BACKGROUND AND OBJECTIVE:The morbidity of lung adenocarcinoma (LUAD) has been increasing year by year and the prognosis is poor. This has prompted researchers to study the survival of LUAD patients to ensure that patients can be cured in time or survive after appropriate treatment. There is still no fully valid model that can be applied to clinical practice.METHODS:We introduced struc2vec-based multi-omics data integration (SBMOI), which could integrate gene expression, somatic mutations and clinical data to construct mutation gene vectors representing LUAD patient features. Based on the patient features, the random survival forest (RSF) model was used to predict the long- and short-term survival of LUAD patients. To further demonstrate the superiority of SBMOI, we simultaneously replaced scale-free gene co-expression network (FCN) with a protein-protein interaction (PPI) network and a significant co-expression network (SCN) to compare accuracy in predicting LUAD patient survival under the same conditions.RESULTS:Our results suggested that compared with SCN and PPI network, the FCN based SBMOI combined with RSF model had better performance in long- and short-term survival prediction tasks for LUAD patients. The AUC of 1-year, 5-year, and 10-year survival in the validation dataset were 0.791, 0.825, and 0.917, respectively.CONCLUSIONS:This study provided a powerful network-based method to multi-omics data integration. SBMOI combined with RSF successfully predicted long- and short-term survival of LUAD patients, especially with high accuracy on long-term survival. Besides, SBMOI algorithm has the potential to combine with other machine learning models to complete clustering or stratificational tasks, and being applied to other diseases.

Testing the population covariance matrix is an important topic in multivariate statistical analysis. Owing to the difficulty of establishing the central limit theorem for the test statistic based on sample covariance matrix, in most of the existing literature, it is assumed that the population covariance matrix is bounded in spectral norm as the dimension tends to infinity. Four test statistics are proposed for testing the compound symmetric structure of the population covariance matrix, which has an unbounded spectral norm as the dimension tends to infinity. Three of these tests maintain high power against different kinds of dense alternatives. The asymptotic properties of these statistics are constructed under the null hypothesis and a specific alternative hypothesis. Moreover, extensive simulation studies and an analysis of real data are conducted to evaluate the performance of our proposed tests. The simulation results show that the proposed tests outperform existing methods.

In this paper, we propose some new tests for high-dimensional covariance matrices that are applicable to generally distributed populations with finite fourth moments. The proposed test statistics are the maximum of the likelihood ratio test statistic and the statistic based on the Frobenius norm. The advantage of the new tests is the good performance in terms of power for both the traditional case, in which the dimension is much smaller than the sample size, and the high-dimensional case, in which the dimension is large compared to the sample size. In the one-sample case, the new test is proposed for testing the hypothesis that the high-dimensional covariance matrix equals an identity matrix. In the two-sample case, the new test is developed for testing the equality of two high-dimensional covariance matrices. By using the random matrix theory, the asymptotic distributions of the proposed new tests are derived under the assumption that the dimension and the sample size proportionally tend toward infinity. Finally, numerical studies are conducted to investigate the finite sample performance of the proposed new tests.