Exponentiated Weibull regression for time-to-event data

The Weibull, log-logistic and log-normal distributions are extensively used to model time-to-event data. The Weibull family accommodates only monotone hazard rates, whereas the log-logistic and log-normal are widely used to model unimodal hazard functions. The increasing availability of lifetime data with a wide range of characteristics motivate us to develop more flexible models that accommodate both monotone and nonmonotone hazard functions. One such model is the exponentiated Weibull distribution which not only accommodates monotone hazard functions but also allows for unimodal and bathtub shape hazard rates. This distribution has demonstrated considerable potential in univariate analysis of time-to-event data. However, the primary focus of many studies is rather on understanding the relationship between the time to the occurrence of an event and one or more covariates. This leads to a consideration of regression models that can be formulated in different ways in survival analysis. One such strategy involves formulating models for the accelerated failure time family of distributions. The most commonly used distributions serving this purpose are the Weibull, log-logistic and log-normal distributions. In this study, we show that the exponentiated Weibull distribution is closed under the accelerated failure time family. We then formulate a regression model based on the exponentiated Weibull distribution, and develop large sample theory for statistical inference. We also describe a Bayesian approach for inference. Two comparative studies based on real and simulated data sets reveal that the exponentiated Weibull regression can be valuable in adequately describing different types of time-to-event data.     

Discussion of “Simple Estimators for Invertible Index Models” by H. Ahn,H. Ichimura,J. Powell,and P. Ruud

This is an interesting article that considers the question of inference on unknown linear index coefficients in a general class of models where reduced form parameters are invertible function of one or more linear index. Interpretable sufficient conditions such as monotonicity and or smoothness for the invertibility condition are provided. The results generalize some work in the previous literature by allowing the number of reduced form parameters to exceed the number of indices. The identification and estimation expand on the approach taken in previous work by the authors. Examples include Ahn, Powell, and Ichimura (2004 Ahn, H., Powell, J., and Ichimura, H. (2004), “Simple Estimators for Monotone Index Models,” UC Berkeley Working Paper. [Google Scholar]) for monotone single-index regression models to a multi-index setting and extended by Blundell and Powell (2004 Blundell, R. W., and Powell, J. L. (2004), “Endogeneity in Semiparametric Binary Response Models,” The Review of Economic Studies, 71, 655–679.[Crossref], [Web of Science ®] , [Google Scholar]) and Powell and Ruud (2008 Powell, J., and Ruud, P. (2008), “Simple Estimators for Semiparametric Multinomial Choice Models,” UC Berkeley Working Paper. [Google Scholar]) to models with endogenous regressors and multinomial response, respectively. A key property of the inference approach taken is that the estimator of the unknown index coefficients (up to scale) is computationally simple to obtain (relative to other estimators in the literature) in that it is closed form. Specifically, unifying an approach for all models considered in this article, the authors propose an estimator, which is the eigenvector of a matrix (defined in terms of a preliminary estimator of the reduced form parameters) corresponding to its smallest eigenvalue. Under suitable conditions, the proposed estimator is shown to be root-n-consistent and asymptotically normal.     

Inference about the parameters of a bi-variate simultaneous equation model: structural approach

The paper considers a system of bi-linear responses having a regression structure with known predetermined variables. In econometric studies, the model is widely used and is known as simultaneous equation model. The probability distribution for the coefficients of the exogenous variables as well as that of the error variances along with the marginal likelihood function of the coefficients of the endogenous variables have been derived. The model in this paper has been analysed in the framework of a conditional structural model (Fraser 1968, 1979), which provides the basis of inference about all the parameters.     

The foster care system in India

The author has undertaken the difficult task of giving us an overall view of the foster care picture of all India, the first such panorama we have received.     

Bayesian Elastic Net Tobit Quantile Regression

In this article, the problem of parameter estimation and variable selection in the Tobit quantile regression model is considered. A Tobit quantile regression with the elastic net penalty from a Bayesian perspective is proposed. Independent gamma priors are put on the l₁ norm penalty parameters. A novel aspect of the Bayesian elastic net Tobit quantile regression is to treat the hyperparameters of the gamma priors as unknowns and let the data estimate them along with other parameters. A Bayesian Tobit quantile regression with the adaptive elastic net penalty is also proposed. The Gibbs sampling computational technique is adapted to simulate the parameters from the posterior distributions. The proposed methods are demonstrated by both simulated and real data examples.     

The Correlated Bivariate Noncentral F Distribution and Its Application

This article proposes the singly and doubly correlated bivariate noncentral F (BNCF) distributions. The probability density function (pdf) and the cumulative distribution function (cdf) of the distributions are derived for arbitrary values of the parameters. The pdf and cdf of the distributions for different arbitrary values of the parameters are computed, and their graphs are plotted by writing and implementing new R codes. An application of the correlated BNCF distribution is illustrated in the computations of the power function of the pre-test test for the multivariate simple regression model (MSRM).     

New influence diagnostics in ridge regression

We occasionally find that a small subset of the data exerts a disproportionate influence on the fitted regression model. We would like to locate these influential points and assess their impact on the model. However, the existence of influential data is complicated by the presence of collinearity (see, e.g. [15 E. Walker and J. Birch, Influence measures in ridge regression, Technometrics 30 (1989), pp. 221–227. doi: 10.1080/00401706.1988.10488370[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]). In this article we develop a new influence statistic for one or a set of observations in linear regression dealing with collinearity. We show that this statistic has asymptotically normal distribution and is able to detect a subset of high ridge leverage outliers. Using this influence statistic we also show that when ridge regression is used to mitigate the effects of collinearity, the influence of some observations can be drastically modified. As an illustrative example, simulation studies and a real data set are analysed.     

Competing constructions of calamity: The April 1991 Bangladesh cyclone

On April 30, 1991, a cyclone of unusual intensity hit the coastline of Bangladesh, causing over one hundred thousand deaths and widespread property damage. An international debate ensued over whether the disaster was due to natural phenomena and should be addressed by relief measures, or whether it was due to social, economic, and political factors and should be addressed by structural change in society. This study explores the dimensions of this debate by means of a content analysis of accounts of the cyclone by the Bangladesh media and government, and by the international media and scholarly community.Bangladeshi accounts of the cyclone emphasize its purported inevitability and natural origins. However, scholars maintain that while cyclones are inevitable, disasters such as occurred in April 1991 are not: they are a function of the historically increasing socioeconomic vulnerability of the Bangladesh population. According to this view, the natural disaster of April 1991 could more accurately be called a social or political disaster. The factor chiefly responsible for transforming natural disasters into sociopolitical disasters is occupation of hazardous areas.The Bangladesh media and government suggest that the cyclone's impact was worsened by the irrational behavior of individuals and the limited resources of the nation. Non-Bangladeshi accounts focus instead on the poverty of individuals and the structural inequities of society, which compel people to live in hazardous areas. Bangladeshi accounts attempted to link the cyclone to global warming and the greenhouse gas emissions of the industrialized nations, thus shifting the focus from internal problems of structure and equity to international problems of structure and equity. Debates such as this promise to become more common, as the global environment becomes increasingly post-natural and the framing of relations between population and environment is increasingly contested.     

Textual data transformations using natural language processing for risk assessment

Underlying information about failure, including observations made in free text, can be a good source for understanding, analyzing, and extracting meaningful information for determining causation. The unstructured nature of natural language expression demands advanced methodology to identify its underlying features. There is no available solution to utilize unstructured data for risk assessment purposes. Due to the scarcity of relevant data, textual data can be a vital learning source for developing a risk assessment methodology. This work addresses the knowledge gap in extracting relevant features from textual data to develop cause–effect scenarios with minimal manual interpretation. This study applies natural language processing and text-mining techniques to extract features from past accident reports. The extracted features are transformed into parametric form with the help of fuzzy set theory and utilized in Bayesian networks as prior probabilities for risk assessment. An application of the proposed methodology is shown in microbiologically influenced corrosion-related incident reports available from the Pipeline and Hazardous Material Safety Administration database. In addition, the trained named entity recognition (NER) model is verified on eight incidents, showing a promising preliminary result for identifying all relevant features from textual data and demonstrating the robustness and applicability of the NER method. The proposed methodology can be used in domain-specific risk assessment to analyze, predict, and prevent future mishaps, ameliorating overall process safety.