Increasing Hazard Rate Research Articles

Bayesian identification and estimation of radon-related increased hazard rates of cancer death in the updated French cohort of uranium miners (1946-2014).

A recent update of the French cohort of uranium miners added seven years of follow-up data. We use these new data to look for new possible radon-related increased risks and refine the estimation of the potential association between cumulative radon exposure and four cancer sites: lung cancer, kidney cancer, brain and central nervous system (CNS) cancer and leukemia (excluding chronic lymphocytic leukemia, which is not radiation-induced). Several parametric survival models are proposed, fitted and compared under the Bayesian paradigm, to perform new and original exposure-risk analyses. In line with recent UNSCEAR recommendations, we consider time-related effect modifiers and exposure rate as potential effect modifying factors. We use Bayesian model selection criteria to identify radon-related increased hazard rates. Under the assumption of a linear exposure-risk relationship, we found a substantial evidence for a strictly positive effect of cumulative radon exposure on the hazard rate of death by lung cancer among French uranium miners. Given the current available data under the assumptions of a linear or log-linear exposure-risk relationship, it is not possible to conclude in favour of the absence or the existence of a strictly positive effect of chronic exposure to radon on the hazard rate of death by kidney cancer. Regarding death by brain and CNS cancer, there is a substantial evidence for the absence of radon-related effect. Finally, under the assumption of a log-linear exposure-risk relationship, a small positive radon-related effect appears when looking at the risk of death by leukemia (excluding CLL). This study investigates the existence of radon-related increased risk of death by lung cancer, kidney cancer, brain and CNS cancer and leukemia under a Bayesian framework and assumptions of linear and log-linear exposure-risk relationships. If there is no doubt in the interpretation of the results for lung cancer and brain and CNS cancer, the conclusion is less clear-cut in the case of kidney cancer and leukemia (excluding CLL). A future update of the French cohort, increasing the follow-up time for miners, may help to reach a clearer conclusion for these two cancer sites.

Antihypertensive Medications and Eczematous Dermatitis in Older Adults

Rates of physician-diagnosed eczema have been increasing among older adults, but little is known regarding the pathophysiologic processes and best treatments in this subgroup. Preliminary data suggest that medications-antihypertensive medications in particular-may contribute to eczematous dermatitis; however, there are limited population-based data on the proportion of eczematous dermatitis diagnoses among older adults that may be attributed to antihypertensive drugs. To determine whether antihypertensive drug use is associated with eczematous dermatitis in older adults. This was a longitudinal cohort study of a population-based sample of individuals 60 years and older without a diagnosis of eczematous dermatitis at baseline. It was conducted at primary care practices participating in The Health Improvement Network in the United Kingdom from January 1, 1994, to January 1, 2015. Data analyses were performed from January 6, 2020, to February 6, 2024. Exposure date by first prescription for an antihypertensive drug within each drug class. Newly active eczematous dermatitis was based on the first date for 1 of the 5 most common eczema codes used in a previously validated algorithm. Among the total study sample of 1 561 358 older adults (mean [SD] age, 67 [9] years; 54% female), the overall prevalence of eczematous dermatitis was 6.7% during a median (IQR) follow-up duration of 6 (3-11) years. Eczematous dermatitis incidence was higher among participants receiving antihypertensive drugs than those who did not (12 vs 9 of 1000 person-years of follow-up). Adjusted Cox proportional hazard models found that participants who received any antihypertensive drugs had a 29% increased hazard rate of any eczematous dermatitis (hazard ratio [HR], 1.29; 95% CI, 1.26-1.31). When assessing each antihypertensive drug class individually, the largest effect size was observed for diuretic drugs (HR, 1.21; 95% CI, 1.19-1.24) and calcium channel blockers (HR, 1.16; 95% CI, 1.14-1.18), and the smallest effect sizes were for angiotensin-converting enzyme inhibitors (HR, 1.02; 95% CI, 1.00-1.04) and β-blockers (HR, 1.04; 95% CI, 1.02-1.06). This cohort study found that antihypertensive drugs were associated with a small increased rate of eczematous dermatitis, with effect sizes largest for calcium channel blockers and diuretic drugs, and smallest for angiotensin-converting enzyme inhibitors and β-blockers. Although additional research is needed to understand the mechanisms underlying the association, these data could be helpful to clinicians to guide management when a patient presents with eczematous dermatitis in older age.

A flexible model for bounded data with bathtub shaped hazard rate function and applications

<p>The unit new X-Lindley distribution, which is a novel one-parameter distribution on the unit interval, is presented in this study. It was developed by altering the new X-Lindley distribution using the exponential transformation. This new one-parameter distribution's fundamental features, including moments, incomplete moments, Lorenz and Bonferroni curves, Gini index, mode, extropy, Havrda and Charvat entropy, Rényi entropy, and Tsallis entropy, are explored. Additionally, it has bathtub-shaped hazard rate functions and monotonically increasing hazard rate functions with a single parameter. The new distribution is therefore sufficiently rich to model real data. Also, different estimation methods, such as maximum likelihood, least-squares, and weighted least-squares, are used to estimate the parameters of this model, and using a simulation research, their respective performances are evaluated. Finally, two real-life datasets are used to demonstrate the suggested model's competency.</p>

Identifying risk factors of anti-TNF induced skin lesions and other adverse events in paediatric patients with inflammatory bowel disease.

While higher infliximab (IFX) trough concentrations (TCs) are associated with better outcomes in patients with inflammatory bowel disease (IBD), they could pose a risk for adverse events (AEs), including IFX-induced skin lesions. Therefore, we studied correlations between IFX TCs and occurrence of AEs in paediatric IBD patients. In this single-centre study, all children with Crohn's disease (CD) and ulcerative colitis (UC) receiving IFX maintenance therapy who underwent proactive drug monitoring between March 2015 and August 2022 were included. IFX doses/intervals/TCs and patient characteristics were systematically registered, as well as AEs and skin lesions appearance. A total of 109 patients (72 CD and 37 UC) contributed 2913 IFX TCs. During a median follow-up of 3.0 [1.5-4.5] years, we observed 684 AEs in 101 patients and 49 skin lesions in 35 patients. There was no significant difference (p = .467) in median TCs between patients with and without skin lesions. However, higher median IFX doses were associated with an increased hazard rate of skin lesions [HR 1.084 (1.024-1.148), p = .005], in addition to female sex [2.210 (1.187-5.310), p = .016] and diagnosis of CD [1.695 (1.241-1.877), p = .011]. Considering IFX therapeutic TC cut-offs of 5.0 and 9.0 µg/mL, there was no significant difference in AE rate (p = .749 and p = .833, respectively). Also, no significant association between IFX doses and AE rate (p = .159). Increasing the IFX dose to achieve therapeutic TCs may not increase the overall risk of AEs in paediatric IBD patients. However, concerns arise regarding the risk of skin lesions, especially in female CD patients.

Preventive Maintenance and Replacement Model for Mechanically Repairable Systems with Linearly Increasing Hazard Rate

Most machines fail due to lack of appropriate preventive maintenance (PM) and replacement schedule, and this failure leads to higher cost of repair maintenance, distortion of production schedule, elongated downtime period and reduced productivity. These could however be avoided by the utilization of optimal PM and replacement models suited for the specific kind of system. It is on this premise that this work develops an optimal PM and replacement model for mechanically repairable systems with linearly increasing hazard rate which failure distribution of the system is characterized by the Rayleigh distribution. The failure times of a Rolls Royce dredging machine was used as real-time data to obtain the PM and replacement schedule for the machine at respective cost ratios. The results showed that the model provided an effective maintenance schedule for the machine and ensures optimal performance.

New Lifetime Distribution with Applications to Single Acceptance Sampling Plan and Scenarios of Increasing Hazard Rates

This article is an extension of the Chris-Jerry distribution (C-JD) in that a two-parameter Chris-Jerry distribution (TPCJD) is suggested and its characteristics are studied. Based on the determined domain of attraction and other major statistical properties, the proposed TPCJD seems to fit into the Gumbel domain. Additionally, it has been confirmed that the stress strength is reliable. The tail study suggests that the TPCJD’s substantial tail makes it suited for a range of applications. The study took into account the single acceptance sampling approach using both simulation and real-life situations. The parameters of the TPCJD were estimated by some classical and Bayesian approaches. The mean squared errors (MSE), linear-exponential, and generalized entropy loss functions were deployed to obtain the Bayesian estimators aided by the Markov chain Monte Carlo (MCMC) simulation. An analysis of lifetime data on two events justified the use of the proposed distribution after comparing the results with some standard lifetime models.

On the Type-I Half-logistic Distribution and Related Contributions: A Review

The half-logistic (HL) distribution is a widely considered statistical model for studying lifetime phenomena arising in science, engineering, finance, and biomedical sciences. One of its weaknesses is that it has a decreasing probability density function and an increasing hazard rate function only. Due to that, researchers have been modifying the HL distribution to have more functional ability. This article provides an extensive overview of the HL distribution and its generalization (or extensions). The recent advancements regarding the HL distribution have led to numerous results in modern theory and statistical computing techniques across science and engineering. This work extended the body of literature in a summarized way to clarify some of the states of knowledge, potentials, and important roles played by the HL distribution and related models in probability theory and statistical studies in various areas and applications. In particular, at least sixty-seven flexible extensions of the HL distribution have been proposed in the past few years. We give a brief introduction to these distributions, emphasizing model parameters, properties derived, and the estimation method. Conclusively, there is no doubt that this summary could create a consensus between various related results in both theory and applications of the HL-related models to develop an interest in future studies.

Simulation Study of the Bayesian and Non-Bayesian Estimation of a new Lifetime Distribution Parameters with Increasing Hazard Rate

In this paper, a new distribution known as the Shifted Chris-Jerry (SHCJ) distribution is proposed. The proposition is motivated by the need to compare the efficiency of various classical estimation methods as well as the bayesian estimation using gamma prior at linear-exponential loss, squared error loss and generalized entropy loss functions. Some useful mathematical properties are derived. Single acceptance sampling plans (SASPs) are created for the distribution when the life test is truncated at a predetermined period. The median lifetime of the SHCJ distribution with pre-defined constants is taken as the truncation time. To guarantee that the specific life test is obtained at the defined risk to the user, the minimum sample size is required. For a particular consumer’s risk, the SHCJ distribution’s parameters, and the truncation time including numerical results are obtained. A simulation study is carried out for the bayesian and non-bayesian estimation of the parameters. Data on blood cancer patients is used to demonstrate the usefuleness of the proposed distribution.

The association between sociodemographic, clinical, and potentially preventive therapies with oxaliplatin-induced peripheral neuropathy in colorectal cancer patients.

The purpose of this retrospective cohort study was to evaluate whether several potentially preventive therapies reduced the rate of oxaliplatin-induced peripheral neuropathy (OIPN) in colorectal cancer patients and to assess the relationship of sociodemographic/clinical factors with OIPN diagnosis. Data were obtained from the Surveillance, Epidemiology, and End Results database combined with Medicare claims. Eligible patients were diagnosed with colorectal cancer between 2007 and 2015, ≥ 66years of age, and treated with oxaliplatin. Two definitions were used to denote diagnosis of OIPN based on diagnosis codes: OIPN 1 (specific definition, drug-induced polyneuropathy) and OIPN 2 (broader definition, additional codes for peripheral neuropathy). Cox regression was used to obtain hazard ratios (HR) with 95% confidence intervals (CI) for the relative rate of OIPN within 2years of oxaliplatin initiation. There were 4792 subjects available for analysis. At 2years, the unadjusted cumulative incidence of OIPN 1 was 13.1% and 27.1% for OIPN 2. For both outcomes, no therapies reduced the rate of OIPN diagnosis. The anticonvulsants gabapentin and oxcarbazepine/carbamazepine were associated with an increased rate of OIPN (both definitions) as were increasing cycles of oxaliplatin. Compared to younger patients, those 75-84years of age experienced a 15% decreased rate of OIPN. For OIPN 2, prior peripheral neuropathy and moderate/severe liver disease were also associated with an increased hazard rate. For OIPN 1, state buy-in health insurance coverage was associated with a decreased hazard rate. Additional studies are needed to identify preventive therapeutics for OIPN in cancer patients treated with oxaliplatin.

Nonparametric inference about increasing odds rate distributions

To improve nonparametric estimates of lifetime distributions, we propose using the increasing odds rate (IOR) model as an alternative to other popular, but more restrictive, ‘adverse ageing’ models, such as the increasing hazard rate one. This extends the scope of applicability of some methods for statistical inference under order restrictions, since the IOR model is compatible with heavy-tailed and bathtub distributions. We study a strongly uniformly consistent estimator of the cumulative distribution function of interest under the IOR constraint. Numerical evidence shows that this estimator often outperforms the classic empirical distribution function when the underlying model does belong to the IOR family. We also study two different tests to detect deviations from the IOR property and establish their consistency. The performance of these tests is also evaluated through simulations.

Association of pathogen-specific clinical mastitis in the first 100 days of first lactation with productive lifetime: An observational study comparing competing risks models for death and sale with the Cox model.

The objective of this observational study was to study the association between clinical mastitis (CM) (Streptococcus spp., Staphylococcus aureus, Staphylococcus spp., Escherichia coli, Klebsiella spp., cases with other treated or other not treated organisms, CM without growth) occurring in a dairy cow's first 100 days (d) of her first lactation and her total productive lifetime, ending in death or sale (for slaughter). Data were collected from 24,831 cows in 5 New York Holstein herds from 2004 to 2014. Two analytical approaches were compared. First, removals (death, sale) were treated as competing events in separate survival analyses, in proportional subdistribution hazards models. In one, death was coded as the event of interest and sale as the competing event; in another, sale was the event of interest and death the competing event. Second, traditional survival analysis (Cox proportional hazards) was conducted. In all models, the time variable was number of days from date of first calving until event (death or sale) date; if the cow was alive at study end, she was censored. Models were stratified by herd. Ten percent of cows died; 48.4 % were sold. In the competing risks analysis, E. coli and CM without growth were associated with death; the former with an increased hazard rate of death, the latter with a lower one. Streptococcus spp., Staph. aureus, Klebsiella spp., cases with other treated or untreated organisms, and CM without growth were associated with higher hazard rates of sale. The Cox proportional hazards model's hazard rates were higher than those in the competing risks model in which death was the event of interest, and resembled those in the model in which sale was the event of interest. Four additional Cox models, omitting dead or sold cows, or censoring each, were also fitted; hazard ratios were similar to the above models. Proportional subdistribution hazards models were appropriate due to competing risks (death, sale); they produce less-biased estimates. A study limitation is that while proportional subdistribution hazards models were appropriate, they have the illogical feature of keeping subjects at risk for the event of interest even after experiencing the competing event. This is, however, necessary in estimating cumulative incidence functions. Another limitation concerns pathogen variability among study farms, implying that CM decisions are farm-specific. Misclassification of 'dead' vs. 'sold' cows was also possible. Nevertheless, the findings may help in optimizing management of cows contracting specific types of CM early in productive lifetime.

Mixture of Shanker Distributions: Estimation, Simulation and Application

The Shanker distribution, a one-parameter lifetime distribution with an increasing hazard rate function, is recommended by Shanker for modelling lifespan data. In this study, we examine the theoretical and practical implications of 2-component mixture of Shanker model (2-CMSM). A significant feature of proposed model’s hazard rate function is that it has rising, decreasing, and upside-down bathtub forms. We investigate the statistical characteristics of a mixed model, such as the probability-generating function, the factorial-moment-generating function, cumulants, the characteristic function, the Mills ratio, the mean residual life, and the mean time to failure. There is a graphic representation of density, mean, hazard rate functions, coefficient of variation, skewness, and kurtosis. Our final approach is to estimate the parameters of the mixture model using appropriate approaches such as maximum likelihood, least squares, and weighted least squares. Using a simulation analysis, we examined how the estimates behaved graphically. The simulation results demonstrated that, in the majority of cases, the maximum likelihood estimates have the smallest mean square errors among all other estimates. Finally, we observed that when the sample size rises, the precision measures decrease for all of the estimation techniques, indicating that all of the estimation approaches are consistent. Through two real data analyses, the suggested model’s validity and adaptability are contrasted with those of other models, including the mixture of the exponential distributions and the Lindley distributions .

Testing departures from the increasing hazard rate property

This paper proposes a nonparametric test to detect violations of the increasing hazard rate property, based on the distance between the empirical distribution function and a shape-constrained estimator. The test is consistent. The behaviour of the power function in some critical cases is evaluated through simulations.

Association between Long-Term Ambient PM2.5 Exposure and Cardiovascular Outcomes among U.S. Hemodialysis Patients

Background and Aim: Ambient PM2.5 is a ubiquitous air pollutant with established adverse cardiovascular (CV) effects. However, quantitative estimates of PM2.5 exposure associations on CV outcomes in susceptible populations are limited. This study assessed the impact of long-term PM2.5 on CV events and cardiovascular disease (CVD)-specific mortality among patients receiving maintenance in-center hemodialysis (HD). Methods: We conducted a retrospective cohort study with 314,079 adult kidney failure patients initiating HD between 2011 and 2016 identified from the United State Renal Data System. Estimated daily ZIP code-level PM2.5 concentrations were used to calculate each participant’s annual-average PM2.5 exposure based on the dialysis clinics visited during the 365 days prior to the outcome. CV event and CVD-specific mortality were ascertained based on ICD-9/ICD-10 diagnostic codes and recorded cause of death from form 2746. Discrete time hazards models were used to estimate hazards ratios (HRs) per 1 µg/m3 in annual-average PM2.5 adjusting for temperature, humidity, day of the week, season, age at baseline, race, employment status, and geographic region. Effect measure modification was assessed for age, sex, race, and baseline comorbidities. Results: Annual-average PM2.5 of 1 µg/m3 was associated with increased hazard rates in CV events (HR: 1.02, 95% CI: 1.01, 1.02) and CVD-specific mortality (1.02, 95% CI: 1.02, 1.03). The association was more pronounced for people who initiated dialysis at an older age, had COPD at baseline, or were Asian. Evidence of effect modification was also observed across strata of race, and other baseline comorbidities. Conclusions: Long-term ambient PM2.5 exposure was positively associated with CV outcomes among patients receiving maintenance in-center HD. Patients who had advanced age, COPD, or reported to be Asian, appeared to be more susceptible to long-term PM2.5 adverse effects. Keywords: Air pollution, long-term, vulnerable population, dialysis patients

Attributable mortality and excess length of stay associated with third-generation cephalosporin-resistant Enterobacterales bloodstream infections: a prospective cohort study in Suva, Fiji

There are scant primary clinical data on antimicrobial resistance (AMR) burden from low- and middle-income countries (LMICs). We adapted recent World Health Organization methodology to measure the effect of third-generation cephalosporin resistance (3GC-R) on mortality and excess length of hospital stay in Fiji. We conducted a prospective cohort study of inpatients with Enterobacterales bloodstream infections (BSIs) at Colonial War Memorial Hospital, Suva. We used cause-specific Cox proportional hazards models to estimate the effect of 3GC-R on the daily risk (hazard) of in-hospital mortality and being discharged alive (competing risks), and we used multistate modelling to estimate the excess length of hospital stay. From July 2020 to February 2021 we identified 162 consecutive Enterobacterales BSIs; 3GC-R was present in 66 (40.7%). Crude mortality for patients with 3GC-susceptible and 3GC-R BSIs was 16.7% (16/96) and 30.3% (20/66), respectively. 3GC-R was not associated with the in-hospital mortality hazard rate (adjusted hazard ratio [aHR] 1.13, 95% confidence interval [CI] 0.51-2.53) or being discharged alive (aHR 0.99, 95% CI 0.65-1.50), whereas Charlson comorbidity index score (aHR 1.62, 95% CI 1.36-1.93) and Pitt bacteraemia score (aHR 3.57, 95% CI 1.31-9.71) were both associated with an increased hazard rate of in-hospital mortality. 3GC-R was associated with an increased length of stay of 2.6 days (95% CI 2.5-2.8). 3GC-R was more common among hospital-associated infections, but genomics did not identify clonal transmission. Patients with Enterobacterales BSIs in Fiji had high mortality. There were high rates of 3GC-R, which was associated with increased hospital length of stay but not with in-hospital mortality.

Lottery Design for School Choice

This paper studies outcomes of the deferred acceptance algorithm in large random matching markets where priorities are generated either by a single lottery or by independent lotteries. In contrast to prior work, my model permits students to submit lists of varying lengths and schools to vary in their popularity and number of seats. In a limiting regime where the number of students and schools grow while the length of student lists and number of seats at each school remain bounded, I provide exact expressions for the number of students who list l schools and match to one of their top k choices, for each [Formula: see text]. These expressions provide three main insights. First, there is a persistent tradeoff between using a single lottery and independent lotteries. For students who submit short lists, the rank distribution under a single lottery stochastically dominates the corresponding distribution under independent lotteries. However, the students who submit the longest lists are always more likely to match when schools use independent lotteries. Second, I compare the total number of matches in the two lottery systems, and find that the shape of the list length distribution plays a key role. If this distribution has an increasing hazard rate, then independent lotteries match more students. If it has a decreasing hazard rate, the comparison reverses. To my knowledge, this is the first analytical result comparing the size of stable matchings under different priority rules. Finally, I study the fraction of assigned students who receive their first choice. Under independent lotteries, this fraction may be arbitrarily small, even if schools are equally popular. Under a single lottery, we provide a tight lower bound on this fraction which depends on the ratio r of the popularity of the most to least popular school. When each school has a single seat, the fraction of assigned students who receive their first choice is at least [Formula: see text]. This guarantee increases to [Formula: see text] as the number of seats at each school increases. This paper was accepted by Gabriel Weintraub, revenue management and market analytics. Supplemental Material: The data files and online appendix are available at https://doi.org/10.1287/mnsc.2022.4338 .

Properties of increasing odds rate distributions with a statistical application

We study the family of distributions characterised by an increasing odds rate (IOR), showing that this provides an alternative interpretation of the “adverse ageing” notion, comparable to the well known increasing hazard rate (IHR) model. We prove some preservation properties of this class under several transformations that are often considered in reliability and life testing problems, including formation of order statistics. Moreover, the IOR assumption enables the derivation of survival bounds and tolerance limits, extending the scope of applicability of some known results, which are based, for instance, on the IHR assumption. Finally, we propose a test for the IOR null hypothesis, establishing its consistency and providing a table of simulated p-values.

On a Modified Weighted Exponential Distribution with Applications

Practitioners in all applied domains value simple and adaptable lifetime distributions. They make it possible to create statistical models that are relatively easy to manage. A novel simple lifetime distribution with two parameters is proposed in this article. It is based on a parametric mixture of the exponential and weighted exponential distributions, with a mixture weight depending on a parameter of the involved distribution; no extra parameter is added in this mixture operation. It can also be viewed as a special generalized mixture of two exponential distributions. This decision is based on sound mathematical and physical reasoning; the weight modification allows us to combine some joint properties of the exponential and weighted exponential distribution, which are known as complementary in several modeling aspects. As a result, the proposed distribution may have a decreasing or unimodal probability density function and possess the demanded increasing hazard rate property. Other properties are studied, such as the moments, Bonferroni and Lorenz curves, Rényi entropy, stress-strength reliability, and mean residual life function. Subsequently, a part is devoted to the associated model, which demonstrates how it can be used in a real-world statistical scenario involving data. In this regard, we demonstrate how the estimated model performs well using five different estimation methods and simulated data. The analysis of two data sets demonstrates these excellent results. The new model is compared to the weighted exponential, Weibull, gamma, and generalized exponential models for performance. The obtained comparison results are overwhelmingly in favor of the proposed model according to some standard criteria.

Pricing with Samples

This paper studies the value of data for pricing purposes. Although pricing is central across industries, little is known about the minimal amount of data needed to achieve good pricing decisions. The present paper proposes a novel approach to quantify the informational content of data, through the introduction of a new class of robust data-driven policies and the development of factor-revealing dynamic programs. Studying the prototypical case of data coming in the form of samples from the willingness to pay of customers, we show that even a few samples (as few as 10) go a very long way in uncovering “good” prices. For example, quite strikingly, against a general class of distributions (monotone increasing hazard rate distributions), a single observation guarantees 64% of the performance an oracle with full knowledge of the distribution would achieve, two samples suffice to ensure 71%, and 10 samples guarantee 80% of such performance.

On estimating of the stress-strength model with more than two states under Gompertz distribution

The Gompertz distribution, one of statistical distributions, is considered in survival analysis because it has an increasing hazard rate function. It has many applications in various fields such as medical and reliability. The problem of estimation of stress-strength model with more than two states is considered by other authors under exponential and Weibull distribution. The main aim of this paper is to consider the same problem under Gompertz distribution based on progressive type-II censoring data. Three estimation methods are considered to estimate the reliability parameter, maximum likelihood (MLE), uniformly minimum variance unbiased estimator (UMVE) and Bayes estimator. To compare and study the performance of three estimators, Monte Carlo simulation study is performed.