Journal of Data Science

Extensive literature has been proposed for the analysis of correlated survival data. Subjects within a cluster share some common characteristics, e.g., genetic and environmental factors, so their time-to-event outcomes are correlated. The frailty model under proportional hazards assumption has been widely applied for the analysis of clustered survival outcomes. However, the prediction performance of this method can be less satisfactory when the risk factors have complicated effects, e.g., nonlinear and interactive. To deal with these issues, we propose a neural network frailty Cox model that replaces the linear risk function with the output of a feed-forward neural network. The estimation is based on quasi-likelihood using Laplace approximation. A simulation study suggests that the proposed method has the best performance compared with existing methods. The method is applied to the clustered time-to-failure prediction within the kidney transplantation facility using the national kidney transplant registry data from the U.S. Organ Procurement and Transplantation Network. All computer programs are available at https://github.com/rivenzhou/deep_learning_clustered.

Deep neural networks have a wide range of applications in data science. This paper reviews neural network modeling algorithms and their applications in both supervised and unsupervised learning. Key examples include: (i) binary classification and (ii) nonparametric regression function estimation, both implemented with feedforward neural networks ($\mathrm{FNN}$); (iii) sequential data prediction using long short-term memory ($\mathrm{LSTM}$) networks; and (iv) image classification using convolutional neural networks ($\mathrm{CNN}$). All implementations are provided in $\mathrm{MATLAB}$, making these methods accessible to statisticians and data scientists to support learning and practical application.

There are many methods of scoring the importance of variables in prediction of a response but not much is known about their accuracy. This paper partially fills the gap by introducing a new method based on the GUIDE algorithm and comparing it with 11 existing methods. For data without missing values, eight methods are shown to give biased scores that are too high or too low, depending on the type of variables (ordinal, binary or nominal) and whether or not they are dependent on other variables, even when all of them are independent of the response. Among the remaining four methods, only GUIDE continues to give unbiased scores if there are missing data values. It does this with a self-calibrating bias-correction step that is applicable to data with and without missing values. GUIDE also provides threshold scores for differentiating important from unimportant variables with 95 and 99 percent confidence. Correlations of the scores to the predictive power of the methods are studied in three real data sets. For many methods, correlations with marginal predictive power are much higher than with conditional predictive power.

Climate change is widely recognized as one of the most challenging, urgent and complex problem facing humanity. There are rising interests in understanding and quantifying climate changing. We analyze the climate trend in Canada using Canadian monthly surface air temperature, which is longitudinal data in nature with long time span. Analysis of such data is challenging due to the complexity of modeling and associated computation burdens. In this paper, we divide this type of longitudinal data into time blocks, conduct multivariate regression and utilize a vine copula model to account for the dependence among the multivariate error terms. This vine copula model allows separate specification of within-block and between-block dependence structure and has great flexibility of modeling complex association structures. To release the computational burden and concentrate on the structure of interest, we construct composite likelihood functions, which leave the connecting structure between time blocks unspecified. We discuss different estimation procedures and issues regarding model selection and prediction. We explore the prediction performance of our vine copula model by extensive simulation studies. An analysis of the Canada climate dataset is provided.