Journal of Data Science

We fit a Cox proportional hazards (PH) model to interval-censored survival data by first subdividing each individual's failure interval into nonoverlapping sub-intervals. Using the set of all interval endpoints in the data set, those that fall into the individual's interval are then used as the cut points for the sub-intervals. Each sub-interval has an accompanying weight calculated from a parametric Weibull model based on the current parameter estimates. A weighted PH model is then fit with multiple lines of observations corresponding to the sub-intervals for each individual, where the lower end of each sub-interval is used as the observed failure time with the accompanying weights incorporated. Right-censored observations are handled in the usual manner. We iterate between estimating the baseline Weibull distribution and fitting the weighted PH model until the regression parameters of interest converge. The regression parameter estimates are fixed as an offset when we update the estimates of the Weibull distribution and recalculate the weights. Our approach is similar to Satten et al.'s (1998) method for interval-censored survival analysis that used imputed failure times generated from a parametric model in a PH model. Simulation results demonstrate apparently unbiased parameter estimation for the correctly specified Weibull model and little to no bias for a mis-specified log-logistic model. Breast cosmetic deterioration data and ICU hyperlactemia data are analyzed.

In this article, we introduce a class of distributions that have heavy tails as compared to Pareto distribution of third kind, which we termed as Heavy Tailed Pareto (HP) distribution. Various structural properties of the new distribution are derived. It is shown that HP distribution is in the domain of attraction of minimum of Weibull distribution. A representation of HP distribution in terms of Weibull random variable is obtained. Two characterizations of HP distribution are obtained. The method of maximum likelihood is used for estimation of model parameters and simulation results are presented to assess the performance of new model. Marshall-Olkin Heavy Tailed Pareto (MOHP) distribution is also introduced and some of its properties are studied. It is shown that MOHP distribution is geometric extreme stable. An autoregressive time series model with the new model as marginal distribution is developed and its properties are studied.

Abstract: In this paper we introduce a Bayesian analysis of a spherical distri bution applied to rock joint orientation data in presence or not of a vector of covariates, where the response variable is given by the angle from the mean and the covariates are the components of the normal upwards vector. Standard simulation MCMC (Markov Chain Monte Carlo) methods have been used to obtain the posterior summaries of interest obtained from Win Bugs software. Illustration of the proposed methodology are given using a simulated data set and a real rock spherical data set from a hydroelectrical site.

In this paper a new two-parameter distribution is proposed. This new model provides more flexibility to modeling data with increasing and bathtub hazard rate function. Several statistical and reliability properties of the proposed model are also presented in this paper, such as moments, moment generating function, order statistics and stress-strength reliability. The maximum likelihood estimators for the parameters are discussed as well as a bias corrective approach based on bootstrap techniques. A numerical simulation is carried out to examine the bias and the mean square error of the proposed estimators. Finally, an application using a real data set is presented to illustrate our model.

Abstact:The problem of estimating lifetime distribution parameters under general progressive censoring originated in the context of reliability. But traditionally it is assumed that the available data from this censoring scheme are performed in exact numbers. However, in many life testing and reliability studies, it is not possible to obtain the measurements of a statistical experiment exactly, but is possible to classify them into fuzzy sets. This paper deals with the estimation of lifetime distribution parameters under general progressive Type-II censoring scheme when the lifetime observations are reported by means of fuzzy numbers. A new method is proposed to determine the maximum likelihood estimates of the parameters of interest. The methodology is illustrated with two popular models in lifetime analysis, the Rayleigh and Lognormal lifetime distributions.

In this paper, parameters estimation for the generalized Rayleigh (GR) distribution are discussed under the adaptive type-II progressive censoring schemes based on maximum product spacing. A comparison studies with another methods as maximum likelihood, and Bayesian estimation by use Markov chain Monte Carlo (MCMC) are discussed. Also, reliability estimation and hazard function are obtained. A numerical study using real data and Monte Carlo Simulation are performed to compare between different methods.

A new class of distributions called the beta linear failure rate power series (BLFRPS) distributions is introduced and discussed. This class of distributions contains new and existing sub-classes of distributions including the beta exponential power series (BEPS) distribution, beta Rayleigh power series (BRPS) distribution, generalized linear failure rate power series (GLFRPS) distribution, generalized Rayleigh power series (GRPS) distribution, generalized exponential power series (GEPS) distribution, Rayleigh power series (RPS) distributions, exponential power series (EPS) distributions, and linear failure rate power series (LFRPS) distribution of Mahmoudi and Jafari (2014). The special cases of the BLFRPS distribution include the beta linear failure rate Poisson (BLFRP) distribution, beta linear failure rate geometric (BLFRG) distribution of Oluyede, Elbatal and Huang (2014), beta linear failure rate binomial (BLFRB) distribution, and beta linear failure rate logarithmic (BLFRL) distribution. The BLFRL distribution is also discussed in details as a special case of the BLFRPS class of distributions. Its structural properties including moments, conditional moments, deviations, Lorenz and Bonferroni curves and entropy are derived and presented. Maximum likelihood estimation method is used for parameters estimation. Maximum likelihood estimation technique is used for parameter estimation followed by a Monte Carlo simulation study. Application of the model to a real dataset is presented.

One of the main features of bipolar disorder is repletion of relapse overtime. Many studies have focused on time-to-first relapse using the most popular Cox proportional hazard model which discards subsequent information on recurrent relapses. The aim of this study was to identify some risk factors of time-to-recurrent relapses in bipolar disorder inpatients by using appropriate recurrent event model. Data on 206 inpatients, available at Amanuel mental specialized hospital, were collected by reviewing the medical records from September 11, 2013 to March 12, 2019. Different extended cox proportional hazard models including AG, PWP-TT, PWP-GT and semiparametric shared gamma frailty models were used. R package FrailtyEM package used to fit semi-parametric shared gamma frailty models through EM algorithm. The mean age of the patients was 33.33 years. Within the study time, a total of 418 inpatient admissions (relapses) were registered for 206 inpatients. Among these admissions, about 49.3% of the patients had first relapse and 50.7% of the patients had more than one relapses. The likelihood test results indicated that the appropriate model is the gap-time based semi-parametric shared gamma frailty model and the important risk factors that have effect on time since the end of the most recent relapse to the start of the next relapses are marital status, substance abuse, employment status and residence. Recurrent relapse may be reduced by giving more intensive forms of treatment and creating awareness on each risk factor.

Abstract:In clinical studies, subjects or patients might be exposed to a succession of diagnostic tests or medication over time and interest is on determining whether there is progressive remission of conditions, disease or symptoms that have measured collectively as quality of life or outcome scores. In addition, subjects or study participants may be required, perhaps early in an experiment, to improve significantly in their performance rates at the current trial relative to an immediately preceding trial, otherwise the decision of withdrawal or dropping out is ineviTable. The common research interest would then be to determine some critical minimum marginal success rate to guide the management in decision making for implementing certain policies. Success rates lower than the minimum expected value would indicate a need for some remedial actions. In this article, a method of estimating these rates is proposed assuming the requirement is at the second trial of any particular study. Pairwise comparisons of proportions of success or failure by subjects is considered in repeated outcome measure situation to determine which subject or combinations is responsible for the rejection of the null hypothesis. The proposed method is illustrated with the help of a dataset on palliative care outcome scores (POS) of cancer patients.

This paper proposes the Topp-Leone Gompertz distribution; an extension of the Gompertz distribution for modeling real life time data. The new model is obtained by transforming the cumulative distribution function of the Gompertz random variable, while taking the Topp-Leone as the generator. Some statistical properties of the new distribution are derived. Maximum likelihood estimates of model parameters are also derived. A Monte Carlo simulation study is carried out to examine the accuracy of the maximum likelihood estimate of the distribution parameters. Two real data sets are used to illustrate the applicability of the new distribution, and the results show that the new distribution outperforms some related lifetime distributions.