Network estimation for censored time-to-event data for multiple events based on multivariate survival analysis.

Yoojoong Kim,Junhee Seok,Leto Peel

doi:10.1371/journal.pone.0239760

Abstract

In general survival analysis, multiple studies have considered a single failure time corresponding to the time to the event of interest or to the occurrence of multiple events under the assumption that each event is independent. However, in real-world events, one event may impact others. Essentially, the potential structure of the occurrence of multiple events can be observed in several survival datasets. The interrelations between the times to the occurrences of events are immensely challenging to analyze because of the presence of censoring. Censoring commonly arises in longitudinal studies in which some events are often not observed for some of the subjects within the duration of research. Although this problem presents the obstacle of distortion caused by censoring, the advanced multivariate survival analysis methods that handle multiple events with censoring make it possible to measure a bivariate probability density function for a pair of events. Considering this improvement, this paper proposes a method called censored network estimation to discover partially correlated relationships and construct the corresponding network composed of edges representing non-zero partial correlations on multiple censored events. To demonstrate its superior performance compared to conventional methods, the selecting power for the partially correlated events was evaluated in two types of networks with iterative simulation experiments. Additionally, the correlation structure was investigated on the electronic health records dataset of the times to the first diagnosis for newborn babies in South Korea. The results show significantly improved performance as compared to edge measurement with competitive methods and reliability in terms of the interrelations of real-life diseases.

Highlights

With the recent emergence of large-scale and complex data, it is important to uncover relationships among variables during data analyses
This method is based on the estimation for the joint probability density function for time-to-event data for multiple events and selection of non-zero partial correlation with inverse covariance estimation by lasso regression with vector-wise permutation
The proposed method achieved a remarkable performance of 0.95 area under the curve (AUC) with a 0.81 true positive rate (TPR) controlled at 0.05 false positive rates (FPRs), and 0.87 TPR controlled at 0.1 FPR

Summary

Introduction

With the recent emergence of large-scale and complex data, it is important to uncover relationships among variables during data analyses. There is difficulty in constructing the network for the variables of the censored data because of some missing values, and this difficulty is compounded by the multiple dimensionalities of the data To solve this problem, multivariate survival analysis is considered to handle right-censored data. Graphical Lasso is employed to select the non-zero entries of the inverse covariance matrix [6] Using this procedure, the conditional dependencies are discovered, and the network that implies a partially correlated relationship between variables is constructed. This paper proposes a method to detect pairs of partially correlated events for the multivariate survival data based on times to the occurrence of events. The remainder of this manuscript is organized as follows.

Materials and methods

Findings

Discussion