Search Results (64)

Background/Objectives: Ibrutinib has significantly improved outcomes in chronic lymphocytic leukemia (CLL), but evidence from real-world settings on the impact of early dose modifications and consequent relative dose intensity (RDI) maintenance on survival outcomes is limited. This study evaluated the impact of dose reductions and RDI maintenance during the first 90 days of treatment on clinical outcomes in patients with CLL receiving ibrutinib in routine clinical practice. Methods: A post hoc analysis of the prospective observational EVIdeNCE study (NCT03720561) was conducted, including 275 patients with CLL treated with ibrutinib. Baseline clinical and biological factors associated with early dose modifications and RDI maintenance over the first 90 days were analyzed. Cox proportional hazards models, adjusted for disease- and patient-related covariates, were applied to assess associations with overall survival (OS) and progression-free survival (PFS), using a landmark approach to control for immortal time bias. Results: Patients with higher comorbidity burden—indicated by higher Cumulative Illness Rating Scale scores and poorer ECOG performance status—were more likely to undergo early dose reductions. RDI declined slightly over 90 days, but most patients maintained ≥80% of their RDI. The impact of disease-risk factors appeared more clearly when assessing the relationship between 100% RDI at 90 days and PFS, with ibrutinib at 100% RDI associated with improved PFS (hazard ratio, HR 2.26, 95% confidence interval, CI: 1.23–4.15). However, after adjusting for patient characteristics (e.g., comorbidity burden and cardiovascular history), the 100% RDI rate no longer showed a statistically significant effect on PFS (HR 1.84, 95% CI: 0.93–3.63). Conclusions: Baseline comorbidities and functional status drive early dose modifications, but these adjustments and RDI variability do not independently impact survival outcomes, confirming the overall tolerability of ibrutinib in real-world CLL management. Full article

The choice of probability distribution is strongly data-dependent, as observed in several studies. Given the central role of statistical distribution in predictive analytics, researchers have continued to develop new models that accurately capture underlying data behaviours. This study proposes the Hybrid Weibull–Exponentiated Rayleigh distribution developed by compounding the Weibull and Exponentiated Rayleigh distributions via the T-X transformation framework. The new three-parameter distribution is formulated to provide a flexible modelling framework capable of handling data exhibiting non-monotone failure rates. The properties of the proposed distribution, such as the cumulative distribution function, probability density function, survival function, hazard function, linear representation, moments, and entropy, are studied. We estimate the parameters of the distribution using the Maximum Likelihood Estimation technique. Furthermore, the impact of the proposed distribution parameters on the distribution’s shape is studied, particularly its symmetry properties. The shape of the distribution varies with its parameter values, thereby enabling it to model diverse data patterns. This flexibility makes it especially useful for describing the presence or absence of symmetry in real-world failure processes. Simulation studies are conducted to assess the behaviour of the estimators under different parameter settings. The proposed distribution is applied to real-world data to demonstrate its performance. Comparative analysis is performed against other well-established models. The results indicate that the proposed distribution outperforms other models in terms of goodness-of-fit, demonstrating its potential as a superior alternative for modelling lifetime data and reliability analysis based on Akaike Information Criterion and Bayesian Information Criterion. Full article

We develop a unified likelihood-based framework for limited outcomes built on the two-piece normal family. The framework includes a censored specification that accommodates boundary inflation, a doubly truncated specification on $(0,1)$ for rates and proportions, and a survival formulation with a log-two-piece normal baseline and Gamma frailty to account for unobserved heterogeneity. We derive closed-form building blocks (pdf, cdf, survival, hazard, and cumulative hazard), full log-likelihoods with score functions and observed information, and stable reparameterizations that enable routine optimization. Monte Carlo experiments show a small bias and declining RMSE with increasing sample size; censoring primarily inflates the variability of regression coefficients; the scale parameter remains comparatively stable, and the shape parameter is most sensitive under heavy censoring. Applications to HIV-1 RNA with a detection limit, household food expenditure on $(0,1)$, labor-supply hours with a corner solution, and childhood cancer times to hospitalization demonstrate improved fit over Gaussian, skew-normal, and beta benchmarks according to AIC/BIC/CAIC and goodness-of-fit diagnostics, with model-implied censoring closely matching the observed fraction. The proposed formulations are tractable, flexible, and readily implementable with standard software. Full article

The entropy measure of residual cumulative Sharma–Taneja–Mittal is an alternative measure of uncertainty for residual cumulative entropy. This study investigates further theoretical properties and develops nonparametric estimation procedures for the proposed measure. The performance of the estimator is evaluated through simulation experiments, and its practical relevance is illustrated using a real-world dataset on malignant tumor cases. Moreover, we investigate the properties of its dynamic version, including stochastic comparisons and its connections with the hazard rate function, mean residual function, and equilibrium random variables. Moreover, we introduce an alternative version of dynamic residual cumulative Sharma–Taneja–Mittal entropy and examine its monotonic properties. Additionally, we discuss this alternative version and its conditional form in the circumstances of record values. We introduce this alternative expression for the residual lifespan of upper record quantities in general distributions, characterizing it as a measure of upper record quantities derived from a distribution of uniform. Since Sharma–Taneja–Mittal entropy measures uncertainty, we also investigate its use in determining the entropy of the lifespan of mixed and coherent mechanisms, in which the lives of its constituent components are identically distributed and independent. Full article

This article defines an inverted Topp–Leone distribution. Several mathematical properties and maximum likelihood estimation of parameters of this distribution are considered. The shape of the distribution for different sets of parameters is discussed. Several mathematical properties such as the cumulative distribution function, mode, moment-generating function, survival function, hazard rate function, stress-strength reliability R, moments, Rényi entropy, Shannon entropy, Fisher information matrix, and partial ordering associated with this distribution, have been derived. Distributions of the sum and quotient of two independent inverted Topp–Leone variables have also been obtained. Full article

This paper introduces the Marshall–Olkin unit-exponentiated-half-logistic (MO-UEHL) distribution, a novel three-parameter model designed to enhance the flexibility of the unit-exponentiated-half-logistic distribution through the incorporation of the Marshall–Olkin transformation. Defined on the unit interval $(0,1)$, the MO-UEHL distribution is well-suited for modeling proportional data exhibiting asymmetry. The Marshall–Olkin tilt parameter $\alpha$ explicitly controls the degree and direction of asymmetry, enabling the density to range from highly right-skewed to nearly symmetric unimodal forms, and even to left-skewed configurations for certain parameter values, thereby offering a direct mathematical representation of symmetry breaking in bounded proportional data. The resulting model achieves this versatility without relying on exponential terms or special functions, thus simplifying computational procedures. We derive its key mathematical properties, including the probability density function, cumulative distribution function, survival function, hazard rate function, quantile function, moments, and information-theoretic measures such as the Shannon and residual entropy. Parameter estimation is explored using maximum likelihood, maximum product spacing, ordinary and weighted least-squares, and Cramér–von Mises methods, with simulation studies evaluating their performance across varying sample sizes and parameter sets. The practical utility of the MO-UEHL distribution is demonstrated through applications to four real datasets from environmental and engineering contexts. The results highlight the MO-UEHL distribution’s potential as a valuable tool in reliability analysis, environmental modeling, and related fields. Full article

This paper introduces the Lambert-Lindley distribution, a two-parameter extension of the Lindley model constructed through the Lambert-F generator. The new distribution retains the non-negative support of the Lindley distribution and provides additional flexibility by incorporating a shape parameter that controls skewness and tail behavior. Structural properties are derived, including the probability density function, cumulative distribution function, quantile function, hazard rate, and moments. Parameter estimation is addressed using the method of moments and maximum likelihood, and a Monte Carlo simulation study carried out to evaluate the performance of the proposed estimators. The practical applicability of the Lambert–Lindley distribution is demonstrated with two real datasets: stress rupture times of Kevlar/epoxy composites and hospital stay durations of breast cancer patients. Comparative analyses using goodness-of-fit tests and information criteria demonstrate that the proposed model can outperform classical alternatives such as the Gamma and Weibull distributions. Consequently, the Lambert–Lindley distribution emerges as a flexible alternative for modeling positive unimodal data in contexts such as material reliability studies and clinical duration analysis. Full article

In this study, we introduced and analyzed the Slash–Log–Logistic (SlaLL) distribution, a novel statistical model developed by applying the slash methodology to log–logistic and beta distributions. The SlaLL distribution is particularly suited for modeling datasets characterized by heavy tails and extreme values, frequently encountered in survival time analyses. We derived the mathematical representation of the distribution involving Gauss hypergeometric and beta functions, explicitly established the probability density function, cumulative distribution function, hazard rate function, and reliability function, and provided clear definitions of its moments. Through comprehensive simulation studies, the accuracy and robustness of maximum likelihood and Bayesian methods for parameter estimation were validated. Comparative empirical analyses demonstrated the SlaLL distribution’s superior fitting performance over well-known slash-based models, emphasizing its practical utility in accurately capturing the complexities of real-world survival time data. Full article

The paper is intended to put forward a modified Weibull-type lifetime model. Modification consists of replacing the shape parameter of the original Weibull model with the shape function. It is self-evidently a novelty among lifetime models. The model in question will further be named the Weibull-sf model. To present the Weibull-sf, we need appropriate background. The background comes from an extensive review performed on 165 Weibull-type lifetime models we found in the source literature. Performing this review, we focused on two properties of the models: modality of failure density functions, as well as shape of the hazard rate functions. It does not matter that these are strongly interrelated, incidentally. The Weibull-sf lifetime model has the valuable property of flexibility. It may have a bathtub-like hazard rate function and bimodal density function. This is exactly what reliability analysts want to have. Foreseeing the huge numerical problems one will face when trying the maximum-likelihood method, we promote the method of the least absolute values that is a “close relative” to the method of least squares. Examples of fitting the Weibull-sf to real data are given. The cumulative failure functions of bimodal models with a bathtub-like hazard rate function and R codes are given. Full article

Background and Aims: Glecaprevir/pibrentasvir achieves sustained virologic response (SVR) rates above 95% in chronic hepatitis C (CHC). Nevertheless, the residual risk of hepatocellular carcinoma (HCC) after SVR, especially in patients with advanced liver disease, has not been fully defined. We prospectively evaluated longitudinal changes in liver function and fibrosis and sought predictors of post-SVR HCC in a real-world multicenter cohort. Methods: A total of 395 CHC patients who attained SVR with glecaprevir/pibrentasvir were followed prospectively. Liver function tests, noninvasive fibrosis indices, and clinical outcomes were recorded at predefined intervals. Cox proportional hazards regression identified factors associated with incident HCC. Results: Over a median follow-up of 31.1 months, HCC occurred in 16 patients (4.1%). From univariate analysis, baseline FIB-4 > 3.25, APRI > 1.5, MELD ≥ 10, Child–Pugh score ≥ 6, and clinically significant portal hypertension were associated with HCC. Multivariate analysis retained FIB-4 > 3.25 (p = 0.003) and MELD ≥ 10 (p = 0.032) as independent predictors. Cumulative incidence rose stepwise with the number of risk factors. Conclusions: Despite a virologic cure, patients with advanced fibrosis or impaired liver function remain susceptible to HCC. Risk stratification using FIB-4 and MELD and continued surveillance are therefore warranted. Full article

The Maxwell–Boltzmann (MB) distribution is fundamental in statistical physics, providing an exact description of particle speed or energy distributions. In this study, a discrete formulation derived via the survival function discretization technique extends the MB model’s theoretical strengths to realistically handle lifetime and reliability data recorded in integer form, enabling accurate modeling under inherently discrete or censored observation schemes. The proposed discrete MB (DMB) model preserves the continuous MB’s flexibility in capturing diverse hazard rate shapes, while directly addressing the discrete and often censored nature of real-world lifetime and reliability data. Its formulation accommodates right-skewed, left-skewed, and symmetric probability mass functions with an inherently increasing hazard rate, enabling robust modeling of negatively skewed and monotonic-failure processes where competing discrete models underperform. We establish a comprehensive suite of distributional properties, including closed-form expressions for the probability mass, cumulative distribution, hazard functions, quantiles, raw moments, dispersion indices, and order statistics. For parameter estimation under Type-II censoring, we develop maximum likelihood, Bayesian, and bootstrap-based approaches and propose six distinct interval estimation methods encompassing frequentist, resampling, and Bayesian paradigms. Extensive Monte Carlo simulations systematically compare estimator performance across varying sample sizes, censoring levels, and prior structures, revealing the superiority of Bayesian–MCMC estimators with highest posterior density intervals in small- to moderate-sample regimes. Two genuine datasets—spanning engineering reliability and clinical survival contexts—demonstrate the DMB model’s superior goodness-of-fit and predictive accuracy over eleven competing discrete lifetime models. Full article

Background/Objectives: Patients with peripheral artery disease (PAD) have a heightened risk of major adverse cardiovascular events (MACE), including myocardial infarction, stroke, and death. Despite this, limited progress has been made in identifying reliable biomarkers to prognosticate such outcomes. Circulating growth factors, known to influence endothelial function and the progression of atherosclerosis, may hold prognostic value in this context. The objective of this research was to evaluate a broad range of blood-based growth factors to investigate their potential as predictors of MACE in patients diagnosed with PAD. Methods: A total of 465 patients with PAD were enrolled in a prospective cohort study. Baseline plasma levels of five different growth factors were measured, and participants were monitored over a two-year period. The primary outcome was the occurrence of MACE within those two years. Comparative analysis of protein levels between patients who did and did not experience MACE was performed using the Mann–Whitney U test. To assess the individual prognostic significance of each protein for predicting MACE within two years, Cox proportional hazards regression was performed, adjusting for clinical and demographic factors including a history of coronary and cerebrovascular disease. Subgroup analysis was performed to assess the prognostic value of these proteins in females, who may be at higher risk of PAD-related adverse events. Net reclassification improvement (NRI), integrated discrimination improvement (IDI), and area under the receiver operating characteristic curve (AUROC) were calculated to assess the added value of significant biomarkers to model performance for predicting 2-year MACE when compared to using demographic/clinical features alone. Kaplan–Meier curves stratified by IGFBP-1 tertiles compared using log-rank tests and Cox proportional hazards analysis were used to assess 2-year MACE risk trajectory based on plasma protein levels. Results: The average participant age was 71 years (SD 10); 31.1% were female and 47.2% had diabetes. By the end of the two-year follow-up, 18.1% (n = 84) had experienced MACE. Of all proteins studied, only insulin-like growth factor-binding protein 1 (IGFBP-1) showed a significant elevation among patients who suffered MACE versus those who remained event-free (20.66 [SD 3.91] vs. 13.94 [SD 3.80] pg/mL; p = 0.012). IGFBP-1 remained a significant independent predictor of 2-year MACE occurrence in the multivariable Cox analysis (adjusted hazard ratio [HR] 1.57, 95% CI 1.21–1.97; p = 0.012). Subgroup analyses revealed that IGFBP-1 was significantly associated with 2-year MACE occurrence in both females (adjusted HR 1.52, 95% CI 1.16–1.97; p = 0.015) and males (adjusted HR 1.04, 95% CI 1.02–1.22; p = 0.045). Incorporating IGFBP-1 into the clinical risk prediction model significantly enhanced its predictive performance, with an increase in the AUROC from 0.73 (95% CI 0.71–0.75) to 0.79 (95% CI 0.77–0.81; p = 0.01), an NRI of 0.21 (95% CI 0.07–0.36; p = 0.014), and an IDI of 0.041 (95% CI 0.015–0.066; p = 0.008), highlighting the prognostic value of IGFBP-1. Kaplan–Meier analysis showed an increase in the cumulative incidence of 2-year MACE across IGFBP-1 tertiles. Patients in the highest IGFBP-1 tertile experienced a significantly higher event rate compared to those in the lowest tertile (log-rank p = 0.008). In the Cox proportional hazards analysis, the highest tertile of IGFBP-1 was associated with increased 2-year MACE risk compared to the lowest tertile (adjusted HR 1.81; 95% CI: 1.31–2.65; p = 0.001). Conclusions: Among the growth factors analyzed, IGFBP-1 emerged as the sole biomarker independently linked to the development of MACE over a two-year span in both female and male PAD patients. The addition of IGFBP-1 to clinical features significantly improved model predictive performance for 2-year MACE. Measuring IGFBP-1 levels may enhance risk stratification and guide the intensity of therapeutic interventions and referrals to cardiovascular specialists, ultimately supporting more personalized and effective management strategies for patients with PAD to reduce systemic vascular risk. Full article

This study introduces the truncated $(u,v)$-half-normal distribution, a novel probability model defined on the bounded interval $(u,v)$, with parameters $\sigma$ and b. This distribution is designed to model processes with restricted domains, ensuring realistic and analytically tractable outcomes. Some key properties of the proposed model, including its cumulative distribution function, probability density function, survival function, hazard rate, and moments, are derived and analyzed. Parameter estimation of $\sigma$ and b is achieved through a hybrid approach, combining maximum likelihood estimation (MLE) for $\sigma$ and a likelihood-free-inspired technique for b. A sensitivity analysis highlighting the dependence of $\sigma$ on b, and an optimal estimation algorithm is proposed. The proposed model is applied to two real-world data sets, where it demonstrates superior performance over some existing models based on goodness-of-fit criteria, such as the known AIC, BIC, CAIC, KS, AD, and CvM statistics. The results emphasize the model’s flexibility and robustness for practical applications in modeling data with bounded support. Full article

Background/Objectives: Glucagon-like peptide-1 receptor agonists (GLP-1RAs) have revolutionized the treatment of type 2 diabetes and obesity. While their metabolic benefits are well-established, their potential effects on vestibular function remain unexplored. This study investigated the association between GLP-1RA use and the risk of vestibular disorders. Methods: Using the TriNetX research network (accessed 3 November 2024), we conducted a retrospective cohort study of adults prescribed semaglutide (n = 419,497) or tirzepatide (n = 77,259) between January 2018 and October 2024. Cases were matched 1:1 with controls using propensity scores based on demographics and comorbidities. The primary outcome was new-onset vestibular disorders, analyzed at 6 months, 1 year, and 3 years after treatment initiation. Results: Both medications were associated with an increased risk of vestibular disorders. Semaglutide users showed a higher cumulative incidence (0.12% at 6 months to 0.41% at 3 years) compared to controls (0.03% to 0.16%, p < 0.001), with hazard ratios ranging from 4.02 (95% CI: 3.33–4.86) at 6 months to 4.95 (95% CI: 4.51–5.43) at 3 years. Tirzepatide users demonstrated similar patterns but lower absolute rates (0.10% at 6 months to 0.19% at 3 years vs. controls 0.04% to 0.15%), with hazard ratios from 3.19 (95% CI: 2.11–4.81) to 4.55 (95% CI: 3.43–6.03). The direct comparison showed a higher risk with semaglutide versus tirzepatide (RR 1.53–2.04, p < 0.001). Conclusions: GLP-1RA therapy is associated with an increased risk of vestibular disorders, with a higher risk observed with semaglutide compared to tirzepatide. These findings suggest the need for vestibular symptom monitoring in patients receiving these medications and warrant further investigation into underlying mechanisms. Full article

This study introduces two bivariate extensions of the recently proposed weighted discretized Fréchet–Weibull distribution, termed as bivariate weighted discretized Fréchet–Weibull (BWDFW) distributions. These models are specifically designed for analyzing two-dimensional discrete datasets and are developed using two distinct structural approaches: the minimum operator (BWDFW-I) and the maximum operator (BWDFW-II). A rigorous mathematical formulation is presented, encompassing the joint cumulative distribution function, joint probability mass function, and joint (reversed) hazard rate function. The dependence structure of the models is investigated, demonstrating their capability to capture positive quadrant dependence. Additionally, key statistical measures, including covariance, Pearson’s correlation coefficient, Spearman’s rho, and Kendall’s tau, are derived using the joint probability-generating function. For robust statistical inferences, the parameters of the proposed models are estimated via the maximum likelihood estimation method, with extensive simulation studies conducted to assess the efficiency and accuracy of the estimators. The practical applicability of the BWDFW distributions is demonstrated through their implementation in two real-world datasets: one from the aviation sector and the other from the security and safety domain. Comparative analyses against four existing discrete bivariate Weibull extensions reveal the superior performance of the BWDFW models, with BWDFW-I (minimum operator based) exhibiting greater flexibility and predictive accuracy than BWDFW-II (maximum operator based). These findings underscore the potential of the BWDFW models as effective tools for modeling and analyzing bivariate discrete data in diverse applied contexts. Full article