With the development of high-throughput technologies, more and more high-dimensional or ultra-high-dimensional genomic data are being generated. Therefore, effectively analyzing such data has become a significant challenge. Machine learning (ML) algorithms have been widely applied for modeling nonlinear and complicated interactions in a variety of practical fields such as high-dimensional survival data. Recently, multilayer deep neural network (DNN) models have made remarkable achievements. Thus, a Cox-based DNN prediction survival model (DNNSurv model), which was built with Keras and TensorFlow, was developed. However, its results were only evaluated on the survival datasets with high-dimensional or large sample sizes. In this paper, we evaluated the prediction performance of the DNNSurv model using ultra-high-dimensional and high-dimensional survival datasets and compared it with three popular ML survival prediction models (i.e., random survival forest and the Cox-based LASSO and Ridge models). For this purpose, we also present the optimal setting of several hyperparameters, including the selection of a tuning parameter. The proposed method demonstrated via data analysis that the DNNSurv model performed well overall as compared with the ML models, in terms of the three main evaluation measures (i.e., concordance index, time-dependent Brier score, and the time-dependent AUC) for survival prediction performance.

Competing risks data often exist within a center in multi-center randomized clinical trials where the treatment effects or baseline risks may vary among centers. In this paper, we propose a subdistribution hazard regression model with multivariate frailty to investigate heterogeneity in treatment effects among centers from multi-center clinical trials. For inference, we develop a hierarchical likelihood (or h-likelihood) method, which obviates the need for an intractable integration over the frailty terms. We show that the profile likelihood function derived from the h-likelihood is identical to the partial likelihood, and hence it can be extended to the weighted partial likelihood for the subdistribution hazard frailty models. The proposed method is illustrated with a dataset from a multi-center clinical trial on breast cancer as well as with a simulation study. We also demonstrate how to present heterogeneity in treatment effects among centers by using a confidence interval for the frailty for each individual center and how to perform a statistical test for such heterogeneity using a restricted h-likelihood.

Statistical process control for count data has difficulty overcoming multicollinearity. In this paper, we propose a new deep learning residual control chart based on the asymmetrical count response variable when there are highly correlated explanatory variables. We implement and compare different methods such as neural network, deep learning, principal component analysis based Poisson regression, principal component analysis based negative binomial regression, nonlinear principal component analysis based Poisson regression, and nonlinear principal component analysis based negative binomial regression in terms of the root mean squared error. Using two asymmetrical simulated datasets generated by the combined multivariate normal, binary and copula functions, the neural network and deep learning have a smaller mean, median, and interquartile range when compared to the principal component analysis based Poisson regression, principal component analysis based negative binomial regression, nonlinear principal component analysis based Poisson regression, and nonlinear principal component analysis based negative binomial regression. We also compare the deep learning and neural network based residual control charts in terms of the average run length with the copula based asymmetrical simulated data and real takeover bids data.