A proportional hazards model for interval-censored failure time data

This paper develops a method for fitting the proportional hazards regression model when the data contain left-, right-, or interval-censored observations. Results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log-rank test for comparison of several survival curves. The method is used to analyze data from an animal tumorigenicity study and also a clinical trial.     

A multistate model for bivariate interval-censored failure time data

SUMMARY: Interval-censored life-history data arise when the events of interest are only detectable at periodic assessments. When interest lies in the occurrence of two such events, bivariate-interval censored event time data are obtained. We describe how to fit a four-state Markov model useful for characterizing the association between two interval-censored event times when the assessment times for the two events may be generated by different inspection processes. The approach treats the two events symmetrically and enables one to fit multiplicative intensity models that give estimates of covariate effects as well as relative risks characterizing the association between the two events. An expectation-maximization (EM) algorithm is described for estimation in which the maximization step can be carried out with standard software. The method is illustrated by application to data from a trial of HIV patients where the events are the onset of viral shedding in the blood and urine among individuals infected with cytomegalovirus.     

A proportional hazards model for multivariate interval-censored failure time data

This paper focuses on the methodology developed for analyzing a multivariate interval-censored data set from an AIDS observational study. A purpose of the study was to determine the natural history of the opportunistic infection cytomeglovirus (CMV) in an HIV-infected individual. For this observational study, laboratory tests were performed at scheduled clinic visits to test for the presence of the CMV virus in the blood and in the urine (called CMV shedding in the blood and urine). The study investigators were interested in determining whether the stage of HIV disease at study entry was predictive of an increased risk for CMV shedding in either the blood or the urine. If all patients had made each clinic visit, the data would be multivariate grouped failure time data and published methods could be used. However, many patients missed several visits, and when they returned, their lab tests indicated a change in their blood and/or urine CMV shedding status, resulting in interval-censored failure time data. This paper outlines a method for applying the proportional hazards model to the analysis of multivariate interval-censored failure time data from a study of CMV in HIV-infected patients.     

Semiparametric regression analysis of interval-censored data

We propose a semiparametric approach to the proportional hazards regression analysis of interval-censored data. An EM algorithm based on an approximate likelihood leads to an M-step that involves maximizing a standard Cox partial likelihood to estimate regression coefficients and then using the Breslow estimator for the unknown baseline hazards. The E-step takes a particularly simple form because all incomplete data appear as linear terms in the complete-data log likelihood. The algorithm of Turnbull (1976, Journal of the Royal Statistical Society, Series B 38, 290-295) is used to determine times at which the hazard can take positive mass. We found multiple imputation to yield an easily computed variance estimate that appears to be more reliable than asymptotic methods with small to moderately sized data sets. In the right-censored survival setting, the approach reduces to the standard Cox proportional hazards analysis, while the algorithm reduces to the one suggested by Clayton and Cuzick (1985, Applied Statistics 34, 148-156). The method is illustrated on data from the breast cancer cosmetics trial, previously analyzed by Finkelstein (1986, Biometrics 42, 845-854) and several subsequent authors.     

A goodness-of-fit test for the marginal Cox model for correlated interval-censored failure time data

The marginal Cox model approach is perhaps the most commonly used method in the analysis of correlated failure time data (Cai, 1999; Cai and Prentice, 1995; Lin, 1994; Wei, Lin and Weissfeld, 1989). It assumes that the marginal distributions for the correlated failure times can be described by the Cox model and leaves the dependence structure completely unspecified. This paper discusses the assessment of the marginal Cox model for correlated interval-censored data and a goodness-of-fit test is presented for the problem. The method is applied to a set of correlated interval-censored data arising from an AIDS clinical trial.     

A Bayesian semiparametric accelerated failure time model

A Bayesian semiparametric approach is described for an accelerated failure time model. The error distribution is assigned a Pólya tree prior and the regression parameters a noninformative hierarchical prior. Two cases are considered: the first assumes error terms are exchangeable; the second assumes that error terms are partially exchangeable. A Markov chain Monte Carlo algorithm is described to obtain a predictive distribution for a future observation given both uncensored and censored data.     

Generalized log-rank tests for partly interval-censored failure time data

In this paper, we consider incomplete survival data: partly interval-censored failure time data where observed data include both exact and interval-censored observations on the survival time of interest. We present a class of generalized log-rank tests for this type of survival data and establish their asymptotic properties. The method is evaluated using simulation studies and illustrated by a set of real data from a diabetes study.     

Maximum likelihood estimation for interval-censored data using a Weibull-based accelerated failure time model.

The accelerated failure time regression model is most commonly used with right-censored survival data. This report studies the use of a Weibull-based accelerated failure time regression model when left- and interval-censored data are also observed. Two alternative methods of analysis are considered. First, the maximum likelihood estimates (MLEs) for the observed censoring pattern are computed. These are compared with estimates where midpoints are substituted for left- and interval-censored data (midpoint estimator, or MDE). Simulation studies indicate that for relatively large samples there are many instances when the MLE is superior to the MDE. For samples where the hazard rate is flat or nearly so, or where the percentage of interval-censored data is small, the MDE is adequate. An example using Framingham Heart Study data is discussed.     

A semiparametric joint model for cluster size and subunit-specific interval-censored outcomes

Clustered data frequently arise in biomedical studies, where observations, or subunits, measured within a cluster are associated. The cluster size is said to be informative, if the outcome variable is associated with the number of subunits in a cluster. In most existing work, the informative cluster size issue is handled by marginal approaches based on within-cluster resampling, or cluster-weighted generalized estimating equations. Although these approaches yield consistent estimation of the marginal models, they do not allow estimation of within-cluster associations and are generally inefficient. In this paper, we propose a semiparametric joint model for clustered interval-censored event time data with informative cluster size. We use a random effect to account for the association among event times of the same cluster as well as the association between event times and the cluster size. For estimation, we propose a sieve maximum likelihood approach and devise a computationally-efficient expectation-maximization algorithm for implementation. The estimators are shown to be strongly consistent, with the Euclidean components being asymptotically normal and achieving semiparametric efficiency. Extensive simulation studies are conducted to evaluate the finite-sample performance, efficiency and robustness of the proposed method. We also illustrate our method via application to a motivating periodontal disease dataset.     

Regression analysis of multivariate interval-censored failure time data with application to tumorigenicity experiments

This paper discusses multivariate interval-censored failure time data that occur when there exist several correlated survival times of interest and only interval-censored data are available for each survival time. Such data occur in many fields. One is tumorigenicity experiments, which usually concern different types of tumors, tumors occurring in different locations of animals, or together. For regression analysis of such data, we develop a marginal inference approach using the additive hazards model and apply it to a set of bivariate interval-censored data arising from a tumorigenicity experiment. Simulation studies are conducted for the evaluation of the presented approach and suggest that the approach performs well for practical situations.     

A semiparametric model for the analysis of recurrent-event panel data

In many longitudinal studies, interest focuses on the occurrence rate of some phenomenon for the subjects in the study. When the phenomenon is nonterminating and possibly recurring, the result is a recurrent-event data set. Examples include epileptic seizures and recurrent cancers. When the recurring event is detectable only by an expensive or invasive examination, only the number of events occurring between follow-up times may be available. This article presents a semiparametric model for such data, based on a multiplicative intensity model paired with a fully flexible nonparametric baseline intensity function. A random subject-specific effect is included in the intensity model to account for the overdispersion frequently displayed in count data. Estimators are determined from quasi-likelihood estimating functions. Because only first- and second-moment assumptions are required for quasi-likelihood, the method is more robust than those based on the specification of a full parametric likelihood. Consistency of the estimators depends only on the assumption of the proportional intensity model. The semiparametric estimators are shown to be highly efficient compared with the usual parametric estimators. As with semiparametric methods in survival analysis, the method provides useful diagnostics for specific parametric models, including a quasi-score statistic for testing specific baseline intensity functions. The techniques are used to analyze cancer recurrences and a pheromone-based mating disruption experiment in moths. A simulation study confirms that, for many practical situations, the estimators possess appropriate small-sample characteristics.     

Testing for dependence between failure time and visit compliance with interval-censored data

Interval-censored failure-time data arise when subjects miss prescheduled visits at which the failure is to be assessed. The resulting intervals in which the failure is known to have occurred are overlapping. Most approaches to the analysis of these data assume that the visit-compliance process is ignorable with respect to likelihood analysis of the failure-time distribution. While this assumption offers considerable simplification, it is not always plausible. Here we test for dependence between the failure- and visit-compliance processes, applicable to studies in which data collection continues after the occurrence of the failure. We do not make any of the assumptions made by previous authors about the joint distribution of the visit-compliance process, a covariate process, and the failure time. Instead, we consider conditional models of the true failure history given the current visit compliance at each visit time, allowing for correlation across visit times. Because failure status is not known at some visit times due to missed visits, only models of the observed failure history given current visit compliance are estimable. We describe how the parameters from these models can be used to test for a negative association and how bounds on unestimable parameters provided by the observed data are needed additionally to infer a positive association. We illustrate the method with data from an AIDS study and we investigate the power of the test through a simulation study.     

Hazard regression for interval-censored data with penalized spline

This article introduces a new approach for estimating the hazard function for possibly interval- and right-censored survival data. We weakly parameterize the log-hazard function with a piecewise-linear spline and provide a smoothed estimate of the hazard function by maximizing the penalized likelihood through a mixed model-based approach. We also provide a method to estimate the amount of smoothing from the data. We illustrate our approach with two well-known interval-censored data sets. Extensive numerical studies are conducted to evaluate the efficacy of the new procedure.     

Bayesian analysis and model selection for interval-censored survival data

Interval-censored data occur in survival analysis when the survival time of each patient is only known to be within an interval and these censoring intervals differ from patient to patient. For such data, we present some Bayesian discretized semiparametric models, incorporating proportional and nonproportional hazards structures, along with associated statistical analyses and tools for model selection using sampling-based methods. The scope of these methodologies is illustrated through a reanalysis of a breast cancer data set (Finkelstein, 1986, Biometrics 42, 845-854) to test whether the effect of covariate on survival changes over time.     

"Smooth" semiparametric regression analysis for arbitrarily censored time-to-event data

Summary .   A general framework for regression analysis of time-to-event data subject to arbitrary patterns of censoring is proposed. The approach is relevant when the analyst is willing to assume that distributions governing model components that are ordinarily left unspecified in popular semiparametric regression models, such as the baseline hazard function in the proportional hazards model, have densities satisfying mild "smoothness" conditions. Densities are approximated by a truncated series expansion that, for fixed degree of truncation, results in a "parametric" representation, which makes likelihood-based inference coupled with adaptive choice of the degree of truncation, and hence flexibility of the model, computationally and conceptually straightforward with data subject to any pattern of censoring. The formulation allows popular models, such as the proportional hazards, proportional odds, and accelerated failure time models, to be placed in a common framework; provides a principled basis for choosing among them; and renders useful extensions of the models straightforward. The utility and performance of the methods are demonstrated via simulations and by application to data from time-to-event studies.