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In competing risks problem, a subset of risks is needed more attention for inferential purposes. In the objective Bayesian paradigm, reference priors enable to achieve such inferential objectives. In this article, the Marshall-Olkin bivariate Weibull distribution is considered to model the competing risks data. In the availability of partial information for some of the parameters, the reference priors are derived as per the importance of the parameters. The Dirichlet prior is taken as a conditional subjective prior and the marginal reference prior has been derived. Also, the propriety of the resulting posterior density has been proved. The Bayesian estimates of the parameters are obtained under squared error and linear-exponential loss functions. Further, the derived reference prior is used for the computation of Bayes factors or posterior odds in testing the hypothesis that the competing risks are identical. The performance of established Bayesian estimators is illustrated using the Diabetic Retinopathy Study (DRS) and Prostate Cancer data sets. Finally, the model compatibility is done for the considered data sets under Bayesian Paradigm. [ABSTRACT FROM AUTHOR]

In competing risks model, subjects are exposed to failure due to more than one cause. In this study, we develop a model for recall-based competing risks data when the causes associated with time to event are assumed to follow different distributions respectively. The chances of an individual recalling an event will be high if elapsed time between monitoring time and time to event is less. This information is utilized by taking non-recall probability as a function of this elapsed time. For point estimation, an expectation-maximization based algorithm is developed. For interval estimation, we construct the observed Fisher information matrix by using the missing information principle. The study is further extended to the Bayesian paradigm under suitable choices of prior distributions. The samples from full conditionals are drawn using a Gibbs sampling-based algorithm. To assess the performance of proposed estimators, an extensive simulation study is carried out for different proportions of non-recall and censored data with varying sample sizes under uniform and exponential monitoring patterns. Finally, the median duration of breastfeeding cessation for US women is estimated. [ABSTRACT FROM AUTHOR]

The assumption of independence of causes for modeling a competing risks scenario is not presumable always. In this article, cause dependent competing risks model has been analyzed under Marshall-Olkin set-up. A Marshall-Olkin generalized lifetime distribution has been established to address a competing risks model. The essential statistical properties have been derived for this distribution to utilize in a competing risks model. The estimators of unknown simple/transformed parameters are obtained by using two approaches: maximum likelihood method and Bayesian estimation through reference prior. To examine the performance of the five models under generalized lifetime family, a simulation study has been performed. For illustration, two real data sets namely, prostate cancer and diabetic retinopathy study are considered. For both data sets, analysis is performed using the most suitable model from Marshall-Olkin generalized lifetime family. [ABSTRACT FROM AUTHOR]

In many cross-sectional studies, the chances that an individual will be able to exactly recall the event are very low. The possibility of recalling the exact time as well as the cause of occurrence of an event usually decreases as the gap between event and monitoring time increases. This gives rise to non-recall current status data. In this article, an efficient approach to deal with such non-recall current status data is established in a competing risk set up. In the classical method, a nested Expectation–Maximization technique is worked out for the estimation purpose and the information matrix is evaluated using the missing information principle. In the Bayesian paradigm, point and interval estimates are obtained using the Gibbs sampling algorithm. A recent anthropometric study data containing the menarcheal status of girls and age at menarche is analyzed using the considered methodology. [ABSTRACT FROM AUTHOR]

In real-life situations, performing an experiment up to a certain period of time or getting the desired number of failures is time-consuming and costly. Many of the available observations remain censored and only give the survival information of testing units up to a noted time and not about the exact failure times. In this study, we consider inverse Maxwell distribution having an upside-down hazard rate as a survival lifetime model. The censoring time is also assumed to follow the inverse Maxwell distribution with a different parameter. The probability of failure of an item before censoring and expected and observed time on the test is derived from a random censoring scheme. The maximum likelihood estimators with their confidence intervals for the parameters are obtained for a randomly censored setup. We obtain the Bayes estimators by taking the inverted gamma distribution as a prior under squared error loss function. In Bayesian analysis, the two techniques, i.e. Markov Chain Monte Carlo and Tierney-Kadane approximation methods are used for estimation purposes. For checking the performances of proposed estimators, we perform an extensive simulation study. A real data, guinea pigs, is analyzed to support the proposed study. [ABSTRACT FROM AUTHOR]

Competing risk analysis of time to failure data is preferred when failure of the unit occurs due to any one of several mutually exclusive causes. Masked data refer to the competing risk data with missing cause of failure. Masking in such data may depend on cause of failure or time to failure of the unit or may be independent of both. In this paper, we discuss competing risk models based on Lindley distribution assuming masking to be symmetric, cause dependent and time dependent. We consider maximum likelihood as well as Bayesian approaches for point and interval estimation of model parameters. We perform extensive simulation study to observe performance of various estimators. Finally, we analyze a real life masked data of cancer patients and select the best masking model for the same. [ABSTRACT FROM AUTHOR]

In cross-sectional retrospective studies, the observations are ascertained based on the responses of individuals or past records. Thus, the problem of non-recall is very common in such studies. It is observed that memory fades when the difference between the time to event and monitoring time is farther. This information is utilized in the modeling by choosing non-recall probability as a function of the difference between monitoring time and time to event. In this study, we analyze exponential distribution under recall-based data for three causes. Under the classical framework, an equivalent quantity approach based Expectation-Maximization algorithm is proposed for point estimation. The interval estimates are obtained by using the missing information principle. The study is further extended to the Bayesian paradigm, where a Gibbs sampling algorithm is proposed using data augmentation approach for generating samples from full conditional posterior densities. For checking the behavior of proposed estimators, an extensive simulation study is carried out with maintaining different proportions of non-recall and censored data for varying sample sizes. [ABSTRACT FROM AUTHOR]

In this paper, Marshall-Olkin inverse Maxwell distribution is proposed by generalizing the inverse Maxwell distribution under the Marshall-Olkin family of distribution that leads to greater flexibility in modeling various new data types. The basic statistical properties for the proposed distribution including moments, quantile function, median, skewness, kurtosis, and stochastic ordering are derived. Point estimates for the parameters are obtained by using two well known methods maximum likelihood and maximum spacing methods. The confidence intervals are used by using asymptotic properties of maximum likelihood estimators and boot-p methods. We have applied the proposed distribution under different real-life scenarios such as record value problem, system lifetime distributions, stress-strength reliability and random censored problems. For illustration purposes, simulation and real data results are established. [ABSTRACT FROM AUTHOR]

We present an analysis of three K-prime equations of state (EoS) by studying the pressure-volume relationship, the isothermal bulk modulus (K) and first pressure derivativeof isothermal bulk modulus (K') for geophysical minerals or earth minerals such as MgO, Mg2SiO4, MgSiO3, Al2O3 and CaO at selected temperatures ranging from room temperature upto their melting temperature under high compressions down to V/V0 = 0.60, where V0 is the volume V at atmospheric pressure i.e., P = 0. The values of P, K, and K' are calculated through threeequations of state viz., Keane EOS, Stacey EOS, and Sinha EOS, which are generally found to be the same throughout the compression range for all the geophysical minerals or earth minerals under study. The results obtained in the present study compare well with available experimental P-V-T data for MgO and MgSiO3 at 300 K. [ABSTRACT FROM AUTHOR]