Kernel density estimation under negative superadditive dependence and its application for real data

In this paper, the kernel density estimator for negatively superadditive dependent random variables is studied. The exponential inequalities and the exponential rate for the kernel estimator of density function with a uniform version, over compact sets are investigated. Also, the optimal bandwidth rate of the estimator is obtained using mean integrated squared error. The results are generalized and used to improve the ones obtained for the case of associated sequences. As an application, FGM sequences that fulfil our assumptions are investigated. Also, the convergence rate of the kernel density estimator is illustrated via a simulation study. Moreover, a real data analysis is presented.     

An extended semiparametric model for short-term and long-term hazard ratios

In survival analysis, one way to deal with non-proportional hazards is to model short-term and long-term hazard ratios. The existing model of this nature has no control over how fast the hazard ratio is changing over time. We add a parameter to the existing model to allow the hazard ratio to change over time at different speed. A nonparametric maximum likelihood approach is used to estimate the model parameters. The existing model is a special case of the extended model when the speed parameter is 0, which leads naturally to a way of testing the adequacy of the existing model. Simulation results show that there can be substantial bias in the estimation of the short-term and long-term hazard ratio if the speed parameter is fixed incorrectly at 0 rather than estimated. The extended model is fitted to three real data sets to shed new insights, including the observation that converging hazards does not necessarily imply the odds are proportional.     

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.     

Quantile regression for large-scale data via sparse exponential transform method

In recent decades, quantile regression has received much more attention from academics and practitioners. However, most of existing computational algorithms are only effective for small or moderate size problems. They cannot solve quantile regression with large-scale data reliably and efficiently. To this end, we propose a new algorithm to implement quantile regression on large-scale data using the sparse exponential transform (SET) method. This algorithm mainly constructs a well-conditioned basis and a sampling matrix to reduce the number of observations. It then solves a quantile regression problem on this reduced matrix and obtains an approximate solution. Through simulation studies and empirical analysis of a 5% sample of the US 2000 Census data, we demonstrate efficiency of the SET-based algorithm. Numerical results indicate that our new algorithm is effective in terms of computation time and performs well for large-scale quantile regression.     

Health insurance literacy: A mixed methods study of college students

Objective: This study examines the health insurance literacy, or the ability to use health insurance effectively, of college students. Participants: A total of 455 students from a large, public university completed an online questionnaire in November 2016. Methods: A questionnaire examined students’ knowledge of commonly encountered health insurance terms and ability to apply that knowledge to determine cost-sharing in a clinical setting. Results: The majority of students were able to correctly identify the most commonly encountered terms, but could not identify terms related to plan types and options. Eighty-eight percent of students could not determine their cost-sharing for two presented scenarios. Approximately half of the students indicated they had been confused about their health insurance plan, with one-quarter of students stopping or delaying medical care due to confusion. Conclusions: Outreach and education for students should target specific deficits in knowledge such as those identified in this study.     

Implementing a college mental health program – an overview of the first twelve months

Objective: To evaluate the demographics and clinical utilization patterns among college students during the initial 12 months of a novel, multi-disciplinary, collaborative, college mental health program (CMHP). Participants: Undergraduate and graduate students receiving treatment at the CMHP from Jan-Dec 2015. Methods: De-identified data was obtained via electronic health records for all students receiving care through the CMHP. Results: 1.2 FTE clinical providers treated 278 undergraduate and graduate students during the year (65.1% < age 26, 53.6% female, 49.6% caucasian). There were 1822 CMHP outpatient visits, 318 other medical visits and 103 total emergency room (ER)/inpatient visits. Ten students were identified as high utilizers of ER/inpatient services, while charges to the CMHP totaled $470,157 and total charges to the Health System were $2,378,315. Conclusions: Students with complex psychiatric/medical co-morbidities received cost effective, convenient and integrative treatment. Over time, we hope to intervene earlier and decrease ER/inpatient visits.     

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.     

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.