Log-logistic Distribution Research Articles

Robust Explicit Estimation of the Log-Logistic Distribution with Applications

The parameters of the log-logistic distribution are generally estimated based on classical methods such as maximum likelihood estimation, whereas these methods usually result in severe biased estimates when the data contain outliers. In this paper, we consider several alternative estimators, which not only have closed-form expressions, but also are quite robust to a certain level of data contamination. We investigate the robustness property of each estimator in terms of the breakdown point. The finite sample performance and effectiveness of these estimators are evaluated through Monte Carlo simulations and a real-data application. Numerical results demonstrate that the proposed estimators perform favorably in a manner that they are comparable with the maximum likelihood estimator for the data without contamination and that they provide superior performance in the presence of data contamination.

Applications to Bio-Medical data and statistical inference for a Kavya-Manoharan log-logistic model

The log-logistic (LoL) distribution was studied by different authors, but in this article the Kavya-Manoharan log-logistic (KMLoL) distribution is proposed as a new extension of the LoL distribution. Furthermore, the new suggested distribution has two parameters, but it is a very flexible model, as evidenced by the application results. Some statistical features of the KMLoL distribution are derived. The parameters are estimated utilizing three techniques. A simulation study is carried out to evaluate the performance of three different estimation approaches. One real-world data set is utilized to highlight the importance and applicability of the proposed suggested model. The new suggested model compared to well-known distributions which have two, three and four parameters, also it outperform them all of these models.

New Modified Anderson Darling Goodness of Fit Test for Lognormal and Gamma distributions

The purpose of this study is to present the new modified Anderson-Darling goodness of fit test, and compare to the efficiency of three tests; Kolmogorov Smirnov test, Anderson-Darling test and Zhang (2002) test. A simulation study is used to estimate the critical values at a significance level of 0.05. The type I error rate and test power are calculated using Monte Carlo simulation with 10,000 replicates. The data are generated from the specified distribution; i.e., Lognormal and Gamma distributions with sample size of 10, 20, 30, 50, 100 and 200. The results demonstrate that every test has control over the type I error probability. The new test has the highest power for two alternative hypotheses; Loglogistic and Logistic distributions. Moreover, when the alternative distribution is Normal distribution and the sample size is small, the new test has the highest power.

Distribution of Computerized Datasets To Fit Weibull, Log-Logistics and Gompertz Survival Models

The lack of detailed and analytic study on the risk factors of Breast cancer in Nigerian presents us with the challenge of not knowing the risk factors distinct to the Nigerian settings. Effectively handling the breast cancer treatment in co-infected patients is delicate. Some challenges to the treatment of breast cancer infection include drug-to-drug interactions between procedures required to treat the cancer cells, thus the hormonal drugs burdens patient’s inability to comply with dosage intake thereby making women with breast cancer prone to developing other forms of cancer. The aim of the research was to analyzed distributed dataset to fit Weibull, Log-logistics and Gompertz survival models. The research methodology involved the collection of data cases on oncological study analyzed using descriptive statistics and parametric survival models. The result shows that the Cramer-von Misses (W), the Anderson Darling (A) and the Kolmogorov Smirnov (D) statistics, Log-logistic distribution has greater p-value than other distributions, hence it is the best fit for survival times of a group of patients given chemotherapy treatment. The research concluded that Gompertz model was the best fitted model to survival times of a group of patients given chemotherapy treatment data, while log-logistic distribution was the best fit distribution for the data. It also concluded that Weibull and log-logistic models perform better than Gompertz model in fatigue fracture data, while log-logistic distribution was the best fit for the data and Gompertz model and the distribution was the best fit to nicotine measurements.

Mixed-Effects Parametric Proportional Hazard Model with Generalized Log-Logistic Baseline Distribution

Clustered survival data are widely observed in a variety of setting. Most survival models incorporate clustering and grouping of data accounting for between-cluster variability that creates correlation in order to prevent underestimate of the standard errors of the parameter estimators but do not include random effects. In this study, we developed a mixed-effect parametric proportional hazard (MEPPH) model with a generalized log-logistic distribution baseline. The parameters of the model were estimated by the application of the maximum likelihood estimation technique with an iterative optimization procedure (quasi-Newton Raphson). The developed MEPPH model’s performance was evaluated using Monte Carlo simulation. The Leukemia dataset with right-censored data was used to demonstrate the model’s applicability. The results revealed that all covariates, except age in PH models, were significant in all considered distributions. Age and Townsend score were significant when the GLL distribution was used in MEPPH, while sex, age and Townsend score were significant in MEPPH model when other distributions were used. Based on information criteria values, the Generalized Log-Logistic Mixed-Effects Parametric Proportional Hazard model (GLL-MEPPH) outperformed other models.

Neutrosophic Structure of the Log-logistic Model with Applications to Medical Data

In practical scenarios, it is common to encounter fuzzy data that contains numerous imprecise observations. The uncertainty associated with this type of data often leads to the use of interval statistical measures and the proposal of neutrosophic versions of probability distributions to better handle such data. This study introduces a new generalized design of the log-logistic distribution within a neutrosophic framework, building upon encouraging applications of this distribution in fields such as economics, engineering, survival analysis, and lifetime modeling. The proposed neutrosophic log-logistic distribution (NLLD) is analyzed in terms of statistical properties, including moments, shape coefficients, and various survival characteristics. To evaluate the performance of the predicted neutrosophic parameters, an estimation procedure is conducted. Finally, the practical application of the proposed model is demonstrated using a sample dataset consisting of 128 bladder cancer patients.

A novel bivariate Lomax-G family of distributions: Properties, inference, and applications to environmental, medical, and computer science data

<abstract><p>This paper presents a novel family of bivariate continuous Lomax generators known as the BFGMLG family, which is constructed using univariate Lomax generator (LG) families and the Farlie Gumbel Morgenstern (FGM) copula. We have derived several structural statistical properties of our proposed bivariate family, such as marginals, conditional distribution, conditional expectation, product moments, moment generating function, correlation, reliability function, and hazard rate function. The paper also introduces four special submodels of the new family based on the Weibull, exponential, Pareto, and log-logistic baseline distributions. The study establishes metrics for local dependency and examines the significant characteristics of the proposed bivariate model. To provide greater flexibility, a multivariate version of the continuous FGMLG family are suggested. Bayesian and maximum likelihood methods are employed to estimate the model parameters, and a Monte Carlo simulation evaluates the performance of the proposed bivariate family. Finally, the practical application of the proposed bivariate family is demonstrated through the analysis of four data sets.</p></abstract>

Attribute control chart based on SkSP-R scheme under assumption of Log-logistic (LL) distribution

Attribute control chart based on SkSP-R scheme under assumption of Log-logistic (LL) distribution

The Generalized Weibull Uniform Log Logistic Distribution

The Generalized Weibull Uniform Log Logistic Distribution

The Determination of the Most Appropriate Probability Distribution Models for the Meteorological Variables

Every component of the hydrological cycle is essential for controlling water supplies and assessing the potential catastrophic events like floods and droughts. The variables of hydrological system are unexpected and unique to each place. In this paper, the most crucial variables including precipitation, temperature, relative humidity, and evaporation are examined for Ankara province. For meteorological parameters, the Lognormal, Log-logistic, Gamma, Weibull, Normal, and Gumbel models are used to find the best suitable distributions. Kolmogorov-Smirnov, Cramers-von Mises, Akaike's Information Criterion, Bayesian Information Criterion, Anderson-Darling, and Maximum Loglikelihood methods are utilized to test these models. Results shows that there is a distinct distribution model for each parameter. In particular, it has been determined that the Gumbel distribution is a better model for annual total precipitation, whereas the Normal distribution is a better model for annual minimum temperature. At stations 17130 and 17664, the gamma distribution is observed to be the best fit distribution at annual total precipitation, but station 17128 is found to be the most appropriate Log-logistic and normal distribution. Stations 17128, 17130, and 17664 for annual maximum temperature series are fitted with the Normal, Log-logistic, and Lognormal, respectively. Gamma is found to be the best fit when analyzing annual mean temperature for stations 17128 and 17130, whereas Lognormal is selected for station 17664. It is expected that these results will contribute to the planning of water resources projects in the region.

A Versatile Family of Generalized Log-logistic Distributions: Unimodality, Bimodality, Regression, and Applications

In real-world applications, it is not uncommon to encounter situations in which a set of data exhibits asymmetry and bimodality. Because of this, this paper proposes a new versatile family of generalized log-logistic distributions using the method of T-R{Y} framework. The resulting flexible classes of this family includes both unimodal and bimodal distributions which can be expected to model a wide variety of data with different levels of skewness. The distributional and structural properties of the classes are discussed. The method of maximum likelihood is used for estimating the distributions parameters and a simulation study is conducted to examine its performance. The usefulness and goodness-of-fit of some members of these classes are illustrated by means of six real data sets. The strength of these members is shown consistently by giving better fits than some of the competitors with the same number of parameters. In addition, a new generalized log-logistic lifetime regression model is introduced and applied to fit a right-censored data with covariates. The flexibility provided by this model could be very helpful in describing and explaining different types of lifetime data.

The distribution of COVID-19 mortality.

We estimate the distribution of COVID-19 mortality (measured as daily deaths) from the start of the pandemic until July 31st, 2022, for six European countries and the USA. We use the Pareto, the stretched exponential, the log-normal and the log-logistic distributions as well as mixtures of the log-normal and log-logistic distributions. The main results are that the Pareto does not describe well the data and that mixture distributions tend to offer a very good fit to the data. We also compute Value-at-Risk measures as well as mortality probabilities with our estimates. We also discuss the implications of our results and findings from the point of view of public health planning and modelling.

Generalised Lindley shared additive frailty regression model for bivariate survival data

Abstract Frailty models are the possible choice to counter the problem of the unobserved heterogeneity in individual risks of disease and death. Based on earlier studies, shared frailty models can be utilised in the analysis of bivariate data related to survival times (e.g. matched pairs experiments, twin or family data). In this article, we assume that frailty acts additively to the hazard rate. A new class of shared frailty models based on generalised Lindley distribution is established. By assuming generalised Weibull and generalised log-logistic baseline distributions, we propose a new class of shared frailty models based on the additive hazard rate. We estimate the parameters in these frailty models and use the Bayesian paradigm of the Markov Chain Monte Carlo (MCMC) technique. Model selection criteria have been applied for the comparison of models. We analyse kidney infection data and suggest the best model.

Flexible Parametric Accelerated Hazard Model: Simulation and Application to Censored Lifetime Data with Crossing Survival Curves

This study aims to propose a flexible, fully parametric hazard-based regression model for censored time-to-event data with crossing survival curves. We call it the accelerated hazard (AH) model. The AH model can be written with or without a baseline distribution for lifetimes. The former assumption results in parametric regression models, whereas the latter results in semi-parametric regression models, which are by far the most commonly used in time-to-event analysis. However, under certain conditions, a parametric hazard-based regression model may produce more efficient estimates than a semi-parametric model. The parametric AH model, on the other hand, is inappropriate when the baseline distribution is exponential because it is constant over time; similarly, when the baseline distribution is the Weibull distribution, the AH model coincides with the accelerated failure time (AFT) and proportional hazard (PH) models. The use of a versatile parametric baseline distribution (generalized log-logistic distribution) for modeling the baseline hazard rate function is investigated. For the parameters of the proposed AH model, the classical (via maximum likelihood estimation) and Bayesian approaches using noninformative priors are discussed. A comprehensive simulation study was conducted to assess the performance of the proposed model’s estimators. A real-life right-censored gastric cancer dataset with crossover survival curves is used to demonstrate the tractability and utility of the proposed fully parametric AH model. The study concluded that the parametric AH model is effective and could be useful for assessing a variety of survival data types with crossover survival curves.

Cost-Effectiveness of Azacitidine and Ivosidenib in Newly Diagnosed Older, Intensive Chemotherapy-Ineligible Patients with IDH1-Mutant Acute Myeloid Leukemia

Introduction Ivosidenib (IVO) is an oral inhibitor of mIDH1 that is approved in the USA as monotherapy for pts with mIDH1AML, either relapsed/refractory or newly diagnosed, but older/unfit for intensive therapy. The recent AGILE trial (Montesinos et al. NEJM 2022) randomized newly diagnosed, older/intensive chemotherapy-ineligible mIDH1 AML pts to IVO + AZA vs placebo + AZA and showed improved event-free survival (EFS) and overall survival (OS) in the intervention arm. We sought to understand the health economic implications by conducting a cost-effectiveness analysis. Methods Pts with newly diagnosed mIDH1 AML entered our partitioned survival model at age 75 years and received either IVO/AZA or AZA monotherapy. We used recreated pt-level data derived from the Kaplan-Meier curves and at-risk tables for EFS and OS from the AGILE trial for the IVO/AZA arm to fit loglogistic parametric survival distributions. Hazard ratios (HRs) for EFS and OS were used to derive the EFS and OS curves for the AZA arm, respectively. Medication costs were derived from the average sales price (ASP) for AZA and cytarabine listed by the Centers for Medicare and Medicaid Services or the average wholesale price (AWP) for IVO and venetoclax (Ven), respectively. As ASP ranges between 26-30% below the AWP, we used a 28% discount off the AWP for the base-case scenario and varied this discount during sensitivity analyses between 18% and 38%. Costs and practice patterns of treatment discontinuation or treatment interruption due to adverse events, subsequent treatments, supportive and terminal care, and incidence of complications were derived from the original trial or published literature (Table 1). Costs were adjusted for inflation to 2021 US dollars using the personal consumption expenditure health index. Utilities were derived from the literature and were assumed to be equal between treatment arms for the base case scenario as the quality-of-life assessment were not statistically significantly different for IVO/AZA vs AZA in the AGILE trial at most timepoints. Costs and utilities were modeled over a 30-year time horizon and discounted by 3% annually. Model outputs were used to calculate the incremental cost-effectiveness ratio (ICER) for IVO/AZA, which represents the cost in 2021 US dollars (USD) of each additional quality adjusted life-year (QALY) gained compared to AZA. One-way sensitivity analyses were performed to evaluate the impact of individual parameters on the overall model. Utility values were varied with a 10% range and all other variables were varied across a 50% range. We also performed probabilistic sensitivity analyses, in which we described each parameter using a distribution and performed 10,000 Monte Carlo simulations, each time randomly sampling from the distributions of model inputs. Results In the base case scenario, IVO/AZA and AZA resulted in life-time costs of $652,088 and $242,828, respectively, for an incremental cost of $409,260 with IVO/AZA. With an incremental gain of 2.21 QALYs with IVO/AZA (IVO/AZA: 3.10 QALYs; AZA: 0.89 QALYs), the ICER of IVO/AZA compared to AZA was $185,024/QALY. In one-way sensitivity analyses, only a reduction in the AWP of IVO by 32.4% (from $33,693 to $22,788 per 28-day cycle) would yield a reduction in the ICER to below the conventional willingness-to-pay (WTP) threshold of $150,000/QALY. Figure 1 shows the ten variables with the greatest influence on the ICER demonstrating that variations in any of the variables would not achieve an ICER of less than $150,000/QALY. Probabilistic sensitivity analysis yielded a median ICER of $205,124/QALY (95% CI: $129,344 - $346,479) with AZA favored in 91.2% of 10,000 iterations at a WTP threshold of $150,000/QALY. Conclusion Even in the best-case scenario in favor of the IVO arm following AGILE trial assumptions, we calculated an ICER of $185,024/QALY, which makes IVO/AZA unlikely to be cost-effective compared to AZA alone when applying the traditional WTP threshold of $150,000/QALY in patients with newly diagnosed mIDH1 AML. Only a reduction in the price of IVO by 32.4% lowered the ICER to below $150,000/QALY. The influence of more frequent use of 2nd line IVO in the control arm, comparison against an AZA-Ven control arm, differences in utilities, and extended duration of follow up in the prematurely terminated trial on the ICER warrant additional analyses but are likely to further worsen the cost effectiveness of IVO. Figure 1View largeDownload PPTFigure 1View largeDownload PPT Close modal

Characterizing breaking wave slamming loads on bridge piers with probabilistic models of slamming maxima, rise and decay times

The piers of sea-crossing bridges always suffer from considerable breaking wave loads. But the uncertainties and variability of wave slamming maxima and time history have yet been understood quantitatively. This paper conducted a series of experiments in a wave flume to investigate the slamming load of breaking waves on bridge piers with different cross-sections. Four piers with three kinds of cross-sections under three breaking wave conditions were employed in the experimental program. The time history of breaking wave slamming load was characterized by three parameters, i.e., slamming maxima, rise and decay times. To account for the statistical variability of breaking wave load, a pair-copula decomposed trivariate joint probability model was developed to determine the joint distribution of slamming maxima, rise and decay times. The effects of pier geometry on the probabilistic modeling of slamming maxima, rise and decay times are analyzed based on the experimental results. The slamming maxima, rise and decay times follow the generalized extreme value (GEV), log-logistic, and gamma distribution, respectively. Their marginal and joint probabilities are sensitive to the pier shape. This study provides an effective probability method to characterize breaking wave slamming loads based on the experimental results.

MODELING STOCK-CLOSING PRICES: EVIDENCE FROM THE BANKING SECTOR OF JORDAN

This study aims to find the best-fitted distribution of the average closing price (ACP) for the Amman Stock Exchange banking sector using various distributions models, namely, Normal, Gamma, Burr, Weibull, Bareto, lognormal, Log logistic, Exponential, and Gumbel distribution. This will enable financial analysts to forecast stock prices to build their buying and selling decisions. The methodology was applied according to the comparison between maximum likelihood estimation, moment matching, quantile matching and maximum goodness-of-fit estimation. The result of computing the different goodness of fit statistics (K.S), (CvM) and (A.D) and the other statistics based on the log-likelihood (AIC and BIC). The best-fitted distributions have the smaller values for each goodness of fit statistics. The results emphasized that the Gamma distribution is the most appropriate one, which has the lowest values of AIC (364.6), and BIC (373.9).

Rate of publication hastens, but number of publications slows academic promotion.

Openings for an assistant professor often attract a hundred or more applicants. This allows hiring committees to select highly productive candidates based on their number of publications. Applicants with more rapid publication would be hired with little or no postgraduate experience, but those with slower rates of publication would need more postgraduate experience. Our results show an association of more postgraduate experience, slower rates of publication, a smaller research group, and slower promotion when years are measured from PhD granting; conversely little or no postgraduate experience is generally associated with more rapid publication, a larger research group, and faster promotion. These results suggest the unexpected result that the number and rate of publication have opposite effects on the years from PhD granting to promotion which parametric survival analysis using a log-logistic distribution with gamma frailty confirmed. Statistical analysis revealed that number and rate of publication are reciprocal suppressor variables which were individually weaker predictors of years to promotion, but much more powerful when combined. Intuitively, this is probably because number and rate of publication contain information about other variables with: (1) number of publications being associated with more postgraduate experience, a smaller research group, and slower rates of publication; and (2) rate of publication being associated with a larger research group, and less postgraduate experience. Further, we found that promotion committees closely follow institutional tenure policy requiring promotion a fixed number of years after hiring as an assistant professor which may partially explain why promotion committees fail adjust the number and rate of publication for research group size as fairness in promotion might favor. Our results suggest that both postgraduate experience and research group size influence a professor’s career.

Bayesian and Frequentist Approaches for a Tractable Parametric General Class of Hazard-Based Regression Models: An Application to Oncology Data

In this study, we consider a general, flexible, parametric hazard-based regression model for censored lifetime data with covariates and term it the “general hazard (GH)” regression model. Some well-known models, such as the accelerated failure time (AFT), and the proportional hazard (PH) models, as well as the accelerated hazard (AH) model accounting for crossed survival curves, are sub-classes of this general hazard model. In the proposed class of hazard-based regression models, a covariate’s effect is identified as having two distinct components, namely a relative hazard ratio and a time-scale change on hazard progression. The new approach is more adaptive to modelling lifetime data and could give more accurate survival forecasts. The nested structure that includes the AFT, AH, and PH models in the general hazard model may offer a numerical tool for identifying which of them is most appropriate for a certain dataset. In this study, we propose a method for applying these various parametric hazard-based regression models that is based on a tractable parametric distribution for the baseline hazard, known as the generalized log-logistic (GLL) distribution. This distribution is closed under all the PH, AH, and AFT frameworks and can incorporate all of the basic hazard rate shapes of interest in practice, such as decreasing, constant, increasing, V-shaped, unimodal, and J-shaped hazard rates. The Bayesian and frequentist approaches were used to estimate the model parameters. Comprehensive simulation studies were used to evaluate the performance of the proposed model’s estimators and its nested structure. A right-censored cancer dataset is used to illustrate the application of the proposed approach. The proposed model performs well on both real and simulation datasets, demonstrating the importance of developing a flexible parametric general class of hazard-based regression models with both time-independent and time-dependent covariates for evaluating the hazard function and hazard ratio over time.

Trabectedin use in soft-tissue sarcoma patients in a real-world setting: Data from an Italian national drug-access registry.

Trabectedin is a marine-derived anticancer drug approved for the treatment of patients with advanced soft-tissue sarcomas (STS). Here, we aimed to analyze its use in a large cohort of STS patients treated in Italy in a real-world setting. Data on STS patients treated with trabectedin in Italy were prospectively collected from January 2013 to December 2019 by the national drug regulator, the Italian Medicines Agency (AIFA). Time-to-off-treatment (TToT) was defined as the time between the initial prescription of trabectedin and the date of treatment discontinuation for any cause. The impact of the different baseline covariates, including the initial prescribed dose of trabectedin, on TToT was evaluated using an accelerated failure time (AFT) models with log-logistic distribution. In total, we analyzed data from 2633 sarcoma patients and 14 950 individual cycles of trabectedin. The median number of cycles of trabectedin received per patient was 3 (interquartile range 2-7). The labeled 1.5mg/sqm dose was used in 27.3% of all first prescriptions. Overall, the median TToT was 93 days. In the final AFT model, the variables significantly associated to longer TToT were female gender (+13% increase in TToT); ECOG performance status 0 (+50%); histological diagnosis of leiomyosarcoma (+22%), well-differentiated/dedifferentiated liposarcoma (+72%) or myxoid liposarcoma (+61%); receiving treatment in a high-volume center (+23%). In this large real-world cohort of STS patients treated with trabectedin, our findings support the use of trabectedin in STS patients, in particular in leiomyosarcoma and liposarcoma patients, and highlight the role of treatment center volume in their management.