A frailty model for informative censoring

To account for the correlation between failure and censoring, we propose a new frailty model for clustered data. In this model, the risk to be censored is affected by the risk of failure. This model allows flexibility in the direction and degree of dependence between failure and censoring. It includes the traditional frailty model as a special case. It allows censoring by some causes to be analyzed as informative while treating censoring by other causes as noninformative. It can also analyze data for competing risks. To fit the model, the EM algorithm is used with Markov chain Monte Carlo simulations in the E-steps. Simulation studies and analysis of data for kidney disease patients are provided. Consequences of incorrectly assuming noninformative censoring are investigated.     

Regression survival analysis with an assumed copula for dependent censoring: a sensitivity analysis approach

SUMMARY: In clinical studies, when censoring is caused by competing risks or patient withdrawal, there is always a concern about the validity of treatment effect estimates that are obtained under the assumption of independent censoring. Because dependent censoring is nonidentifiable without additional information, the best we can do is a sensitivity analysis to assess the changes of parameter estimates under different assumptions about the association between failure and censoring. This analysis is especially useful when knowledge about such association is available through literature review or expert opinions. In a regression analysis setting, the consequences of falsely assuming independent censoring on parameter estimates are not clear. Neither the direction nor the magnitude of the potential bias can be easily predicted. We provide an approach to do sensitivity analysis for the widely used Cox proportional hazards models. The joint distribution of the failure and censoring times is assumed to be a function of their marginal distributions. This function is called a copula. Under this assumption, we propose an iteration algorithm to estimate the regression parameters and marginal survival functions. Simulation studies show that this algorithm works well. We apply the proposed sensitivity analysis approach to the data from an AIDS clinical trial in which 27% of the patients withdrew due to toxicity or at the request of the patient or investigator.     

Regression analysis for recurrent events data under dependent censoring

Summary Recurrent events data are commonly seen in longitudinal follow‐up studies. Dependent censoring often occurs due to death or exclusion from the study related to the disease process. In this article, we assume flexible marginal regression models on the recurrence process and the dependent censoring time without specifying their dependence structure. The proposed model generalizes the approach by Ghosh and Lin (2003, Biometrics 59, 877–885). The technique of artificial censoring provides a way to maintain the homogeneity of the hypothetical error variables under dependent censoring. Here we propose to apply this technique to two Gehan‐type statistics. One considers only order information for pairs whereas the other utilizes additional information of observed censoring times available for recurrence data. A model‐checking procedure is also proposed to assess the adequacy of the fitted model. The proposed estimators have good asymptotic properties. Their finite‐sample performances are examined via simulations. Finally, the proposed methods are applied to analyze the AIDS linked to the intravenous experiences cohort data.     

Analysis of times to repeated events in two-arm randomized trials with noncompliance and dependent censoring

This article develops randomization-based methods for times to repeated events in two-arm randomized trials with noncompliance and dependent censoring. Structural accelerated failure time models are assumed to capture causal effects on repeated event times and dependent censoring time, but the dependence structure among repeated event times and dependent censoring time is unspecified. Artificial censoring techniques to accommodate nonrandom noncompliance and dependent censoring are proposed. Estimation of the acceleration parameters are based on rank-based estimating functions. A simulation study is conducted to evaluate the performance of the developed methods. An illustration of the methods using data from an acute myeloid leukemia trial is provided.     

Shared frailty models for recurrent events and a terminal event

There has been an increasing interest in the analysis of recurrent event data (Cook and Lawless, 2002, Statistical Methods in Medical Research 11, 141-166). In many situations, a terminating event such as death can happen during the follow-up period to preclude further occurrence of the recurrent events. Furthermore, the death time may be dependent on the recurrent event history. In this article we consider frailty proportional hazards models for the recurrent and terminal event processes. The dependence is modeled by conditioning on a shared frailty that is included in both hazard functions. Covariate effects can be taken into account in the model as well. Maximum likelihood estimation and inference are carried out through a Monte Carlo EM algorithm with Metropolis-Hastings sampler in the E-step. An analysis of hospitalization and death data for waitlisted dialysis patients is presented to illustrate the proposed methods. Methods to check the validity of the proposed model are also demonstrated. This model avoids the difficulties encountered in alternative approaches which attempt to specify a dependent joint distribution with marginal proportional hazards and yields an estimate of the degree of dependence.     

Correcting for noncompliance and dependent censoring in an AIDS Clinical Trial with inverse probability of censoring weighted (IPCW) log-rank tests

AIDS Clinical Trial Group (ACTG) randomized trial 021 compared the effect of bactrim versus aerosolized pentamidine (AP) as prophylaxis therapy for pneumocystis pneumonia (PCP) in AIDS patients. Although patients randomized to the bactrim arm experienced a significant delay in time to PCP, the survival experience in the two arms was not significantly different (p = .32). In this paper, we present evidence that bactrim therapy improves survival but that the standard intent-to-treat comparison failed to detect this survival advantage because a large fraction of the subjects either crossed over to the other therapy or stopped therapy altogether. We obtain our evidence of a beneficial bactrim effect on survival by artificially regarding the subjects as dependently censored at the first time the subject either stops or switches therapy; we then analyze the data with the inverse probability of censoring weighted Kaplan-Meier and Cox partial likelihood estimators of Robins (1993, Proceedings of the Biopharmaceutical Section, American Statistical Association, pp. 24-33) that adjust for dependent censoring by utilizing data collected on time-dependent prognostic factors.     

Quality-adjusted survival estimation with periodic observations

Quality-adjusted survival is a measure that integrates both longevity and quality-of-life information. The analysis of quality-adjusted survival in a clinical study with data collected at periodic intervals encounters difficulties due to incomplete information. Based on observed time points, the time axis is partitioned into a set of disjoint time intervals, and under a Markovian assumption on patient's health status, the expected quality-adjusted survival is estimated as the summed product of the quality of life and its mean sojourn time of each health state within partitioned intervals. It is shown that the estimator is asymptotically normal with a simple variance calculation. A simulation study is conducted to investigate the behavior of the estimator, and a stroke study illustrates the use of the estimator.     

Nonparametric estimation of the concordance correlation coefficient under univariate censoring

Assessing agreement is often of interest in clinical studies to evaluate the similarity of measurements produced by different raters or methods on the same subjects. Lin's (1989, Biometrics 45, 255-268) concordance correlation coefficient (CCC) has become a popular measure of agreement for correlated continuous outcomes. However, commonly used estimation methods for the CCC do not accommodate censored observations and are, therefore, not applicable for survival outcomes. In this article, we estimate the CCC nonparametrically through the bivariate survival function. The proposed estimator of the CCC is proven to be strongly consistent and asymptotically normal, with a consistent bootstrap variance estimator. Furthermore, we propose a time-dependent agreement coefficient as an extension of Lin's (1989) CCC for measuring the agreement between survival times among subjects who survive beyond a specified time point. A nonparametric estimator is developed for the time-dependent agreement coefficient as well. It has the same asymptotic properties as the estimator of the CCC. Simulation studies are conducted to evaluate the performance of the proposed estimators. A real data example from a prostate cancer study is used to illustrate the method.     

Nonparametric estimation for the three-stage irreversible illness-death model

In this paper, we present new nonparametric estimators of the stage-occupation probabilities in the three-stage irreversible illness-death model. These estimators use a fractional risk set and a reweighting approach and are valid under stage-dependent censoring. Using a simulated data set, we compare the behavior of our estimators with previously proposed estimators. We also apply our estimators to data on time to Pneumocystis pneumonia and death obtained from an AIDS cohort study.     

A simple local sensitivity analysis tool for nonignorable coarsening: application to dependent censoring

Right- and interval-censored data are common special cases of coarsened data (Heitjan and Rubin, 1991, Annals of Statistics19, 2244-2253). As with missing data, standard statistical methods that ignore the random nature of the coarsening mechanism may lead to incorrect inferences. We extend a simple sensitivity analysis tool, the index of local sensitivity to nonignorability (Troxel, Ma, and Heitjan, 2004, Statistica Sinica14, 1221-1237), to the evaluation of nonignorability of the coarsening process in the general coarse-data model. By converting this index into a simple graphical display one can easily assess the sensitivity of key inferences to nonignorable coarsening. We illustrate the validity of the method with a simulated example, and apply it to right-censored data from an observational study of cardiac transplantation and to interval-censored data on time to detectable viral load from a clinical trial in HIV disease.     

Sensitivity analysis for informative censoring in parametric survival models

Most statistical methods for censored survival data assume there is no dependence between the lifetime and censoring mechanisms, an assumption which is often doubtful in practice. In this paper we study a parametric model which allows for dependence in terms of a parameter delta and a bias function B(t, theta). We propose a sensitivity analysis on the estimate of the parameter of interest for small values of delta. This parameter measures the dependence between the lifetime and the censoring mechanisms. Its size can be interpreted in terms of a correlation coefficient between the two mechanisms. A medical example suggests that even a small degree of dependence between the failure and censoring processes can have a noticeable effect on the analysis.     

Applications of a parametric model for informative censoring

In this article, we explore the use of a parametric model (for analyzing survival data) which is defined to allow sensitivity analysis for the presence of informative censoring. The dependence between the failure and the censoring processes is expressed through a parameter delta and a general bias function B(t, theta). We calculate the expectation of the potential bias due to informative censoring, which is an overall measure of how misleading our results might be if censoring is actually nonignorable. Bounds are also calculated for quantities of interest, e.g., parameter of the distribution of the failure process, which do not depend on the choice of the bias function for fixed delta. An application that relates to systematic lupus erythematosus data illustrates how additional information can result in reducing the uncertainty on estimates of the location parameter. Sensitivity analysis on a relative risk parameter is also explored.     

Double Inverse‐Weighted Estimation of Cumulative Treatment Effects Under Nonproportional Hazards and Dependent Censoring

Summary In medical studies of time‐to‐event data, nonproportional hazards and dependent censoring are very common issues when estimating the treatment effect. A traditional method for dealing with time‐dependent treatment effects is to model the time‐dependence parametrically. Limitations of this approach include the difficulty to verify the correctness of the specified functional form and the fact that, in the presence of a treatment effect that varies over time, investigators are usually interested in the cumulative as opposed to instantaneous treatment effect. In many applications, censoring time is not independent of event time. Therefore, we propose methods for estimating the cumulative treatment effect in the presence of nonproportional hazards and dependent censoring. Three measures are proposed, including the ratio of cumulative hazards, relative risk, and difference in restricted mean lifetime. For each measure, we propose a double inverse‐weighted estimator, constructed by first using inverse probability of treatment weighting (IPTW) to balance the treatment‐specific covariate distributions, then using inverse probability of censoring weighting (IPCW) to overcome the dependent censoring. The proposed estimators are shown to be consistent and asymptotically normal. We study their finite‐sample properties through simulation. The proposed methods are used to compare kidney wait‐list mortality by race.