Sparse Estimation of Cox Proportional Hazards Models via Approximated Information Criteria

We propose a new sparse estimation method for Cox (1972) proportional hazards models by optimizing an approximated information criterion. The main idea involves approximation of the inline image norm with a continuous or smooth unit dent function. The proposed method bridges the best subset selection and regularization by borrowing strength from both. It mimics the best subset selection using a penalized likelihood approach yet with no need of a tuning parameter. We further reformulate the problem with a reparameterization step so that it reduces to one unconstrained nonconvex yet smooth programming problem, which can be solved efficiently as in computing the maximum partial likelihood estimator (MPLE). Furthermore, the reparameterization tactic yields an additional advantage in terms of circumventing postselection inference. The oracle property of the proposed method is established. Both simulated experiments and empirical examples are provided for assessment and illustration

Associations between maternal hormonal biomarkers and maternal mental and physical health of very low birth weight infants

The purpose of this study was to determine whether maternal mental and physical health is associated with maternal testosterone and cortisol levels, parenting of very low birth weight infants, physical exercise, and White vs non-White race. A total of 40 mothers of very low birth weight infants were recruited from a neonatal intensive care unit at a University Hospital in the Southeast United States. Data were collected through a review of medical records, standardized questionnaires, and biochemical measurement. Maternal mental and physical health status using questionnaires as well as maternal testosterone and cortisol levels using an enzyme immunoassay were measured four times (birth, 40 weeks postmenstrual age [PMA], and 6 and 12 months [age of infant, corrected age]). General linear models showed that higher testosterone levels were associated with greater depressive symptoms, stress, and poorer physical health at 40 weeks PMA, and at 6 and 12 months. High cortisol levels were associated with greater anxiety at 40 weeks PMA; however, with better mental and physical health at 40 weeks PMA, and 6 and 12 months. Physical activity was associated with lower maternal perceived stress at 12 months. Maternal health did not differ by race, except anxiety, which was higher in White than non-White mothers after birth. As very low birth weight infants grew up, maternal physical health improved but mental health deteriorated. Testosterone and cortisol levels were found to be positively correlated in women but testosterone was more predictive of maternal mental and physical health than cortisol. Indeed testosterone consistently showed its associations with maternal health. Maternal stress might be improved through regular physical exercise

Simultaneous Inference on All Linear Combinations of Means with Heteroscedastic Errors

We proposed a statistical method to construct simultaneous confidence intervals on all linear combinations of means without assuming equal variance where the classical Scheffé's simultaneous confidence intervals no longer preserve the familywise error rate (FWER). The proposed method is useful when the number of comparisons on linear combinations of means is extremely large. The FWERs for proposed simultaneous confidence intervals under various configurations of mean variances are assessed through simulations and are found to preserve the predefined nominal level very well. An example of pairwise comparisons on heteroscedastic means is given to illustrate the proposed method

Subgroup Analysis via Recursive Partitioning

Subgroup analysis is an integral part of comparative analysis where assessing the treatment effect on a response is of central interest. Its goal is to determine the heterogeneity of the treatment effect across subpopulations. In this paper, we adapt the idea of recursive partitioning and introduce an interaction tree (IT) procedure to conduct subgroup analysis. The IT procedure automatically facilitates a number of objectively defined subgroups, in some of which the treatment effect is found prominent while in others the treatment has a negligible or even negative effect. The standard CART (Breiman et al., 1984) methodology is inherited to construct the tree structure. Also, in order to extract factors that contribute to the heterogeneity of the treatment effect, variable importance measure is made available via random forests of the interaction trees. Both simulated experiments and analysis of census wage data are presented for illustration