Extended Bayesian information criterion in the Cox model with a high-dimensional feature space

Looks and longevity: Do prettier people live longer?

Social scientists have given relatively scant attention to the association between attractiveness and longevity. But attractiveness may convey underlying health, and it systematically structures critical social stratification processes. We evaluated these issues using the Wisconsin Longitudinal Study (WLS, N = 8386), a survey of Wisconsin high school graduates from 1957 which provided large samples of women and men observed until their death (or through their early 80s). In doing so, we utilized a meticulously constructed measure of facial attractiveness based on the independent ratings of high-school yearbook photographs. We used linked death information from the National Death Index-plus through 2022 and Cox proportional hazard models as well as standard life-table techniques. We found that the least attractive rated sextile of the sample had significantly higher hazards of mortality (HR: 1.168, p < 0.01) compared to the middle rated four sextiles of attractiveness. This finding remained robust to the inclusion of covariates describing high-school achievement, intelligence, family background, earnings as adults, as well as mental and physical health in middle adulthood. We also found that different specifications of the attractiveness measure consistently indicated no significant differences in the mortality hazard between highly attractive and average-looking people. Using life-table techniques, we next illustrated that among women in the least attractive sextile, at age 20 their life expectancy was nearly 2 years less than others'; among men in the least attractive sextile, it was nearly 1 year less at age 20.

The unique role of smartphone addiction and related factors among university students: a model based on cross-sectional and cross-lagged network analyses

Smartphone addiction is a global problem affecting university students. Previous studies have explored smartphone addiction and related factors using latent variables. In contrast, this study examines the role of smartphone addiction and related factors among university students using a cross-sectional and cross-lagged panel network analysis model at the level of manifest variables. A questionnaire method was used to investigate smartphone addiction and related factors twice with nearly six-month intervals among 1564 first-year university students (M = 19.14, SD = 0.66). The study found that procrastination behavior, academic burnout, self-control, fear of missing out, social anxiety, and self-esteem directly influenced smartphone addiction. Additionally, smartphone addiction predicted the level of self-control, academic burnout, social anxiety, and perceived social support among university students. Self-control exhibited the strongest predictive relationship with smartphone addiction. Overall, self-control, self-esteem, perceived social support, and academic burnout were identified as key factors influencing smartphone addiction among university students. Developing prevention and intervention programs that target these core influencing factors would be more cost-effective.

A General Framework for Identifying Hierarchical Interactions and Its Application to Genomics Data

The analysis of hierarchical interactions has long been a challenging problem due to the large number of candidate main effects and interaction effects, and the need for accommodating the "main effects, interactions" hierarchy. The two-stage analysis methods enjoy simplicity and low computational cost, but contradict the fact that the outcome of interest is attributable to the joint effects of multiple main factors and their interactions. The existing joint analysis methods can accurately describe the underlying data generating process, but suffer from prohibitively high computational cost. And it is not straightforward to extend their optimization algorithms to general loss functions. To address this need, we develop a new computational method that is much faster than the existing joint analysis methods and rivals the runtimes of two-stage analysis. The proposed method, HierFabs, adopts the framework of the forward and backward stagewise algorithm and enjoys computational efficiency and broad applicability. To accommodate hierarchy without imposing additional constraints, it has newly developed forward and backward steps. It naturally accommodates the strong and weak hierarchy, and makes optimization much simpler and faster than in the existing studies. Optimality of HierFabs sequences is investigated theoretically. Simulations show that it outperforms the existing methods. The analysis of TCGA data on melanoma demonstrates its competitive practical performance.

Bayesian information criterion approximations to Bayes factors for univariate and multivariate logistic regression models

Schwarz's criterion, also known as the Bayesian Information Criterion or BIC, is commonly used for model selection in logistic regression due to its simple intuitive formula. For tests of nested hypotheses in independent and identically distributed data as well as in Normal linear regression, previous results have motivated use of Schwarz's criterion by its consistent approximation to the Bayes factor (BF), defined as the ratio of posterior to prior model odds. Furthermore, under construction of an intuitive unit-information prior for the parameters of interest to test for inclusion in the nested models, previous results have shown that Schwarz's criterion approximates the BF to higher order in the neighborhood of the simpler nested model. This paper extends these results to univariate and multivariate logistic regression, providing approximations to the BF for arbitrary prior distributions and definitions of the unit-information prior corresponding to Schwarz's approximation. Simulations show accuracies of the approximations for small samples sizes as well as comparisons to conclusions from frequentist testing. We present an application in prostate cancer, the motivating setting for our work, which illustrates the approximation for large data sets in a practical example.

Consistent Estimation of Generalized Linear Models with High Dimensional Predictors via Stepwise Regression

Predictive models play a central role in decision making. Penalized regression approaches, such as least absolute shrinkage and selection operator (LASSO), have been widely used to construct predictive models and explain the impacts of the selected predictors, but the estimates are typically biased. Moreover, when data are ultrahigh-dimensional, penalized regression is usable only after applying variable screening methods to downsize variables. We propose a stepwise procedure for fitting generalized linear models with ultrahigh dimensional predictors. Our procedure can provide a final model; control both false negatives and false positives; and yield consistent estimates, which are useful to gauge the actual effect size of risk factors. Simulations and applications to two clinical studies verify the utility of the method.

Building generalized linear models with ultrahigh dimensional features: A sequentially conditional approach

Conditional screening approaches have emerged as a powerful alternative to the commonly used marginal screening, as they can identify marginally weak but conditionally important variables. However, most existing conditional screening methods need to fix the initial conditioning set, which may determine the ultimately selected variables. If the conditioning set is not properly chosen, the methods may produce false negatives and positives. Moreover, screening approaches typically need to involve tuning parameters and extra modeling steps in order to reach a final model. We propose a sequential conditioning approach by dynamically updating the conditioning set with an iterative selection process. We provide its theoretical properties under the framework of generalized linear models. Powered by an extended Bayesian information criterion as the stopping rule, the method will lead to a final model without the need to choose tuning parameters or threshold parameters. The practical utility of the proposed method is examined via extensive simulations and analysis of a real clinical study on predicting multiple myeloma patients' response to treatment based on their genomic profiles.

Forward regression for Cox models with high-dimensional covariates

Forward regression, a classical variable screening method, has been widely used for model building when the number of covariates is relatively low. However, forward regression is seldom used in high-dimensional settings because of the cumbersome computation and unknown theoretical properties. Some recent works have shown that forward regression, coupled with an extended Bayesian information criterion (EBIC)-based stopping rule, can consistently identify all relevant predictors in high-dimensional linear regression settings. However, the results are based on the sum of residual squares from linear models and it is unclear whether forward regression can be applied to more general regression settings, such as Cox proportional hazards models. We introduce a forward variable selection procedure for Cox models. It selects important variables sequentially according to the increment of partial likelihood, with an EBIC stopping rule. To our knowledge, this is the first study that investigates the partial likelihood-based forward regression in high-dimensional survival settings and establishes selection consistency results. We show that, if the dimension of the true model is finite, forward regression can discover all relevant predictors within a finite number of steps and their order of entry is determined by the size of the increment in partial likelihood. As partial likelihood is not a regular density-based likelihood, we develop some new theoretical results on partial likelihood and use these results to establish the desired sure screening properties. The practical utility of the proposed method is examined via extensive simulations and analysis of a subset of the Boston Lung Cancer Survival Cohort study, a hospital-based study for identifying biomarkers related to lung cancer patients' survival.

Tuning Parameter Selection in Cox Proportional Hazards Model with a Diverging Number of Parameters

Regularized variable selection is a powerful tool for identifying the true regression model from a large number of candidates by applying penalties to the objective functions. The penalty functions typically involve a tuning parameter that control the complexity of the selected model. The ability of the regularized variable selection methods to identify the true model critically depends on the correct choice of the tuning parameter. In this study we develop a consistent tuning parameter selection method for regularized Cox's proportional hazards model with a diverging number of parameters. The tuning parameter is selected by minimizing the generalized information criterion. We prove that, for any penalty that possesses the oracle property, the proposed tuning parameter selection method identifies the true model with probability approaching one as sample size increases. Its finite sample performance is evaluated by simulations. Its practical use is demonstrated in the Cancer Genome Atlas (TCGA) breast cancer data.