is also proposed. The paper provides the best unbiased and Bayesian predictors for future failure times based on the observed joint type-II censored data, including point and interval predictions. Extensive simulations across various sample sizes evaluate the proposed methods, and their practical application is illustrated using two real datasets.

The Beta Regression (BR) model is useful in the analysis of bounded continuous outcomes such as proportions. It is well-known that for any regression model, the presence of multicollinearity leads to poor performance of the maximum likelihood estimators. Furthermore, when some predictors have insignificant or weak effects on the outcomes, it is desirable to recover as much information as possible from these predictors instead of discarding them altogether. In this paper, we propose ridge-type shrinkage estimators for the BR model that, addressing both multicollinearity and information recovery from weak predictors in low- and high-dimensional settings. For the high-dimensional case, we adopt a two-stage "screen-then-shrink" strategy in the first stage, we apply a machine learning variable selection algorithm known as Boruta, and in the second stage we construct ridge-type shrinkage estimators using the selected variables. We show that, under mild conditions, the Boruta screening step enjoys a sure-screening property and controls the number of false positives. Furthermore, we show that the second-stage ridge-type estimators operate in a low-dimensional regime and achieve oracle efficiency. We illustrate the usefulness of the methods by simulations as well as application to two real data sets, one in economics and the other in health care.

Variable selection is a central challenge in logistic regression, particularly in high-dimensional biomedical applications where correlated predictors and limited sample sizes complicate reliable identification of relevant variables. This study aims to systematically compare three widely used variable selection approaches - Boruta, LASSO, and Elastic Net - under a range of data-generating conditions and to illustrate their performance using an ovarian cancer miRNA dataset. We conducted a simulation study across 36 logistic regression scenarios varying in sample size, dimensionality, predictor correlation, and effect magnitude. Performance was evaluated using true-positive and false-positive selection rates. In addition, all three methods were applied to a real-world serum miRNA expression dataset, and discriminative performance was assessed using the area under the receiver operating characteristic curve (AUC). Boruta, Elastic Net, and LASSO exhibited distinct variable selection behaviors across simulation scenarios. Boruta maintained strong true-positive recovery while controlling false positives in most settings, particularly when predictors were highly correlated. Elastic Net consistently achieved high sensitivity but produced comparatively large false-positive rates. LASSO showed the most conservative behavior, recovering fewer true predictors while maintaining low false-positive rates across nearly all scenarios. In the ovarian cancer miRNA application, all three methods achieved similarly strong test-set AUC performance, despite marked differences in the size of the selected biomarker panels. The results demonstrate clear trade-offs among the three methods. Boruta offers a favorable balance between sensitivity and specificity in highly correlated settings. Elastic Net prioritizes sensitivity at the cost of increased false discoveries, whereas LASSO provides stricter false-positive control with reduced sensitivity. These findings offer practical guidance for selecting variable selection methods in logistic regression, particularly for high-dimensional biomedical applications.

Literature suggested that using the traditional factor analysis for the count data may be inappropriate. With that in mind, discrete factor analysis builds on fitting systems of dependent discrete random variables to data. The data should be in the form of non-negative counts. Data may also be truncated at some positive integer value. The discFA package in R allows for two distributions: Poisson and Negative Binomial, in combination with possible zero inflation and possible truncation, hence, eight different alternatives. A forward search algorithm is employed to find the model optimal factor model with the lowest AIC. Several different illustrative examples from psychology, agriculture, car industry, and a simulated data will be analyzed at the end.

Regularization methods such as LASSO, adaptive LASSO, Elastic-Net, and SCAD are widely employed for variable selection in statistical modeling. However, these methods primarily focus on variables with strong effects while often overlooking weaker signals, potentially leading to biased parameter estimates. To address this limitation, Gao, Ahmed, and Feng (2017) introduced a corrected shrinkage estimator that incorporates both weak and strong signals, though their results were confined to linear models. The applicability of such approaches to survival data remains unclear, despite the prevalence of survival regression involving both strong and weak effects in biomedical research. To bridge this gap, we propose a novel class of post-selection shrinkage estimators tailored to the Cox model framework. We establish the asymptotic properties of the proposed estimators and demonstrate their potential to enhance estimation and prediction accuracy through simulations that explicitly incorporate weak signals. Finally, we validate the practical utility of our approach by applying it to two real-world datasets, showcasing its advantages over existing methods.

Introduction: Road traffic injuries (RTIs) are one of the most important public health problems and causes of mortality worldwide, and especially in Iran. Methods: We used data from 2017-03-19 to 2021-03-20 registered in RTIs by the East Azerbaijan forensic medicine organization database. Information on predictor variables was obtained from traffic monitoring cameras’ data. We developed eight machine learning prediction models: logistic regression (LR), elastic net regression, decision tree (DT), random forest (RF), extreme gradient boosting (EGB), support vector machines (SVM; linear and non-linear), and artificial neural networks (ANNs). We used RF to evaluate the importance of each predictor in the prediction of death. Results: The mean number of classes 1, 2, and 4 vehicles on the road on days when death occurred was significantly higher than on days without death and there was an opposite significant pattern for vehicle types 3 and 5. Similar to the training data, RF provided the highest prediction accuracy with an AUC of 91% (95% CI:88%-93%) in the testing data. The total number of type 2 vehicles on the roads is by far the most important and relevant predictor variable (variable importance:83.95) followed by the number of instances of unsafe distance while driving (58.50). The number of Class 4 vehicles (56.58%) and average speed of vehicles (56.31%) were the next most important variables. Conclusion: Using the RF machine learning algorithm, the occurrence of death in accidents can be predicted with very high accuracy using the number of class 2 vehicles on roads.

Background: This study aimed to identify some risk factors associated with time to diabetes type II events using artificial intelligence (AI) survival models (SM) in a population cohort from East Azerbaijan, Iran. Methods: Data from Azar-Cohort spanning from 2014 to 2020 was analyzed using the random forest (RF) variable selection method along with Cox regression to identify the most relevant risk factors associated with diabetes. We then developed prediction models using RF survival analysis. Lasso-variable selection and RF variable selection were used to select the most important variables. The concordance index (C-index) was used to evaluate the concordance of the prediction models. Results: Our LASSO-Cox regression identified six factors to be significantly associated with diabetes: age, mean corpuscular hemoglobin concentration (MCHC), waist circumference (WC), body mass index (BMI), use of sleep medication, and hypertension stage 1 and stage 2. The model included all variables with a C-index of 76.3%. In contrast, the RF analysis identified 21 important variables predicting a higher probability of having diabetes. Of those, WC, MCHC, triglyceride, and age were the most important predictors of diabetes. The RF model converged after 500 trees with an out-of-bag (OOB) of 0.28 and a C-index of 79.5%. Conclusion: RF machine learning algorithms and LASSO-Cox regression analyses consistently identified WC, hypertension, and MCHC as the main risk factors for developing diabetes. The RF approach demonstrated slightly better accuracy in predicting the likelihood of diabetes at different time points.

In modeling count data with overdispersion and extra zeros, zero-inflated negative binomial (ZINB) regression model is useful. In a regression model, the multicollinearity problem arises when there are some high correlations between predictor variables. This problem leads to the maximum likelihood method will not be an efficient estimator. The ridge and Liu-type estimators have been proposed to combat the multicollinearity problem so that the Liu-type estimator is better. In this paper, we proposed the Liu-type shrinkage estimators, namely linear shrinkage, preliminary test, shrinkage preliminary test, Stein-type, and positive Stein-type Liu estimators to estimate the count parameters in the ZINB model, when some of the predictor variables have not a significant effect to predict the response variable so that a sub-model may be sufficient. The asymptotic distributional biases and variances of the proposed estimators are nicely demonstrated. We also compared the performance of the Liu-type shrinkage estimators along with the Liu-type unrestricted estimator by using an extensive Monte Carlo simulation study. The results show that the performances of the proposed estimators are superior to those based on Liu-type unrestricted estimators. We also applied the proposed estimation methods to Expenditure and Default Data.

Estimation of reliability and stress–strength parameters is important in the manufacturing industry. In this paper, we develop shrinkage-type estimators for the reliability and stress–strength parameters based on progressively censored data from a rich class of distributions. These new estimators improve the performance of the commonly used Maximum Likelihood Estimators (MLEs) by reducing their mean squared errors. We provide analytical asymptotic and bootstrap confidence intervals for the targeted parameters. Through a detailed simulation study, we demonstrate that the new estimators have better performance than the MLEs. Finally, we illustrate the application of the new methods to two industrial data sets, showcasing their practical relevance and effectiveness.

To predict preterm birth (PTB) in multiparous women, comparing machine learning approaches with traditional logistic regression. A population-based cohort study was conducted using data from the Ontario Better Outcomes Registry and Network (BORN). The cohort included all multiparous women who delivered a singleton birth at 20-42 weeks' gestation in an Ontario hospital between April 1, 2012 and March 31, 2014. The primary outcome was PTB < 37 weeks, with spontaneous PTB analyzed as a secondary outcome. Stepwise logistic regression and the Boruta machine learning were used to select the important variables during the first and second trimester. For building prediction models, the whole data set were divided for the two independent parts: two-third for training the classifiers (Logistic regression, random forests, decision trees, and artificial neural networks) and one-third for model validation. Then, the training data set were balanced by random over sampling technique. The best hyper parameters were obtained by the tenfold cross validation. The performance of all models was evaluated by sensitivity, specificity, positive predictive value, negative predictive value, and the area under the receiver operating characteristics (AUC). The cohort included 145,846 births, of which 8125 (5.57%) were preterm. In first-trimester models, the strongest predictors of PTB were previous PTB, preexisting diabetes, and abnormal pregnancy-associated plasma protein-A. In the testing data set, the highest predictive ability was seen for artificial neural networks, with an area under the receiver operating characteristic curve (AUC) of 68.8% (95% CI 67.6-70.1%). In second-trimester models, addition of infant sex, attendance at first-trimester appointment, medication exposure, and abnormal alpha-fetoprotein concentrations increased the AUC to 72.1% (95% CI 71.1-73.1%) with logistic regression. With the inclusion of the variable complications during pregnancy, the AUC increased to 80.5% (95% CI 79.6-81.5%) using logistic regression. For both overall and spontaneous PTB, during both the first and second trimesters, models yielded negative predictive values of 97%. Overall, machine learning and logistic regression produced similar performance for prediction of PTB. For overall and spontaneous PTB, both first- and second-trimester models provided negative predictive values of similar to 97%, higher than that of fetal fibronectin.

In this article, we improve parameter estimation in the zero-inflated Poisson regression model using shrinkage strategies when it is suspected that the regression parameter vector may be restricted to a linear subspace. We consider a situation where the response variable is subject to right-censoring. We develop the asymptotic distributional biases and risks of the shrinkage estimators. We conduct an extensive Monte Carlo simulation for various combinations of the inactive predictors and censoring constants to compare the performance of the proposed estimators in terms of their simulated relative efficiencies. The results demonstrate that the shrinkage estimators outperform the classical estimator in certain parts of the parameter space. When there are many inactive predictors in the model, as well as when the censoring percentage is low, the proposed estimators perform better. The performance of the positive Stein-type estimator is superior to the Stein-type estimator in certain parts of the parameter space. We evaluated the estimators' performance using wildlife fish data.

The Burr-XII distribution has been widely applied in engineering, reliability, and survival analysis. Due to its importance, in this article, statistical inferences for Burr-XII distribution under a joint type-II censoring scheme is discussed. The classical likelihood estimation of unknown model parameters is studied via different calculating approaches, such as the expectation-maximization (EM) algorithm and approximate confidence intervals (ACIs) using the observed Fisher information matrix are obtained. The asymptotic bootstrap confidence intervals are also computed. In the sequel, Bayesian estimations of unknown parameters with a gamma prior distribution are considered under squared error, linear-exponential, and generalized entropy loss functions. Subsequently, we calculate the Bayesian credible interval using the importance sample. The performance of the developed methods is investigated through a Monte Carlo simulation study and two real-life examples. The results showed that the proposed estimation strategies have satisfactory results. However, Bayesian approaches were preferable to EM in terms of lower mean square error and higher coverage probability.

IntroductionIn gynecologic oncology, ovarian cancer is a great clinical challenge. Because of the lack of typical symptoms and effective biomarkers for noninvasive screening, most patients develop advanced-stage ovarian cancer by the time of diagnosis. MicroRNAs (miRNAs) are a type of non-coding RNA molecule that has been linked to human cancers. Specifying diagnostic biomarkers to determine non-cancer and cancer samples is difficult. MethodsBy using Boruta, a novel random forest-based feature selection in the machine-learning techniques, we aimed to identify biomarkers associated with ovarian cancer using cancerous and non-cancer samples from the Gene Expression Omnibus (GEO) database: GSE106817. In this study, we used two independent GEO data sets as external validation, including GSE113486 and GSE113740. We utilized five state-of-the-art machine-learning algorithms for classification: logistic regression, random forest, decision trees, artificial neural networks, and XGBoost. ResultsFour models discovered in GSE113486 had an AUC of 100%, three in GSE113740 with AUC of over 94%, and four in GSE113486 with AUC of over 94%. We identified 10 miRNAs to distinguish ovarian cancer cases from normal controls: hsa-miR-1290, hsa-miR-1233-5p, hsa-miR-1914-5p, hsa-miR-1469, hsa-miR-4675, hsa-miR-1228-5p, hsa-miR-3184-5p, hsa-miR-6784-5p, hsa-miR-6800-5p, and hsa-miR-5100. Our findings suggest that miRNAs could be used as possible biomarkers for ovarian cancer screening, for possible intervention.

In this paper, we address the estimation of fixed effects parameters in the zero-inflated negative binomial mixed model based on shrinkage estimators, namely linear shrinkage, pretest, shrinkage pretest, shrinkage, and positive-shrinkage estimators when the random effects are considered as nuisance parameters. We compare the performance of the shrinkage estimators to unrestricted and restricted estimators when certain prior subspace information is available. The asymptotic distributional biases and risks of the proposed estimators are obtained. We also conduct a Monte Carlo simulation study to compare the performance of each estimator in the sense of simulated relative efficiency. The results of simulation study show that the proposed estimation strategies perform strongly better than the maximum likelihood method. Finally, proposed methodologies are applied to a real dataset to appraise their performances.

The paper considers the problem of estimation of the regression coefficients in a Poisson regression model under multicollinearity situation. We propose non-penalty Stein-type shrinkage ridge estimation approach when it is conjectured that some prior information is available in the form of potential linear restrictions on the coefficients. We establish the asymptotic distributional biases and risks of the proposed estimators and investigate their relative performance with respect to the unrestricted ridge estimator. For comparison sake, we consider the two penalty estimators, namely, least absolute shrinkage and selection operator and Elastic-Net estimators and compare numerically their relative performance with the other listed estimators. Monte-Carlo simulation experiment is conducted to evaluate the performance of each estimator in terms of the simulated relative efficiency. The results show that the shrinkage ridge estimators perform better than the penalty estimators in certain parts of the parameter space. Finally, a real data example is illustrated to evaluate of the proposed methods.

Lomax distribution has been widely used in economics, business and actuarial sciences. Due to its importance, we consider the statistical inference of this model under joint type-II censoring scenario. In order to estimate the parameters, we derive the Newton-Raphson(NR) procedure and we observe that most of the times in the simulation NR algorithm does not converge. Consequently, we make use of the expectation-maximization (EM) algorithm. Moreover, Bayesian estimations are also provided based on squared error, linear-exponential and generalized entropy loss functions together with the importance sampling method due to the structure of posterior density function. In the sequel, we perform a Monte Carlo simulation experiment to compare the performances of the listed methods. Mean squared error values, averages of estimated values as well as coverage probabilities and average interval lengths are considered to compare the performances of different methods. The approximate confidence intervals, bootstrap-p and bootstrap-t confidence intervals are computed for EM estimations. Also, Bayesian coverage probabilities and credible intervals are obtained. Finally, we consider the Bladder Cancer data to illustrate the applicability of the methods covered in the paper.

This paper considers the problems of estimation and prediction when lifetime data following Poisson-exponential distribution are observed under type-I hybrid censoring. For both the problems, we compute point and associated interval estimates under classical and Bayesian approaches. For point estimates in the problem of estimation, we compute maximum likelihood estimates using Newton-Raphson, Expectation-Maximization and Stochastic Expectation-Maximization algorithms under classical approach, and under Bayesian approach we compute Bayes estimates with the help of Lindley and importance sampling technique under informative and non-informative priors using symmetric and asymmetric loss functions. The associated interval estimates are obtained using the Fisher information matrix and Chen and Shao method respectively under classical and Bayesian approaches. Further, the predictive point estimates and associated predictive interval estimates are computed by making use of best unbiased and conditional median predictors under classical approach, and Bayesian predictive and associated Bayesian predictive interval estimates in the problem of prediction. We analysis real data set, and conduct Monte Carlo simulation study for the comparison of various proposed methods of estimation and prediction. Finally, a conclusion is given.

In this article, we consider the estimation of unknown parameters of Weibull distribution when the lifetime data are observed in the presence of progressively type-I hybrid censoring scheme. The Newton-Raphson algorithm, Expectation-Maximization (EM) algorithm and Stochastic EM (SEM) algorithm are utilized to derive the maximum likelihood estimates (MLEs) for the unknown parameters. Moreover, Bayesian estimators using Tierney-Kadane Method and Markov Chain Monte Carlo (MCMC) method are obtained under three different loss functions, namely, squared error loss (SEL), linear-exponential (LINEX) and generalized entropy loss (GEL) functions. Also, the shrinkage pre-test estimators are derived. An extensive Monte Carlo simulation experiment is conducted under different schemes so that the performances of the listed estimators are compared using mean squared error, confidence interval length and coverage probabilities. Asymptotic normality and MCMC samples are used to obtain the confidence intervals and highest posterior density (HPD) intervals respectively. Further, a real data example is presented to illustrate the methods. Finally, some conclusive remarks are presented.

In this study, we are aiming to estimate the stress-strength reliability, R=P(Y

Aim: This study aimed to accurately identification of potential miRNAs for gastric cancer (GC) diagnosis at the early stages of the disease. Methods: We used GSE106817 data with 2,566 miRNAs to train the machine learning models. We used the Boruta machine learning variable selection approach to identify the strong miRNAs associated with GC in the training sample. We then validated the prediction models in the independent sample GSE113486 data. Finally, an ontological analysis was done on identified miRNAs to eliciting the relevant relationships. Results: Of those 2,874 patients in the training the model, there were 115 (4%) patients with GC. Boruta identified 30 miRNAs as potential biomarkers for GC diagnosis and hsa-miR-1343-3p was at the highest ranking. All of the machine learning algorithms showed that using hsa-miR-1343-3p as a biomarker, GC can be predicted with very high precision (AUC; 100%, sensitivity; 100%, specificity; 100% ROC; 100%, Kappa; 100) using with the cut-off point of 8.2 for hsa-miR-1343-3p. Also, ontological analysis of 30 identified miRNAs approved their strong relationship with cancer associated genes and molecular events. Conclusion: The hsa-miR-1343-3p could be introduced as a valuable target for studies on the GC diagnosis using reliable biomarkers.