Graphical representation of survival curves in the presence of time-dependent categorical covariates with application to liver transplantation

Graphical representation of survival curves is often used to illustrate associations between exposures and time-to-event outcomes. However, when exposures are time-dependent, calculation of survival probabilities is not straightforward. Our aim was to develop a method to estimate time-dependent survival probabilities and represent them graphically. Cox models with time-dependent indicators to represent state changes were fitted, and survival probabilities were plotted using pre-specified times of state changes. Time-varying hazard ratios for the state change were also explored. The method was applied to data from the Adult-to-Adult Living Donor Liver Transplantation Cohort Study (A2ALL). Survival curves showing a ‘split’ at a pre-specified time t allow for the qualitative comparison of survival probabilities between patients with similar baseline covariates who do and do not experience a state change at time t. Time since state change interactions can be visually represented to reflect changing hazard ratios over time. A2ALL study results showed differences in survival probabilities among those who did not receive a transplant, received a living donor transplant, and received a deceased donor transplant. These graphical representations of survival curves with time-dependent indicators improve upon previous methods and allow for clinically meaningful interpretation.     

Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Empirical Bayes is a versatile approach to “learn from a lot” in two ways: first, from a large number of variables and, second, from a potentially large amount of prior information, for example, stored in public repositories. We review applications of a variety of empirical Bayes methods to several well‐known model‐based prediction methods, including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss “formal” empirical Bayes methods that maximize the marginal likelihood but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross‐validation and full Bayes and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and p, the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters, which model a priori information on variables termed “co‐data”. In particular, we present two novel examples that allow for co‐data: first, a Bayesian spike‐and‐slab setting that facilitates inclusion of multiple co‐data sources and types and, second, a hybrid empirical Bayes–full Bayes ridge regression approach for estimation of the posterior predictive interval.     

Multiple hypothesis tests based On conditional differences in means

Many hypothesis tests are univariate tests and cannot cope with multiple hypothesis without an auxiliary procedure as e. g. the Bonferroni-Holm-procedure. At the same time, there is an urgent need for testing multiple hypothesis due to the very simple existing methods as the Bonferroni-correction or the Bonferroni-Holm-procedure, which suffers from a very small local significance level to detect statistical inferences or the drawback that logical and statistical dependencies among the test statistics are not used, whereby its detection is NP-hard. In honour of this occasion, we present a multiple hypothesis test for i.i.d. random variables based on conditional differences in means, which is capable to cope with multiple hypothesis and does not suffer on such drawbacks as the Bonferroni-correction or the Bonferroni-Holm-procedure. Thereby, the computation time can be neglected.     

Tempered Mittag-Leffler Lévy processes

In this article, we introduce tempered Mittag-Leffler Lévy processes (TMLLP). TMLLP is represented as tempered stable subordinator delayed by a gamma process. Its probability density function and Lévy density are obtained in terms of infinite series and Mittag-Leffler function, respectively. Asymptotic forms of the tails and moments are given. A step-by-step procedure of the parameters estimation and simulation of sample paths is given. We also provide main results available for Mittag-Leffler Lévy processes (MLLP) and some extensions which are not available in a collective way in a single article. Our results generalize and complement the results available on Mittag-Leffler distribution and MLLP in several directions. Further, the asymptotic forms of the moments of the first-exit times of the TMLLP are also discussed.     

On a control chart for the Gini index with simulations

In this work we suggest the use of the Gini index on control charts. The asymptotic properties of Gini index are presented and the control charts based on appropriate confidence intervals are constructed. The suitability of the proposed charts are investigated by means of extensive simulations.     

A new aging concept derived from the increasing convex ordering

In this paper, a comparison between the life distribution of a new unit with that of a used unit in the increasing convex order is made leading to a new class of life distributions which we call “new better than used in convex ordering of second order”. This class includes as subclasses the NBU and the NBUC and is a subclass of the NBUCA class. Preservation properties under convolution, random maxima, mixing and formation of coherent structures are established. Stochastic comparisons of the excess lifetime when the inter-arrival times belong to the NBUC(2) class are developed. Some applications of Poisson shock models and a test of exponentiality against NBUC(2) alternative are presented.     

A reflected feature space for CART

We present an algorithm for learning oblique decision trees, called HHCART(G). Our decision tree combines learning concepts from two classification trees, HHCART and Geometric Decision Tree (GDT). HHCART(G) is a simplified HHCART algorithm that uses linear structure in the training examples, captured by a modified GDT angle bisector, to define splitting directions. At each node, we reflect the training examples with respect to the modified angle bisector to align this linear structure with the coordinate axes. Searching axis parallel splits in this reflected feature space provides an efficient and effective way of finding oblique splits in the original feature space. Our method is much simpler than HHCART because it only considers one reflected feature space for node splitting. HHCART considers multiple reflected feature spaces for node splitting making it more computationally intensive to build. Experimental results show that HHCART(G) is an effective classifier, producing compact trees with similar or better results than several other decision trees, including GDT and HHCART trees.     

White Ethnic Diversity in Small Town Iowa: A Multilevel Analysis of Community Attachment

Community attachment is the feeling of being connected to community life. Within the community attachment literature, two classic approaches frame scholars’ understanding of this important dimension of community life: the linear development and systemic models. Our empirical models emphasize different factors for community attachment, including population size, density, and heterogeneity for the linear development model and age, length of residence, and social status for the systemic model. Surprisingly, heterogeneity has been omitted from analyses of the linear development model throughout the literature since its introduction, a shortcoming our study addresses. Though heterogeneity can be conceptualized in a number of ways, a large—and growing—body of literature focuses on the effects of race and ethnicity for communities. Here, we focus on a particular type of ethnic heterogeneity—European ancestry—and reincorporate this essential dimension of communities back into the linear development model of community attachment. Using data from the 2004 wave of the Iowa Community Survey and multilevel modeling techniques, we explore how white ethnic diversity matters for community life. We conclude with a discussion of the implications of our study, including potential avenues for future research focusing on other ethnicities that are often subsumed under broader racial and panethnic labels.     

Trajectories of Limitations with Activities of Daily Living Among Older Adults of Mexican Descent: The Role of Widowhood

Using seven waves of data from the Hispanic Established Population for the Epidemiologic Study of the Elderly (1993–2011), this study applies multiphase growth models to examine changes in limitations with activities of daily living (ADL) across widowhood experience among 385 older adults of Mexican descent. This study also investigates the implications of demographic characteristics, health, socioeconomic status, living arrangements, and social involvement. ADL limitations increased pre-widowhood, were at higher levels immediately before and especially during the transition to widowhood, and increased at a steeper rate post-widowhood. Age and partially depressive symptoms accounted for these trends in ADL limitations pre-widowhood and to a lesser extent during the transition to widowhood and post-widowhood. Older age, being female, chronic conditions, financial strain, lower educational attainment, coresidence with children and others, and less frequent church attendance were risk factors for higher levels of and greater increases in these functional limitations throughout widowhood experience.