Journal of Data Science

In this paper an attempt has been made to analyze the child mortality by use of a hazard model in Bayesian environment, family effect through multiplicative random effect is also incorporated in the model. For fitting this model real data has taken from District Level Household and Facility Survey (DLHS)-3. The largest state (in population) of India i.e. Uttar Pradesh data is taken for analysis. Deviance information criteria are used for comparison of models. It found that the model with family frailty gives better fit. All the analysis is performed in winBUGS software, which is used Markov chain monte carlo simulation under gibbs sampling.

Abstract: Count data often have excess zeros in many clinical studies. These zeros usually represent “disease-free state”. Although disease (event) free at the time, some of them might be at a high risk of having the putative outcome while others may be at low or no such risk. We postulate these zeros as a one of the two types, either as ‘low risk’ or as ‘high risk’ zeros for the disease process in question. Low risk zeros can arise due to the absence of risk factors for disease initiation/progression and/or due to very early stage of the disease. High risk zeros can arise due to the presence of significant risk factors for disease initiation/ progression or could be, in rare situations, due to misclassification, more specific diagnostic tests, or below the level of detection. We use zero inflated models which allows us to assume that zeros arise from one of the two separate latent processes-one giving low-risk zeros and the other high-risk zeros and subsequently propose a strategy to identify and classify them as such. To illustrate, we use data on the number of involved nodes in breast cancer patients. Of the 1152 patients studied, 38.8% were node- negative (zeros). The model predicted that about a third (11.4%) of negative nodes are “high risk” and the remaining (27.4%) are at “low risk” of nodal positivity. Posterior probability based classification was more appropriate compared to other methods. Our approach indicates that some node negative patients may be re-assessed for their diagnosis about nodal positivity and/or for future clinical management of their disease. The approach developed here is applicable to any scenario where the disease or outcome can be characterized by count-data.

Abstract: Student retention is an important issue for all university policy makers due to the potential negative impact on the image of the university and the career path of the dropouts. Although this issue has been thoroughly studied by many institutional researchers using parametric techniques, such as regression analysis and logit modeling, this article attempts to bring in a new perspective by exploring the issue with the use of three data mining techniques, namely, classification trees, multivariate adaptive regression splines (MARS), and neural networks. Data mining procedures identify transferred hours, residency, and ethnicity as crucial factors to retention. Carrying transferred hours into the university implies that the students have taken college level classes somewhere else, suggesting that they are more academically prepared for university study than those who have no transferred hours. Although residency was found to be a crucial predictor to retention, one should not go too far as to interpret this finding that retention is affected by proximity to the university location. Instead, this is a typical example of Simpson’s Paradox. The geographical information system analysis indicates that non-residents from the east coast tend to be more persistent in enrollment than their west coast schoolmates.

Abstract: Some scientists prefer to exercise substantial judgment in formulating a likelihood function for their data. Others prefer to try to get the data to tell them which likelihood is most appropriate. We suggest here that one way to reduce the judgment component of the likelihood function is to adopt a mixture of potential likelihoods and let the data determine the weights on each likelihood. We distinguish several different types of subjectivity in the likelihood function and show with examples how these subjective elements may be given more equitable treatment.

Abstract: The scheme of doubly type-II censored sampling is an important method of obtaining data in lifetime studies. Statistical analysis of life time distributions under this censoring scheme is based on precise lifetime data. However, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. This paper deals with the prob lem of estimating the scale parameter of Rayleigh distribution under doubly type-II censoring scheme when the lifetime observations are fuzzy and are assumed to be related to underlying crisp realization of a random sample. We propose a new method to determine the maximum likelihood estimate of the parameter of interest. The asymptotic variance of the ML estimate is then derived by using the missing information principle. Their performance is then assessed through Monte Carlo simulations. Finally, an illustrative example with real data concerning 25 ball bearings in a life test is presented.

Abstract: As an extension to previous research efforts, the PPM is applied to the identification of multiple change points in the parameter that indexes the regular exponential family. We define the PPM for Yao’s prior cohesions and contiguous blocks. Because the exponential family provides a rich set of models, we also present the PPM for some particular members of this family in both continuous and discrete cases and the PPM is applied to identify multiple change points in real data. Firstly, multiple changes are identified in the rates of crimes in one of the biggest cities in Brazil. In order to illustrate the continuous case, multiple changes are identified in the volatility (variance) and in the expected return (mean) of some Latin America emerging markets return series.

We propose a lifetime distribution with flexible hazard rate called cubic rank transmuted modified Burr III (CRTMBIII) distribution. We develop the proposed distribution on the basis of the cubic ranking transmutation map. The density function of CRTMBIII is symmetrical, right-skewed, left-skewed, exponential, arc, J and bimodal shaped. The flexible hazard rate of the proposed model can accommodate almost all types of shapes such as unimodal, bimodal, arc, increasing, decreasing, decreasing-increasing-decreasing, inverted bathtub and modified bathtub. To show the importance of proposed model, we present mathematical properties such as moments, incomplete moments, inequality measures, residual life function and stress strength reliability measure. We characterize the CRTMBIII distribution via techniques. We address the maximum likelihood method for the model parameters. We evaluate the performance of the maximum likelihood estimates (MLEs) via simulation study. We establish empirically that the proposed model is suitable for strengths of glass fibers. We apply goodness of fit statistics and the graphical tools to examine the potentiality and utility of the CRTMBIII distribution.

This paper presents a new generalization of the extended Gompertz distribution. We defined the so-called exponentiated generalized extended Gompertz distribution, which has at least three important advantages: (i) Includes the exponential, Gompertz, extended exponential and extended Gompertz distributions as special cases; (ii) adds two parameters to the base distribution, but does not use any complicated functions to that end; and (iii) its hazard function includes inverted bathtub and bathtub shapes, which are particularly important because of its broad applicability in real-life situations. The work derives several mathematical properties for the new model and discusses a maximum likelihood estimation method. For the main formulas related to our model, we present numerical studies that demonstrate the practicality of computational implementation using statistical software. We also present a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators for the EGEG model. Three real- world data sets were used for applications in order to illustrate the usefulness of our proposal.

In this paper, the problem of determining which treatments are statistically significant when compared with a zero-dose or placebo control in a dose-response study is considered. Nonparametric meth- ods developed for the commonly used multiple comparison problem whenever the Jonckheere trend test (JT) is appropriate is extended to the multiple comparisons to control problem. We present four closed testing methods, of which two use an AUC regression model approach for determining the treatment arms that are statistically different from the zero-dose control. A simulation study is performed to compare the proposed methods with two existing rank-based nonparametric mul- tiple comparison procedures. The method is further illustrated using a problem from a clinical setting.