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Mathematics
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Statistical Methods and Models for Survival Data Analysis
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Statistical Methods and Models for Survival Data Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 12983

Special Issue Editor

Dr. Yiqiang Zhan

E-Mail Website
Guest Editor
School of Public Health (Shenzhen), Sun Yat-sen University, Shenzhen 528406, China
Interests: survival analysis; causal inference; Mendelian randomization; aging epidemiology; medical epidemiology

Special Issue Information

Dear Colleagues,

Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. The term survival analysis is predominately used in biomedical sciences where interest is in observing time to death either of patients or of laboratory animals. Time-to-event analysis has also been used widely in the social sciences, where interest is on analyzing time to events such as job changes, marriage, birth of children, and so forth. The goal of this Special Issue is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments of survival analysis. Research and review articles on the applications of survival analysis in medical research are of particular interest.

Dr. Yiqiang Zhan
Guest Editor

Manuscript Submission Information

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Keywords

  • survival analysis
  • epidemiology
  • survival and hazard functions
  • Kaplan–Meier survival estimate
  • important distributions in survival analysis
  • fitting parameters to data
  • non-parametric estimation
  • computer software for survival analysis
  • distributions used in survival analysis
  • applications of survival analysis

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Published Papers (7 papers)

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Research

23 pages, 372 KiB  
Article
Expectation-Maximization Algorithm for the Weibull Proportional Hazard Model under Current Status Data
by Sisi Chen and Fengkai Yang
Mathematics 2023, 11(23), 4826; https://doi.org/10.3390/math11234826 - 29 Nov 2023
Viewed by 1392
Abstract
Due to the flexibility of the Weibull distribution and the proportional hazard (PH) model, Weibull PH is widely used in survival analysis under right censored data and interval censored data but it is seldom investigated under current status data, partially because there is [...] Read more.
Due to the flexibility of the Weibull distribution and the proportional hazard (PH) model, Weibull PH is widely used in survival analysis under right censored data and interval censored data but it is seldom investigated under current status data, partially because there is less information in current status data than in right censored data and interval censored data. This paper considers the Weibull PH model under the current status data and introduces the Poisson latent variables to augment the data, then uses the expectation-maximization (EM) algorithm to obtain the maximum likelihood estimators of the model parameters. The EM algorithm is compared with the Newton–Raphson (NR) algorithm from several perspectives in the simulation studies, and the results show that the proposed method has several highlights, such as computational simplicity, improved convergence stability, and overall estimator results that are either comparable or slightly better in terms of bias. Furthermore, the performance of the Weibull PH model and the semi-parametric PH model is compared under two simulation scenarios, and two standard model selection criteria are used for model selection. The results indicate that the Weibull PH model has significant advantages when failure time follows a Weibull distribution. Lastly, the Weibull PH model along with EM algorithm is applied to lung tumor data and intraocular lens (IOL) calcification data with the aim of assessing the impact of covariates, including environmental factors and gender, on event timing and risk. Full article
(This article belongs to the Special Issue Statistical Methods and Models for Survival Data Analysis)
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34 pages, 1113 KiB  
Article
Sensitivity of Survival Analysis Metrics
by Iulii Vasilev, Mikhail Petrovskiy and Igor Mashechkin
Mathematics 2023, 11(20), 4246; https://doi.org/10.3390/math11204246 - 11 Oct 2023
Cited by 1 | Viewed by 2831
Abstract
Survival analysis models allow for predicting the probability of an event over time. The specificity of the survival analysis data includes the distribution of events over time and the proportion of classes. Late events are often rare and do not correspond to the [...] Read more.
Survival analysis models allow for predicting the probability of an event over time. The specificity of the survival analysis data includes the distribution of events over time and the proportion of classes. Late events are often rare and do not correspond to the main distribution and strongly affect the quality of the models and quality assessment. In this paper, we identify four cases of excessive sensitivity of survival analysis metrics and propose methods to overcome them. To set the equality of observation impacts, we adjust the weights of events based on target time and censoring indicator. According to the sensitivity of metrics, AUPRC (area under Precision-Recall curve) is best suited for assessing the quality of survival models, and other metrics are used as loss functions. To evaluate the influence of the loss function, the Bagging model uses ones to select the size and hyperparameters of the ensemble. The experimental study included eight real medical datasets. The proposed modifications of IBS (Integrated Brier Score) improved the quality of Bagging compared to the classical loss functions. In addition, in seven out of eight datasets, the Bagging with new loss functions outperforms the existing models of the scikit-survival library. Full article
(This article belongs to the Special Issue Statistical Methods and Models for Survival Data Analysis)
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26 pages, 30035 KiB  
Article
Survival Analysis of the PRC Model from Adaptive Progressively Hybrid Type-II Censoring and Its Engineering Applications
by Ahmed Elshahhat, Osama E. Abo-Kasem and Heba S. Mohammed
Mathematics 2023, 11(14), 3124; https://doi.org/10.3390/math11143124 - 14 Jul 2023
Cited by 2 | Viewed by 987
Abstract
A new two-parameter statistical model, obtained by compounding the generalized-exponential and exponential distributions, called the PRC lifetime model, is explored in this paper. This model can be easily linked to other well-known six-lifetime models; namely the exponential, log-logistic, Burr, Pareto and generalized Pareto [...] Read more.
A new two-parameter statistical model, obtained by compounding the generalized-exponential and exponential distributions, called the PRC lifetime model, is explored in this paper. This model can be easily linked to other well-known six-lifetime models; namely the exponential, log-logistic, Burr, Pareto and generalized Pareto models. Adaptive progressively hybrid Type-II censored strategy, used to increase the efficiency of statistical inferential results and save the total duration of a test, has become widely used in various sectors such as medicine, biology, engineering, etc. Via maximum likelihood and Bayes inferential methodologies, given the presence of such censored data, the challenge of estimating the unknown parameters and some reliability time features, such as reliability and failure rate functions, of the PRC model is examined. The Markov-Chain Monte Carlo sampler, when the model parameters are assumed to have independent gamma density priors, is utilized to produce the Bayes’ infer under the symmetric (squared-error) loss of all unknown subjects. Asymptotic confidence intervals as well as the highest posterior density intervals of the unknown parameters and the unknown reliability indices are also created. An extensive Monte Carlo simulation is implemented to investigate the accuracy of the acquired point and interval estimators. Four various optimality criteria, to select the best progressive censored design, are used. To demonstrate the applicability and feasibility of the proposed model in a real-world scenario, two data sets from the engineering sector; one based on industrial devices and the other on aircraft windshield, are analyzed. Numerical evaluations showed that the PRC model furnishes a superior fit compared to seven other models in the literature, including: alpha-power exponential, log-logistic, Nadarajah–Haghighi, generalized-exponential, Weibull, gamma and exponential lifetime distributions. The findings demonstrate that, in order to obtain the necessary estimators, the Bayes’ paradigm via Metropolis–Hastings sampler is recommended compared to its competitive likelihood approach. Full article
(This article belongs to the Special Issue Statistical Methods and Models for Survival Data Analysis)
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23 pages, 419 KiB  
Article
Weighted Competing Risks Quantile Regression Models and Variable Selection
by Erqian Li, Jianxin Pan, Manlai Tang, Keming Yu, Wolfgang Karl Härdle, Xiaowen Dai and Maozai Tian
Mathematics 2023, 11(6), 1295; https://doi.org/10.3390/math11061295 - 8 Mar 2023
Viewed by 1474
Abstract
The proportional subdistribution hazards (PSH) model is popularly used to deal with competing risks data. Censored quantile regression provides an important supplement as well as variable selection methods due to large numbers of irrelevant covariates in practice. In this paper, we study variable [...] Read more.
The proportional subdistribution hazards (PSH) model is popularly used to deal with competing risks data. Censored quantile regression provides an important supplement as well as variable selection methods due to large numbers of irrelevant covariates in practice. In this paper, we study variable selection procedures based on penalized weighted quantile regression for competing risks models, which is conveniently applied by researchers. Asymptotic properties of the proposed estimators, including consistency and asymptotic normality of non-penalized estimator and consistency of variable selection, are established. Monte Carlo simulation studies are conducted, showing that the proposed methods are considerably stable and efficient. Real data about bone marrow transplant (BMT) are also analyzed to illustrate the application of the proposed procedure. Full article
(This article belongs to the Special Issue Statistical Methods and Models for Survival Data Analysis)
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21 pages, 474 KiB  
Article
Optimal Model Averaging for Semiparametric Partially Linear Models with Censored Data
by Guozhi Hu, Weihu Cheng and Jie Zeng
Mathematics 2023, 11(3), 734; https://doi.org/10.3390/math11030734 - 1 Feb 2023
Viewed by 1657
Abstract
In the past few decades, model averaging has received extensive attention, and has been regarded as a feasible alternative to model selection. However, this work is mainly based on parametric model framework and complete dataset. This paper develops a frequentist model-averaging estimation for [...] Read more.
In the past few decades, model averaging has received extensive attention, and has been regarded as a feasible alternative to model selection. However, this work is mainly based on parametric model framework and complete dataset. This paper develops a frequentist model-averaging estimation for semiparametric partially linear models with censored responses. The nonparametric function is approximated by B-spline, and the weights in model-averaging estimator are picked up via minimizing a leave-one-out cross-validation criterion. The resulting model-averaging estimator is proved to be asymptotically optimal in the sense of achieving the lowest possible squared error. A simulation study demonstrates that the method in this paper is superior to traditional model-selection and model-averaging methods. Finally, as an illustration, the proposed procedure is further applied to analyze two real datasets. Full article
(This article belongs to the Special Issue Statistical Methods and Models for Survival Data Analysis)
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17 pages, 613 KiB  
Article
A New Cure Rate Model Based on Flory–Schulz Distribution: Application to the Cancer Data
by Reza Azimi, Mahdy Esmailian, Diego I. Gallardo and Héctor J. Gómez
Mathematics 2022, 10(24), 4643; https://doi.org/10.3390/math10244643 - 8 Dec 2022
Cited by 4 | Viewed by 1978
Abstract
In this article a new flexible survival cure rate model is introduced by assuming that the number of competing causes of the event of interest follows the Flory–Schulz distribution and the competing causes follow the generalized truncated Nadarajah–Haghighi distribution. Parameter estimation for the [...] Read more.
In this article a new flexible survival cure rate model is introduced by assuming that the number of competing causes of the event of interest follows the Flory–Schulz distribution and the competing causes follow the generalized truncated Nadarajah–Haghighi distribution. Parameter estimation for the proposed model is derived based on the maximum likelihood estimation method. A simulation study is performed to show the performance of the ML estimators. We discuss three real data applications related to real cancer data sets to assess the usefulness of the proposed model compared with some existing cure rate models for the sake of comparison. Full article
(This article belongs to the Special Issue Statistical Methods and Models for Survival Data Analysis)
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17 pages, 380 KiB  
Article
Regression Analysis of Multivariate Interval-Censored Failure Time Data under Transformation Model with Informative Censoring
by Mengzhu Yu and Mingyue Du
Mathematics 2022, 10(18), 3257; https://doi.org/10.3390/math10183257 - 7 Sep 2022
Cited by 2 | Viewed by 1725
Abstract
We consider a regression analysis of multivariate interval-censored failure time data where the censoring may be informative. To address this, an approximated maximum likelihood estimation approach is proposed under a general class of semiparametric transformation models, and in the method, the frailty approach [...] Read more.
We consider a regression analysis of multivariate interval-censored failure time data where the censoring may be informative. To address this, an approximated maximum likelihood estimation approach is proposed under a general class of semiparametric transformation models, and in the method, the frailty approach is employed to characterize the informative interval censoring. For the implementation of the proposed method, we develop a novel EM algorithm and show that the resulting estimators of the regression parameters are consistent and asymptotically normal. To evaluate the empirical performance of the proposed estimation procedure, we conduct a simulation study, and the results indicate that it performs well for the situations considered. In addition, we apply the proposed approach to a set of real data arising from an AIDS study. Full article
(This article belongs to the Special Issue Statistical Methods and Models for Survival Data Analysis)
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