Censored Survival Data Research Articles

Testing for Sufficient Follow-Up in Censored Survival Data by Using Extremes.

In survival analysis, it often happens that some individuals, referred to as cured individuals, never experience the event of interest. When analyzing time-to-event data with a cure fraction, it is crucial to check the assumption of "sufficient follow-up," which means that the right extreme of the censoring time distribution is larger than that of the survival time distribution for the noncured individuals. However, the available methods to test this assumption are limited in the literature. In this article, we study the problem of testing whether follow-up is sufficient for light-tailed distributions and develop a simple novel test. The proposed test statistic compares an estimator of the noncure proportion under sufficient follow-up to one without the assumption of sufficient follow-up. A bootstrap procedure is employed to approximate the critical values of the test. We also carry out extensive simulations to evaluate the finite sample performance of the test and illustrate the practical use with applications to leukemia and breast cancer datasets.

Additive Hazards Regression Analysis of Massive Interval-Censored Data via Data Splitting

With the rapid development of data acquisition and storage space, massive data sets exhibited with large sample size emerge increasingly and make more advanced statistical tools urgently need. To accommodate such big volume in the analysis, a variety of methods have been proposed in the circumstances of complete or right censored survival data. However, existing development of big data methodology has not attended to interval-censored outcomes, which are ubiquitous in cross-sectional or periodical follow-up studies. In this work, we propose an easily implemented divide-and-combine approach for analyzing massive interval-censored survival data under the additive hazards model. We establish the asymptotic properties of the proposed estimator, including the consistency and asymptotic normality. In addition, the divide-and-combine estimator is shown to be asymptotically equivalent to the full-data-based estimator obtained from analyzing all data together. Simulation studies suggest that, relative to the full-data-based approach, the proposed divide-and-combine approach has desirable advantage in terms of computation time, making it more applicable to large-scale data analysis. An application to a set of interval-censored data also demonstrates the practical utility of the proposed method.

Advancing Bayesian Inference: Fitting Type I Half-logistic Nadarajah-Haghighi Distribution and its Comparison with Related Distributions for Censored Survival Data

In recent years, the field of Bayesian modeling of generalized distributions has garnered substantial attention. This surge in interest can be attributed to the remarkable strides made in computational capabilities and the enhanced accessibility of sophisticated software tools. This study aims to apply Bayesian inference methods to the Type I Half-logistic Nadarajah- Haghighi model and compares it with the Exponential model and the Type I Half-logistic Exponential model. These distributions are analyzed and fitted to censored survival data using the probabilistic programming language STAN. To incorporate censored mechanisms within the STAN framework, customized codes are developed. The models are then compared using fully Bayesian model selection methods.. KEYWORDS :Censored data, Nadarajah-Haghighi distribution, Type I half-logistic family, LOOIC, WAIC, STAN.

Empirical likelihood MLE for joint modeling right censored survival data with longitudinal covariates

Empirical likelihood MLE for joint modeling right censored survival data with longitudinal covariates

Test for Informative Cluster Size with Right Censored Survival Data

Test for Informative Cluster Size with Right Censored Survival Data

The accelerated failure time regression model under the extended-exponential distribution with survival analysis

<abstract><p>In this paper, we propose a parametric accelerated failure time (AFT) hazard-based regression model with the extended alpha-power exponential (EAPE) baseline distribution. The proposed model is called the extended alpha-power exponential-AFT (EAPE-AFT) regression model. We show that the EAPE distribution is closed under the AFT model. The parameters of the proposed EAPE-AFT model have been estimated by using the method of maximum likelihood estimation. An extensive simulation study was also conducted to examine the performance of the estimates under several scenarios based on the shapes of the baseline hazard function. Finally, real-life censored survival data has been used to illustrate the applicability of the proposed model.</p></abstract>

A new method for clustered survival data: Estimation of treatment effect heterogeneity and variable selection.

We recently developed a new method random-intercept accelerated failure time model with Bayesian additive regression trees (riAFT-BART) to draw causal inferences about population treatment effect on patient survival from clustered and censored survival data while accounting for the multilevel data structure. The practical utility of this method goes beyond the estimation of population average treatment effect. In this work, we exposit how riAFT-BART can be used to solve two important statistical questions with clustered survival data: estimating the treatment effect heterogeneity and variable selection. Leveraging the likelihood-based machine learning, we describe a way in which we can draw posterior samples of the individual survival treatment effect from riAFT-BART model runs, and use the drawn posterior samples to perform an exploratory treatment effect heterogeneity analysis to identify subpopulations who may experience differential treatment effects than population average effects. There is sparse literature on methods for variable selection among clustered and censored survival data, particularly ones using flexible modeling techniques. We propose a permutation-based approach using the predictor's variable inclusion proportion supplied by the riAFT-BART model for variable selection. To address the missing data issue frequently encountered in health databases, we propose a strategy to combine bootstrap imputation and riAFT-BART for variable selection among incomplete clustered survival data. We conduct an expansive simulation study to examine the practical operating characteristics of our proposed methods, and provide empirical evidence that our proposed methods perform better than several existing methods across a wide range of data scenarios. Finally, we demonstrate the methods via a case study of predictors for in-hospital mortality among severe COVID-19 patients and estimating the heterogeneous treatment effects of three COVID-specific medications. The methods developed in this work are readily available in the package .

Generalized k‐variate proportional hazard function for censored survival data

This note develops a generalized ‐variate hazard function for censored data in survival analysis. It introduces a generalized recursive formula, extending the bivariate and trivariate cases introduced by Clayton and Cuzick (1985, Journal of the Royal Statistical Society: Series A (General), 148(2):82–108) and Kittani (1995, Journal of Mathematical Sciences, 67–74), respectively. The newly developed function is explicitly specified by association parameters and marginal hazard functions.

Survival Rate Estimation in Patients with Colorectal Cancer by applying Fuzzy Product Limit Estimator

Background: Survival rates are important to show the progress of the disease and the effect of treatments. The estimation of survival probabilities especially in presence of highly censored data is challenging. In this study, Fuzzy Product Limit Estimator (FPLE) is introduced to mitigate the challenge.
 Methods: In a longitudinal study, data of 173 CRC patients were analyzed. To estimate survival probabilities, mean and median survival time, Fuzzy Product Limit Estimator (FPLE), a data-driven method, was applied to the data. It provides a smooth survival probability curve and the continuation of the survival curve is not a concern in the case while the largest observed time is censored.
 Results: One-year survival rate for CRC patients was estimated to be 83% using FPLE and KM methods. The five-year survival rate was estimated to be 37% and 52% by the FPLE and KM methods, respectively. The largest observed time in data (71.96 months) was censored, so the survival rate after 71.96 months was not estimable by the KM method. But 10-year and 20-year survival rates were estimated by FPLE as 0.21 and 0.09. The mean (median) survival time was estimated 45.97 (65) and 82.69 (41.70) months by KM and FPLE methods, respectively. 
 Conclusion: In presence of highly censored survival data, the FPLE method provides acceptable estimates of CRC patients' survival rate. Also, the continuation of the survival curve was estimated after the largest observed time. The smaller estimates by the FPLE at 5-year could be considered as warning that the actual survival rate is lower than that reported by the KM method.

Survival Analysis and Hazard of Log Logistic Distribution on Type I Censored Data Parametrically

Survival Analysis is a research method that examines the survival time of individuals or experimental units in relation to events such as death, disease, recovery, or other experiences. This study utilizes a parametric survival analysis model with a 2 parameter log logistic distribution and Maximum Likelihood Estimation (MLE) method to analyze the survival of students during their study period. The log logistic distribution is chosen due to its ability to capture early or late failure patterns. The objective of this research is to analyze type I censored survival data using the log logistic distribution applied to secondary data on student study duration. The dataset consists of 98 observations. The calculated values for the β and γ parameters of the 2 parameters log logistic distribution are 2.12831 and 0.0918891, respectively. The probability of students completing their studies by semester 8 (hazard function h(8)) is 0.370102, while the probability of students continuing their studies in semester 9 (survival function s(9)) is 0.320817.

Laplace approximated quasi-likelihood method for heteroscedastic survival data

The classical accelerated failure time model is the major linear model for right censored survival data. It requires the survival data to exhibit homoscedasticity of variance and excludes heteroscedastic survival data that are often seen in practical applications. The least squares method for the classical accelerated failure time model has been extended to accommodate the heteroscedasticity in survival data. However, the estimating equations are discrete and hence they are time consuming and may not be feasible for large datasets. This paper proposes a Laplace approximated quasi-likelihood method with a continuous estimating equation. It utilizes the Laplace approximation to approximate the survival function in the quasi-likelihood, in which the variance function is approximated by a spline function. Then it shows the asymptotic distribution of the Laplace approximated estimator, its estimation bias and the formula for confidence interval estimation for the parameter of interest. The finite sample performance of the proposed approach is evaluated through simulation studies and follows real data examples for illustration.

Estimating the causal effects of multiple intermittent treatments with application to COVID-19

Abstract To draw real-world evidence about the comparative effectiveness of multiple time-varying treatments on patient survival, we develop a joint marginal structural survival model and a novel weighting strategy to account for time-varying confounding and censoring. Our methods formulate complex longitudinal treatments with multiple start/stop switches as the recurrent events with discontinuous intervals of treatment eligibility. We derive the weights in continuous time to handle a complex longitudinal data set without the need to discretise or artificially align the measurement times. We further use machine learning models designed for censored survival data with time-varying covariates and the kernel function estimator of the baseline intensity to efficiently estimate the continuous-time weights. Our simulations demonstrate that the proposed methods provide better bias reduction and nominal coverage probability when analysing observational longitudinal survival data with irregularly spaced time intervals, compared to conventional methods that require aligned measurement time points. We apply the proposed methods to a large-scale COVID-19 data set to estimate the causal effects of several COVID-19 treatments on the composite of in-hospital mortality and intensive care unit (ICU) admission relative to findings from randomised trials.

Variational Bayesian Inference for Exponentiated Weibull Right Censored Survival Data

The exponential, Weibull, log-logistic and lognormal distributions represent the class of light and heavy-tailed distributions that are often used in modelling time-to-event data. The exponential distribution is often applied if the hazard is constant, while the log-logistic and lognormal distributions are mainly used for modelling unimodal hazard functions. The Weibull distribution is on the other hand well-known for modelling monotonic hazard rates. Recently, in practice, survival data often exhibit both monotone and non-monotone hazards. This gap has necessitated the introduction of Exponentiated Weibull Distribution (EWD) that can accommodate both monotonic and non-monotonic hazard functions. It also has the strength of adapting unimodal functions with bathtub shape. Estimating the parameter of EWD distribution poses another problem as the flexibility calls for the introduction of an additional parameter. Parameter estimation using the maximum likelihood approach has no closed-form solution, and thus, approximation techniques such as Newton-Raphson is often used. Therefore, in this paper, we introduce another estimation technique called Variational Bayesian (VB) approach. We considered the case of the accelerated failure time (AFT) regression model with covariates. The AFT model was developed using two comparative studies based on real-life and simulated data sets. The results from the experiments reveal that the Variational Bayesian (VB) approach is better than the competing Metropolis-Hasting Algorithm and the reference maximum likelihood estimates.

Bayesian spatio‐temporal survival analysis for all types of censoring with application to a wildlife disease study

AbstractIn this article, we consider modeling arbitrarily censored survival data with spatio‐temporal covariates. We demonstrate that under the piecewise constant hazard function, the likelihood for uncensored or right‐censored subjects is proportional to the likelihood of multiple conditionally independent Poisson random variables. To address left‐ or interval‐censored subjects, we propose to impute the exact event times and convert them into uncensored subjects, enabling the application of the integrated nested Laplace approximation to update model parameters using the imputed data. We introduce an iterative algorithm that alternates between imputing event times for left‐ and interval‐censored subjects and re‐estimating model parameters. The proposed method is assessed through a simulation study and applied to analyze a spatio‐temporal survival dataset in a wildlife disease study investigating bovine tuberculosis in white‐tailed deer in Michigan.

An Investigational Modeling Approach for Improving Gene Selection using Regularized Cox Regression Model

By producing the required proteins, the process of gene expression establishes the physical properties of living things. Gene expression from DNA or RNA may be recorded using a variety of approaches. Regression analysis has evolved in prominence in the area of genetic research recently. Several of the genes in high dimensional gene expression information for statistical inference may not be related to their illnesses, which is one of the major problems. The ability of gene selection to enhance the outcomes of several techniques has been demonstrated. For censored survival data, the Cox proportional hazards regression model is the most widely used model. In order to identify important genes and achieve high classification accuracy, a new technique for selecting the tuning parameter is suggested in this study using an optimization algorithm. According to experimental findings, the suggested strategy performs much better than the two rival methods in terms of the area under the curve and the number of chosen genes. This study provides a comprehensive assessment of the latest work on performance evaluation of regression analysis in gene selection. In addition to its performance analysis, this research conducts a thorough assessment of the numerous efforts done on various extended models based on gene selection in recent years.

On the maximum penalized full likelihood approach for Cox model with extreme value for heavily censored survival data

In this paper, to deal with heavily censored survival data, a penalized full likelihood (PFL) with extreme value is proposed to estimate the regression coefficients and baseline hazard function in Cox model simultaneously, where multiple penalties are used for variable selection. We present a single-loop algorithm to fit the tail of the baseline distribution beyond a threshold with an extreme value model. The proposed maximum PFL estimators are proved to possess good asymptotic properties, which are validated by simulations and real data analysis.

MC‐KV: A Prognosis‐Oriented Classifier Based on Semi‐Supervised Learning for Molecular Subtyping of Colorectal Cancer

AbstractColorectal cancer (CRC) is the second leading cause of cancer‐related death worldwide. Many molecular classification strategies are proposed for CRC but few studies include survival data in their models. Herein a prognosis‐oriented CRC classifier is constructed by adapting the natural partially labeled censored survival data into a customized semi‐supervised learning algorithm, which is called Monte‐Carlo K‐nearest neighbor voting (MC‐KV) classifier. Three CRC subtypes with distinct prognoses are identified by this classifier using the data from the cancer genome atlas. Furthermore, a six‐gene risk model is constructed by combining weighted gene coexpression network analysis and least absolute selection and shrinkage operator for variable selection and four algorithms (random survival forest, support vector machine, Adaboost, and logistic regression) for optimization. The optimized model shows great performance in distinguishing high‐risk from low‐risk patients with a maximum area under curve of 0.869, 0.906, and 0.921 in 1‐, 3‐, and 5‐year survival, respectively. Additionally, the six‐gene signature identified by MC‐KV exhibits great predictive efficiency for other cancer types. Overall, a tool, Monte‐Carlo K‐nearest neighbor voting (MC‐KV), is provided to identify molecular subtyping of CRC, which suggests the potential contribution of semi‐supervised algorithms and the inclusion of patient‐level survival data in cancer classification.

범주형 전환문항을 포함하는 항목 무응답 대체 방법 비교

In social surveys, unfolding bracket questions are used as a technique to reduce the loss of information due to nonresponse when item nonresponses occur. Item nonresponse, including unfolding bracket questions, has a similar structure to interval censored survival data. However, imputation methods to handle item nonresponses including unfolding bracket questions are limited. In this study, we examine performance of imputation with and without unfolding bracket questions. Also we compare three imputation methods to handle unfolding bracket questions. The First method is a linear regression-based nearest neighbor hotdeck imputation. Secondly, it is possible to consider a uniform distribution that selects a value with the same probability within the section for each individual. The third is an imputation method using the survival function estimated by the nonparametric maximum likelihood estimation method. Hotdeck imputation was considered as an imputation for not using unfolding bracket questions. The performance of these imputation methods was evaluated through simulation and the KLoSA study is used to provide examples of the application of these methods to real data. Imputation methods using unfolding bracket questions showed better performance than the method without unfolding bracket questions. The performance of the imputation method using the survival function estimated by the nonparametric maximum likelihood estimation method was better when the nonresponse rate was low and when the nonresponse rate is large in terms of root mean square error. When the non-response rate is large, the linear regression-based nearest neighbor hotdeck imputation method showed better results in terms of mean bias.

Accountable survival contrast-learning for optimal dynamic treatment regimes

Dynamic treatment regime (DTR) is an emerging paradigm in recent medical studies, which searches a series of decision rules to assign optimal treatments to each patient by taking into account individual features such as genetic, environmental, and social factors. Although there is a large and growing literature on statistical methods to estimate optimal treatment regimes, most methodologies focused on complete data. In this article, we propose an accountable contrast-learning algorithm for optimal dynamic treatment regime with survival endpoints. Our estimating procedure is originated from a doubly-robust weighted classification scheme, which is a model-based contrast-learning method that directly characterizes the interaction terms between predictors and treatments without main effects. To reflect the censorship, we adopt the pseudo-value approach that replaces survival quantities with pseudo-observations for the time-to-event outcome. Unlike many existing approaches, mostly based on complicated outcome regression modeling or inverse-probability weighting schemes, the pseudo-value approach greatly simplifies the estimating procedure for optimal treatment regime by allowing investigators to conveniently apply standard machine learning techniques to censored survival data without losing much efficiency. We further explore a SCAD-penalization to find informative clinical variables and modified algorithms to handle multiple treatment options by searching upper and lower bounds of the objective function. We demonstrate the utility of our proposal via extensive simulations and application to AIDS data.

A promising subgroup identification method based on a genetic algorithm for censored survival data

ABSTRACT Modern precision medicine requires drug development to account for patients’ heterogeneity, as only a subgroup of the patient population is likely to benefit from the targeted therapy. In this paper, we propose a novel method for subgroup identification based on a genetic algorithm. The proposed method can detect promising subgroups defined by predictive biomarkers in which the treatment effects are much higher than the population average. The main idea is to search for the subgroup with the greatest predictive ability in the entire subgroup space via a genetic algorithm. We design a real-valued representation of subgroups that evolves according to a genetic algorithm and derive an objective function that properly evaluates the predictive ability of the subgroups. Compared with model- or tree-based subgroup identification methods, the distinctive search strategy of this new approach offers an improved capability to explore subgroups defined by multiple predictive biomarkers. By embedding a resampling scheme, the multiplicity and complexity issues inherent in subgroup identification methods can be addressed flexibly. We evaluate the performance of the proposed method in comparison with two other methods using simulation studies and a real-world example. The results show that the proposed method exhibits good properties in terms of multiplicity and complexity control, and the subgroups identified are much more accurate. Although we focus on the implementation of censored survival data, this method could easily be extended for the realization of continuous and categorical endpoints.