Right-censored Data Research Articles

Identifying treatment responders using counterfactual modeling and potential outcomes.

Individualizing treatment according to patients' characteristics is central for personalized or precision medicine. There has been considerable recent research in developing statistical methods to determine optimal personalized treatment strategies by modeling the outcome of patients according to relevant covariates under each of the alternative treatments, and then relying on so-called predicted individual treatment effects. In this paper, we use potential outcomes and principal stratification frameworks and develop a multinomial model for left and right-censored data to estimate the probability that a patient is a responder given a set of baseline covariates. The model can apply to RCT or observational study data. This method is based on the monotonicity assumption, which implies that no patients would respond to the control treatment but not to the experimental one. We conduct a simulation study to evaluate the properties of the proposed estimation method. Results showed that the predictions of the probability of being a responder were well calibrated even if we observed variability and a small bias when many parameters were estimated. We finally applied the method to a cohort study on the selection of patients for additional radiotherapy after resection of a soft-tissue sarcoma.

Giniinc: A Stata Package for Measuring Inequality from Incomplete Income and Survival Data

Often, observed income and survival data are incomplete because of left- or right-censoring or left- or right-truncation. Measuring inequality (for instance, by the Gini index of concentration) from incomplete data like these will produce biased results. We describe the package giniinc, which contains three independent commands to estimate the Gini concentration index under different conditions. First, survgini computes a test statistic for comparing two (survival) distributions based on the nonparametric estimation of the restricted Gini index for right-censored data, using both asymptotic and permutation inference. Second, survbound computes nonparametric bounds for the unrestricted Gini index from censored data. Finally, survlsl implements maximum likelihood estimation for three commonly used parametric models to estimate the unrestricted Gini index, both from censored and truncated data. We briefly discuss the methods, describe the package, and illustrate its use through simulated data and examples from an oncology and a historical income study.

Bayesian Computational Methods for Sampling from the Posterior Distribution of a Bivariate Survival Model, Based on AMH Copula in the Presence of Right-Censored Data.

In this paper, we study the performance of Bayesian computational methods to estimate the parameters of a bivariate survival model based on the Ali–Mikhail–Haq copula with marginal distributions given by Weibull distributions. The estimation procedure was based on Monte Carlo Markov Chain (MCMC) algorithms. We present three version of the Metropolis–Hastings algorithm: Independent Metropolis–Hastings (IMH), Random Walk Metropolis (RWM) and Metropolis–Hastings with a natural-candidate generating density (MH). Since the creation of a good candidate generating density in IMH and RWM may be difficult, we also describe how to update a parameter of interest using the slice sampling (SS) method. A simulation study was carried out to compare the performances of the IMH, RWM and SS. A comparison was made using the sample root mean square error as an indicator of performance. Results obtained from the simulations show that the SS algorithm is an effective alternative to the IMH and RWM methods when simulating values from the posterior distribution, especially for small sample sizes. We also applied these methods to a real data set.

A Gamma-frailty proportional hazards model for bivariate interval-censored data

Correlated survival data naturally arise from many clinical and epidemiological studies. For the analysis of such data, the Gamma-frailty proportional hazards (PH) model is a popular choice because the regression parameters have marginal interpretations and the statistical association between the failure times can be explicitly quantified via Kendall’s tau. Despite their popularity, Gamma-frailty PH models for correlated interval-censored data have not received as much attention as analogous models for right-censored data. A Gamma-frailty PH model for bivariate interval-censored data is presented and an easy to implement expectation–maximization (EM) algorithm for model fitting is developed. The proposed model adopts a monotone spline representation for the purposes of approximating the unknown conditional cumulative baseline hazard functions, significantly reducing the number of unknown parameters while retaining modeling flexibility. The EM algorithm was derived from a data augmentation procedure involving latent Poisson random variables. Extensive numerical studies illustrate that the proposed method can provide reliable estimation and valid inference, and is moreover robust to the misspecification of the frailty distribution. To further illustrate its use, the proposed method is used to analyze data from an epidemiological study of sexually transmitted infections.

A validation sampling approach for consistent estimation of adverse drug reaction risk with misclassified right-censored survival data.

Patient electronic health records, viewed as continuous-time right-censored survival data, can be used to estimate adverse drug reaction risk. Temporal outcome misclassification may occur as a result of errors in follow-up. These errors can be due to a failure to observe the incidence time of the adverse event of interest (due to misdiagnosis or nonreporting, etc) or an actual misdiagnosis of a competing adverse event. As the misclassifying event is often unobservable in the original data, we apply an internal validation sampling approach to produce consistent estimation in the presence of such errors. We introduce a univariate survival model and a cause-specific hazards model in which misclassification may also manifest as a diagnosis of an alternate adverse health outcome other than that of interest. We develop a method of maximum likelihood estimation of the model parameters and establish consistency and asymptotic normality of the estimators using standard results. We also conduct simulation studies to numerically investigate the finite sample properties of these estimators and the impact of ignoring the misclassification error.

Simulation shows undesirable results for competing risks analysis with time-dependent covariates for clinical outcomes.

BackgroundWe evaluate three methods for competing risks analysis with time-dependent covariates in comparison with the corresponding methods with time-independent covariates.MethodsWe used cause-specific hazard analysis and two summary approaches for in-hospital death: logistic regression and regression of the subdistribution hazard. We analysed real hospital data (n=1864) and considered pneumonia on admission / hospital-acquired pneumonia as time-independent / time-dependent covariates for the competing events ’discharge alive’ and ’in-hospital death’. Several simulation studies with time-constant hazards were conducted.ResultsAll approaches capture the effect of time-independent covariates, whereas the approaches perform differently with time-dependent covariates. The subdistribution approach for time-dependent covariates detected effects in a simulated no-effects setting and provided counter-intuitive effects in other settings.ConclusionsThe extension of the Fine and Gray model to time-dependent covariates is in general not a helpful synthesis of the cause-specific hazards. Cause-specific hazard analysis and, for uncensored data, the odds ratio are capable of handling competing risks data with time-dependent covariates but the use of the subdistribution approach should be neglected until the problems can be resolved. For general right-censored data, cause-specific hazard analysis is the method of choice.

An embedded estimating equation for the additive risk model with biased-sampling data

This paper presents a novel class of semiparametric estimating functions for the additive model with right-censored data that are obtained from general biased-sampling.The new estimator can be obtained using a weighted estimating equation for the covariate coefficients, by embedding the biased-sampling data into left-truncated and right-censored data.The asymptotic properties (consistency and asymptotic normality) of the proposed estimator are derived via the modern empirical processes theory.Based on the cumulative residual processes, we also propose graphical and numerical methods to assess the adequacy of the additive risk model.The good finite-sample performance of the proposed estimator is demonstrated by simulation studies and two applications of real datasets.

Testing Censoring Point Independence

Identification in censored regression analysis and hazard models of duration outcomes relies on the condition that censoring points are conditionally independent of latent outcomes, an assumption which may be questionable in many settings. This article proposes a test for this assumption based on a Cramer–von-Mises-like test statistic comparing two different nonparametric estimators for the latent outcome cdf: the Kaplan–Meier estimator, and the empirical cdf conditional on the censoring point exceeding (for right-censored data) the cdf evaluation point. The test is consistent and has power against a wide variety of alternatives. Applying the test to unemployment duration data from the NLSY, the SIPP, and the PSID suggests the assumption is frequently suspect.

Nonparametric estimation of median survival times with applications to multi-site or multi-center studies.

We propose a nonparametric shrinkage estimator for the median survival times from several independent samples of right-censored data, which combines the samples and hypothesis information to improve the efficiency. We compare efficiency of the proposed shrinkage estimation procedure to unrestricted estimator and combined estimator through extensive simulation studies. Our results indicate that performance of these estimators depends on the strength of homogeneity of the medians. When homogeneity holds, the combined estimator is the most efficient estimator. However, it becomes inconsistent when homogeneity fails. On the other hand, the proposed shrinkage estimator remains efficient. Its efficiency decreases as the equality of the survival medians is deviated, but is expected to be as good as or equal to the unrestricted estimator. Our simulation studies also indicate that the proposed shrinkage estimator is robust to moderate levels of censoring. We demonstrate application of these methods to estimating median time for trauma patients to receive red blood cells in the Prospective Observational Multi-center Major Trauma Transfusion (PROMMTT) study.

Modeling clustered long-term survivors using marginal mixture cure model.

There is a great deal of recent interests in modeling right-censored clustered survival time data with a possible fraction of cured subjects who are nonsusceptible to the event of interest using marginal mixture cure models. In this paper, we consider a semiparametric marginal mixture cure model for such data and propose to extend an existing generalized estimating equation approach by a new unbiased estimating equation for the regression parameters in the latency part of the model. The large sample properties of the regression effect estimators in both incidence and the latency parts are established. The finite sample properties of the estimators are studied in simulation studies. The proposed method is illustrated with a bone marrow transplantation data and a tonsil cancer data.

Missing Information Principle: A Unified Approach for General Truncated and Censored Survival Data Problems.

It is well known that truncated survival data are subject to sampling bias, where the sampling weight depends on the underlying truncation time distribution. Recently, there has been a rising interest in developing methods to better exploit the information about the truncation time, thus the sampling weight function, to obtain more efficient estimation. In this paper, we propose to treat truncation and censoring as "missing data mechanism" and apply the missing information principle to develop a unified framework for analyzing left-truncated and right-censored data with unspecified or known truncation time distributions. Our framework is structured in a way that is easy to understand and enjoys a great flexibility for handling different types of models. Moreover, a new test for checking the independence between the underlying truncation time and survival time is derived along the same line. The proposed hypothesis testing procedure utilizes all observed data and hence can yield a much higher power than the conditional Kendall's tau test that only involves comparable pairs of observations under truncation. Simulation studies with practical sample sizes are conducted to compare the performance of the proposed method with its competitors. The proposed methodologies are applied to a dementia study and a nursing house study for illustration.

Modeling right-censored medical cost data in regression and the effects of covariates

This paper focuses on the problem of modeling medical costs with covariates when the cost data are subject to right-censoring. The prevailing methods are divided into three categories, (a) the inverse probability weighted (IPW) regressions; (b) the generalized survival-adjusted estimators; and (c) the joint-modeling methods. Comparisons are made both in and between categories to demonstrate their different mechanisms to handle the informative censoring, to take into account the covariates and the way they interpret the covariates effects. Based on the above discussion, we believe that the linear or generalized linear regressions using the IPW scheme are very popular due to its convenience to fit and interpret, which could be a good choice in practice with additional conditional means to address the role of survival to some extent. The recently proposed generalized survival-adjusted estimator is very intuitive as the derivative of the estimation function naturally decomposes the effects of covariates into the intensity part and the survival part, therefore especially useful when the covariates have substantial effect on survival. The joint-modelling methods have the advantage in providing the access to the correlation between medical cost and survival, although they suffer from theoretical and computational complexity. The effect of covariates on cost through survival in this kind of joint-modelling methods could be a desirable topic for further research.

Geecure: An R-package for marginal proportional hazards mixture cure models

Background and objective: Most of available software packages for mixture cure models to analyze survival data with a cured fraction assume independent survival times, and they are not suitable for correlated survival times, such as clustered survival data. The objective of this paper is to present a software package to fit a marginal mixture cure model to clustered survival data with a cured fraction.Methods: We developed an R package geecure that fits the marginal proportional hazards mixture cure (PHMC) models to clustered right-censored survival data with a cured fraction. The dependence among the cure statuses and among the survival times of uncured patients within a cluster are modeled by working correlation matrices through the generalized estimating equations, and the Expectation-Solution algorithm is used to estimate the parameters. The variances of the estimated regression parameters are estimated by either a sandwich method or a bootstrap method.Results: The package geecure can fit the marginal PHMC model where the cumulative baseline hazard function is either a two-parameter Weibull distribution or specified nonparametrically. Fitting the parametric PHMC model with the Weibull baseline hazard function on average takes less time than fitting the semiparametric PHMC model does. Two variance estimation methods are comparable in the simulation study. The sandwich method takes much less time than the bootstrap method in variance estimation.Conclusions: The package geecure provides an easy access to the marginal PHMC models for clustered survival data with a cured fraction in routine survival analysis. It is easy to use and will make the wide applications of the marginal PHMC models possible.

A New Approach to Censored Quantile Regression Estimation

ABSTRACTQuantile regression provides an attractive tool to the analysis of censored responses, because the conditional quantile functions are often of direct interest in regression analysis, and moreover, the quantiles are often identifiable while the conditional mean functions are not. Existing methods of estimation for censored quantiles are mostly limited to singly left- or right-censored data, with some attempts made to extend the methods to doubly censored data. In this article, we propose a new and unified approach, based on a variation of the data augmentation algorithm, to censored quantile regression estimation. The proposed method adapts easily to different forms of censoring including doubly censored and interval censored data, and somewhat surprisingly, the resulting estimates improve on the performance of the best known estimators with singly censored data. Supplementary material for this article is available online.

Nonparametric estimation of transition probabilities for a general progressive multi-state model under cross-sectional sampling.

Nonparametric estimation of the transition probability matrix of a progressive multi-state model is considered under cross-sectional sampling. Two different estimators adapted to possibly right-censored and left-truncated data are proposed. The estimators require full retrospective information before the truncation time, which, when exploited, increases efficiency. They are obtained as differences between two survival functions constructed for sub-samples of subjects occupying specific states at a certain time point. Both estimators correct the oversampling of relatively large survival times by using the left-truncation times associated with the cross-sectional observation. Asymptotic results are established, and finite sample performance is investigated through simulations. One of the proposed estimators performs better when there is no censoring, while the second one is strongly recommended with censored data. The new estimators are applied to data on patients in intensive care units (ICUs).

Likelihood-based inference for the transmuted log-logistic model in the presence of right-censored data

ABSTRACTAlthough new transmuted distributions have been widely proposed in the last few years, it is rarely to find those class of models applied in survival analysis in the presence of censored lifetimes. In this context, we are concerned in applying the transmuted log-logistic model in the study of discharge times of patients treated with the Linezolid drug. For model fitting, we use and compare different profile likelihood methods. Analysis of residuals and influence are also presented. All results are validated in a simulation study by considering the bootstrap techniques.

Sample size determination for semiparametric analysis of current status data.

Semiparametric transformation models, which include the Cox proportional hazards and proportional odds models as special cases, are popular in current practice of survival analysis owing to that, in contrast to parametric models, no assumption on the baseline distribution is required. Although sample size calculations for semiparametric survival analysis with right-censored data are available, no such calculation exits in literature for semiparametric analysis with current status data, where only an examination time and whether the event occurs prior to the examination are observable. We develop sample size calculation for semiparametric two-group comparison or regression analysis with current status data. The proposed formula can be readily implemented with given effect size, power level, covariate group proportions, covariate-specific examination (censoring) time distributions, and proportions of events observed in the control group at a few knot points in the study period. Simulation results show that the proposed sample size calculation is adequate in the sense that it leads to studies with empirical power very close to the planned power level. We illustrate practical applications of the proposal through examples from an animal tumorigenicity study and a cross-sectional survey on osteoporosis status in the elderly.

HYPOTHESIS TESTING FOR THE PARAMETERS OF LOG-LOGISTIC REGRESSION MODEL WITH LEFT-TRUNCATED AND RIGHT-CENSORED SURVIVAL DATA

Left-truncation and right-censoring (LTRC) arise naturally in lifetime data. Data may be left-truncated due to a limitation in the study design. Failure of a unit is observed only if it fails after a certain period. Usually, the units under study may not be followed until all of them have failed but the study has to be stopped at a certain time. This introduces the right censoring into the survival data. Log-logistic model is extended to accommodate the left-truncated and right-censored survival data. The bias, standard error (SE), and root mean square error (RMSE) of the parameter estimates are computed to evaluate the performance of the model at different sample sizes, censoring proportion (CP), and truncation level (TL). The results show that the SE of the parameter estimates increase as the truncation level (TL) and censoring proportion (CP) increase. Having low and high TL (5% and 15%) in the data, the graphs clearly show that the empirical power of both tests increases with the increase of TL for parameter and . The SE and RMSE also decrease as the sample size increases. Following that, power analysis is conducted via simulation to compare the performance of hypothesis tests based on the Wald and Likelihood Ratio (LR) for the parameters. The results clearly indicate that the Wald performs slightly better than the LR when dealing with the proposed model.

Generalized confidence limits for the performance index of the exponentially distributed lifetime

ABSTRACTUnder a two-parameter exponential distribution, this study constructs the generalized lower confidence limit of the lifetime performance index CL based on type-II right-censored data. The confidence limit has to be numerically obtained; however, the required computations are simple and straightforward. Confidence limits of CL computed under the generalized paradigm are compared with those of CL computed under the classical paradigm, citing an illustrative example with real data and two examples with simulated data, to demonstrate the merits and advantages of the proposed generalized variable method over the classical method.

Modified estimators in semiparametric regression models with right-censored data

ABSTRACTIn this work we introduce different modified estimators for the vector parameter and an unknown regression function g in semiparametric regression models when censored response observations are replaced with synthetic data points. The main idea is to study the effects of several covariates on a response variable censored on the right by a random censoring variable with an unknown probability distribution. To provide the estimation procedure for the estimators, we extend the conventional methodology to censored semiparametric regression using different smoothing methods such as smoothing spline (SS), kernel smoothing (KS), and regression spline (RS). In addition to estimating the parameters of the semiparametric model, we also provide a bootstrap technique to make inference on the parameters. A simulation study is carried out to show the performance and efficiency properties of the estimators and analyse the effects of the different censoring levels. Finally, the performance of the estimators is evaluated by a real right-censored data set.