Failure Time Data Research Articles

Impact of sample size, sojourn time distribution on the performance of multistate semi-Markov model for analyzing disease progression: a simulation study

Multistate semi-Markov model (MSSMM) is an alternative to the widely used Multistate Markov Model (MSMM) for analyzing longitudinal failure time data, but there lacks simulation study for its performance. We simulated multistate data and evaluated MSSMM’s performance in various parameter settings. We considered an extended illness-death model with 5 states and 8 transitions. Three kinds of sojourn time distributions and a trivial embedded chain were used for data generation. We used information criteria (IC) to select models and calculated the coverage of model parameter, effect and survival statistics. We also calculated the standard deviation of mean state occupancy probability (MSOPSD) and the standard deviation of restricted expected length of stay (RELOSSD) from the perspective of multistate model. We found that correct identification of model distribution is related to the selected IC; model parameter coverage is related to the true distribution and transition; effect coverage is related to the true distribution; survival statistics coverage is related to the true distribution, transition and covariate; MSOPSD and RELOSSD are both related to the selected information criteria and covariate. These findings provide a basis for the reliability of MSSMM extrapolation and prediction, and inspire future MSSMM research.

An improved extension of Xgamma distribution: Its properties, estimation and application on failure time data

An improved extension of Xgamma distribution: Its properties, estimation and application on failure time data

Sieve Maximum Likelihood Estimation of Partially Linear Transformation Models With Interval-Censored Data.

Partially linear models provide a valuable tool for modeling failure time data with nonlinear covariate effects. Their applicability and importance in survival analysis have been widely acknowledged. To date, numerous inference methods for such models have been developed under traditional right censoring. However, the existing studies seldom target interval-censored data, which provide more coarse information and frequently occur in many scientific studies involving periodical follow-up. In this work, we propose a flexible class of partially linear transformation models to examine parametric and nonparametric covariate effects for interval-censored outcomes. We consider the sieve maximum likelihood estimation approach that approximates the cumulative baseline hazard function and nonparametric covariate effect with the monotone splines and -splines, respectively. We develop an easy-to-implement expectation-maximization algorithm coupled with three-stage data augmentation to facilitate maximization. We establish the consistency of the proposed estimators and the asymptotic distribution of parametric components based on the empirical process techniques. Numerical results from extensive simulation studies indicate that our proposed method performs satisfactorily in finite samples. An application to a study on hypobaric decompression sickness suggests that the variable TR360 exhibits a significant dynamic and nonlinear effect on the risk of developing hypobaric decompression sickness.

Parameter estimation using time-dependent Weibull proportional hazards model for survival analysis with partly interval censored data

OBJECTIVE: To assess the validity and effectiveness of parameter estimation using a time-dependent Weibull proportional hazards model for survival analysis containing partly interval censored data and explore the impact of different covariates on the results of analysis. METHODS: We established a time-dependent Weibull proportional hazards model using the Weibull distribution as the baseline hazard function of the model which incorporated time-varying covariates. Maximum likelihood estimation was employed to estimate the model parameters, which were obtained by optimization of the likelihood function. RESULTS AND CONCLUSION: Numerical simulation results showed that with higher proportions of precise observations across different sample sizes and parameter settings, the proposed model resulted in improved accuracy of parameter estimation with coverage probabilities approximating the theoretical expectation of 95%. As the sample sizes increased, the parameter biases of the model tended to decrease. Experiments with empirical data further validated the effectiveness of the model. Compared with the failure time data for each precisely observed individual, additional interval-censored data helped to obtain more effective estimates of the regression parameters. Comparison with the Cox model that included time-varying covariates further demonstrated the effectiveness of the time-dependent Weibull proportional hazards model for parameter estimation in survival analysis with partly interval censored data.

Estimation and Variable Selection for Interval-censored Failure Time Data with Random Change Point and Application to Breast Cancer Study

Motivated by a breast cancer study, we consider regression analysis of interval-censored failure time data in the presence of a random change point. Although a great deal of literature on interval-censored data has been established, it does not seem to exist an established method that can allow for the existence of random change points. Such data can occur in, for example, clinical trials where the risk of a disease may dramatically change when some biological indexes of the human body exceed certain thresholds. To fill the gap, we will first consider regression analysis of such data under a class of linear transformation models and provide a sieve maximum likelihood estimation procedure. Then a penalized method is proposed for simultaneous estimation and variable selection, and the asymptotic properties of the proposed method are established. An extensive simulation study is conducted and indicates that the proposed methods work well in practical situations. The approaches are applied to the real data from the breast cancer study mentioned above.

Marginal semiparametric accelerated failure time cure model for clustered survival data.

The semiparametric accelerated failure time mixture cure model is an appealing alternative to the proportional hazards mixture cure model in analyzing failure time data with long-term survivors. However, this model was only proposed for independent survival data and it has not been extended to clustered or correlated survival data, partly due to the complexity of the estimation method for the model. In this paper, we consider a marginal semiparametric accelerated failure time mixture cure model for clustered right-censored failure time data with a potential cure fraction. We overcome the complexity of the existing semiparametric method by proposing a generalized estimating equations approach based on the expectation-maximization algorithm to estimate the regression parameters in the model. The correlation structures within clusters are modeled by working correlation matrices in the proposed generalized estimating equations. The large sample properties of the regression estimators are established. Numerical studies demonstrate that the proposed estimation method is easy to use and robust to the misspecification of working matrices and that higher efficiency is achieved when the working correlation structure is closer to the true correlation structure. We apply the proposed model and estimation method to a contralateral breast cancer study and reveal new insights when the potential correlation between patients is taken into account.

Feature screening for case-cohort studies in the presence of interval censoring

A great literature has been established for both feature screening under various situations and the analysis of case-cohort studies. Also several methods have been proposed for feature screening when one faces case-cohort studies but all of the existing methods apply only to right-censored failure time data. In this paper, we discuss feature screening for case-cohort studies in the presence of interval censoring, a type of censoring that occurs more generally and includes right censoring as a special case. For the problem, two methods, a model-based procedure and a model-free procedure, are proposed. The former, an inverse probability weighted joint likelihood screening approach, is developed under the proportional hazards model, the most commonly used model for failure time data analysis. The latter is a weighted smooth partial rank screening method that allows for both ultrahigh-dimensional covariates and covariate-dependent censoring. For the proposed methods, the sure screening properties are established under mild regularity conditions. An extensive simulation study is conducted to assess the performance of the proposed methods and indicates that they work well in practical situations.

Caries Incidence in School-Based Prevention Programs in the Presence of Interval Censoring.

School-based caries prevention can increase access to critical dental services and reduce oral health inequities. However, little is known regarding the incidence of dental caries in children participating in school caries prevention, and caries diagnosis is often interval censored. In this paper, we used data from a longitudinal, school-based, randomized clinical trial of minimally invasive treatments for dental caries to estimate the per-visit incidence rate and compare the hazard of dental caries in children receiving either silver diamine fluoride or glass ionomer dental sealants. To account for interval censoring, we used semiparametric transformation models for univariate failure time data and imputed caries incidence using G-imputation. There were 3040 children that met inclusion criteria for analysis, 1516 (49.9%) of which were randomly assigned to receive silver diamine fluoride and 1524 (50.1%) were assigned to receive glass ionomer dental sealants and atraumatic restorations. There were no differences in the hazard of caries between treatments (HR = 0.99, 95% CI = 0.72, 1.24), while children with caries at baseline had a significant increase in the hazard of new caries (HR = 2.54, 95% CI = 2.26, 2.83) compared to those that were caries free. The per-visit caries incidence ranged from 4.8 to 11.1 at the individual level and increased with each successive study observation. School-based caries prevention can positively affect caries incidence, and the results can be used to inform future program design and implementation.

The survival function NPMLE for combined right-censored and length-biased right-censored failure time data: properties and applications.

Many cohort studies in survival analysis have imbedded in them subcohorts consisting of incident cases and prevalent cases. Instead of analysing the data from the incident and prevalent cohorts alone, there are surely advantages to combining the data from these two subcohorts. In this paper, we discuss a survival function nonparametric maximum likelihood estimator (NPMLE) using both length-biased right-censored prevalent cohort data and right-censored incident cohort data. We establish the asymptotic properties of the survival function NPMLE and utilize the NPMLE to estimate the distribution for time spent in a Montreal area hospital.

Deep Neural Network-Based Accelerated Failure Time Models Using Rank Loss.

An accelerated failure time (AFT) model assumes a log-linear relationship between failure times and a set of covariates. In contrast to other popular survival models that work on hazard functions, the effects of covariates are directly on failure times, the interpretation of which is intuitive. The semiparametric AFT model that does not specify the error distribution is sufficiently flexible and robust to depart from the distributional assumption. Owing to its desirable features, this class of model has been considered a promising alternative to the popular Cox model in the analysis of censored failure time data. However, in these AFT models, a linear predictor for the mean is typically assumed. Little research has addressed the non-linearity of predictors when modeling the mean. Deep neural networks (DNNs) have received much attention over the past few decades and have achieved remarkable success in a variety of fields. DNNs have a number of notable advantages and have been shown to be particularly useful in addressing non-linearity. Here, we propose applying a DNN to fit AFT models using Gehan-type loss combined with a sub-sampling technique. Finite sample properties of the proposed DNN and rank-based AFT model (DeepR-AFT) were investigated via an extensive simulation study. The DeepR-AFT model showed superior performance over its parametric and semiparametric counterparts when the predictor was nonlinear. For linear predictors, DeepR-AFT performed better when the dimensions of the covariates were large. The superior performance of the proposed DeepR-AFT was demonstrated using three real datasets.

Conditional quasi‐likelihood inference for mean residual life regression with clustered failure time data

AbstractIn the analysis of clustered failure time data, Cox frailty models have been extensively studied by incorporating frailty with a prespecified distribution to address potential correlation of data within clusters. In this paper, we propose a frailty proportional mean residual life regression model to analyze such data. A novel conditional quasi‐likelihood inference procedure is developed, utilizing a stochastic process and the inverse probability of censoring weighting (IPCW) to form estimating equations for regression parameters. Our proposal employs conditional inference based on a penalized quasi‐likelihood to address within‐cluster correlation without need to specify the frailty distribution, bringing the method closer to what suffices for real‐world applications. By adopting the Buckley–James estimator in the IPCW, the method further allows for dependent censoring. We establish asymptotic properties of the proposed estimator and evaluate its finite sample performance via simulation studies. An application to the data from a multi‐institutional breast cancer study is presented for illustration.

Improving estimation efficiency of case-cohort studies with interval-censored failure time data.

The case-cohort design is a commonly used cost-effective sampling strategy for large cohort studies, where some covariates are expensive to measure or obtain. In this paper, we consider regression analysis under a case-cohort study with interval-censored failure time data, where the failure time is only known to fall within an interval instead of being exactly observed. A common approach to analyzing data from a case-cohort study is the inverse probability weighting approach, where only subjects in the case-cohort sample are used in estimation, and the subjects are weighted based on the probability of inclusion into the case-cohort sample. This approach, though consistent, is generally inefficient as it does not incorporate information outside the case-cohort sample. To improve efficiency, we first develop a sieve maximum weighted likelihood estimator under the Cox model based on the case-cohort sample and then propose a procedure to update this estimator by using information in the full cohort. We show that the update estimator is consistent, asymptotically normal, and at least as efficient asthe original estimator. The proposed method can flexibly incorporate auxiliary variables to improve estimation efficiency. A weighted bootstrap procedure is employed for variance estimation. Simulation results indicate that the proposed method works well in practical situations. An application to a Phase 3 HIV vaccine efficacy trial is provided for illustration.

Semiparametric varying-coefficient additive hazards model for informatively interval-censored failure time data

The analysis of interval-censored data with informative observation processes has recently attracted much attention and a few methods have been developed. However, all of the existing methods assume that covariate effects are constant and this may not be true sometimes in practice. To address this, in this paper, we propose a varying-coefficient additive hazards model and in the proposed method, frailty variables are used to describe the dependence between the failure time and the informative observation process. For inference, a Bernstein polynomials-based, two-step sieve maximum likelihood method is developed and the proposed method can be easily implemented. Furthermore, the resulting estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the proposed approach works well for practical situations. The proposed method is applied to a cardiac allograft vasculopathy (CAV) study that motivated this investigation.

Estimation of the additive hazards model based on case‐cohort interval‐censored data with dependent censoring

AbstractThe additive hazards model is one of the most commonly used models for regression analysis of failure time data, and many methods have been developed for its estimation. In this article, we consider the situation where one observes informatively interval‐censored data arising from case‐cohort studies where covariate information is collected only for a small subcohort of study subjects. By informative or dependent censoring, we mean that the failure time of interest and the censoring mechanism may be correlated. For estimation, we will develop a sieve inverse probability weighting estimation procedure with the use of Bernstein polynomials. The resulting estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the proposed method works well in practical situations. An example is also provided.

A Simulation-Extrapolation Approach to the Analysis of Interval-Censored Failure Time Data with Mis-Measured Covariates

A Simulation-Extrapolation Approach to the Analysis of Interval-Censored Failure Time Data with Mis-Measured Covariates

Factor-augmented transformation models for interval-censored failure time data.

Interval-censored failure time data frequently arise in various scientific studies where each subject experiences periodical examinations for the occurrence of the failure event of interest, and the failure time is only known to lie in a specific time interval. In addition, collected data may include multiple observed variables with a certain degree of correlation, leading to severe multicollinearity issues. This work proposes a factor-augmented transformation model to analyze interval-censored failure time data while reducing model dimensionality and avoiding multicollinearity elicited by multiple correlated covariates. We provide a joint modeling framework by comprising a factor analysis model to group multiple observed variables into a few latent factors and a class of semiparametric transformation models with the augmented factors to examine their and other covariate effects on the failure event. Furthermore, we propose a nonparametric maximum likelihood estimation approach and develop a computationally stable and reliable expectation-maximization algorithm for its implementation. We establish the asymptotic properties of the proposed estimators and conduct simulation studies to assess the empirical performance of the proposed method. An application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study is provided. An R package ICTransCFA is also available for practitioners. Data used in preparation of this article were obtained from the ADNI database.

Regression trees for interval‐censored failure time data based on censoring unbiased transformations and pseudo‐observations

AbstractInterval‐censored data arise when a failure process is under intermittent observation and failure status is only known at assessment times. We consider the development of predictive algorithms when training samples involve interval censoring. Using censoring unbiased transformations and pseudo‐observations, we define observed data loss functions, which are unbiased estimates of the corresponding complete data loss functions. We show that regression trees based on these loss functions can recover the tree structure and yield good predictive accuracy. An application is given to a study involving individuals with psoriatic arthritis where the aim is to identify genetic markers useful for the prediction of axial disease within 10 years of a baseline assessment.

A conditional approach for regression analysis of case K interval-censored failure time data with informative censoring

This paper discusses regression analysis of case K interval-censored failure time data, a general type of failure time data, in the presence of informative censoring with the focus on simultaneous variable selection and estimation. Although many authors have considered the challenging variable selection problem for interval-censored data, most of the existing methods assume independent or non-informative censoring. More importantly, the existing methods that allow for informative censoring are frailty model-based approaches and cannot directly assess the degree of informative censoring among other shortcomings. To address these, we propose a conditional approach and develop a penalized sieve maximum likelihood procedure for the simultaneous variable selection and estimation of covariate effects. Furthermore, we establish the oracle property of the proposed method and illustrate the appropriateness and usefulness of the approach using a simulation study. Finally we apply the proposed method to a set of real data on Alzheimer's disease and provide some new insights.

AN ADDITIVE SUBDISTRIBUTION HAZARDS MODEL FOR COMPETING RISKS DATA

Competing risk failure time data occur frequently in medical a number of methods have been proposed for the analysis of these data. The classic approach is to model all cause-specific hazards and then estimate the cumulative incidence curve based on these cause-specific hazards. Unfortunately, the cause-specific hazard function does not have a direct interpretation in terms of survival probabilities for the particular failure type. In this paper, we consider a more flexible model for the subdistribution. It is a combination of the additive model and the Cox model and allows one to perform a more detailed study of covariate effects. One advantage of this approach is that our regression modeling allows for non-proportional hazards. This leads to a new simple goodness-of-fit procedure for the proportional subdistribution hazards assumption that is very easy to use. We applied this method to melanoma data and estimated the cumulative death rate for those who died from melanoma after surgical removal of the tumor. It was found that two covariates had a time-varying effect and two other covariates had a constant effect in predicting the cumulative incidence curve in patients who died of melanoma following tumor removal surgery.

Semiparametric analysis of nonparametric proportional hazards models with mixed dependent censored data

To construct a nonparametric proportional hazards (PH) model for mixed informative interval-censored failure time data for predicting the risks in heart transplantation surgeries. Based on the complexity of mixed informative interval-censored failure time data, we considered the interdependent relationship between failure time process and observation time process, constructed a nonparametric proportional hazards (PH) model to describe the nonlinear relationship between the risk factors and heart transplant surgery risks and proposed a two-step sieve estimation maximum likelihood algorithm. An estimation equation was established to estimate frailty variables using the observation process model. Ⅰ-spline and B-spline were used to approximate the unknown baseline hazard function and nonparametric function, respectively, to obtain the working likelihood function in the sieve space. The partial derivative of the model parameters was used to obtain the scoring equation. The maximum likelihood estimation of the parameters was obtained by solving the scoring equation, and a function curve of the impact of risk factors on the risk of heart transplantation surgery was drawn. Simulation experiment suggested that the estimated values obtained by the proposed method were consistent and asymptotically effective under various settings with good fitting effects. Analysis of heart transplant surgery data showed that the donor's age had a positive linear relationship with the surgical risk. The impact of the recipient's age at disease onset increased at first and then stabilized, but increased against at an older age. The donor-recipient age difference had a positive linear relationship with the surgical risk of heart transplantation. The nonparametric PH model established in this study can be used for predicting the risks in heart transplantation surgery and exploring the functional relationship between the surgery risks and the risk factors.