Nonparametric Test for Doubly Interval-Censored Failure Time Data

This paper considers comparison of discrete failure time distributions when the survival time of interest measures elapsed time between two related events and observations on the occurrences of both events could be interval-censored. This kind of data is often referred to as doubly interval-censored failure time data. If the occurrence of the first event defining the survival time can be exactly observed, the data are usually referred to as interval-censored data. For the comparison problem based on interval-censored failure time data, Sun (1996) proposed a nonparametric test procedure. In this paper we generalize the procedure given in Sun (1996) to doubly interval-censored data case and the generalized test is evaluated by simulations.     

Estimation of the joint survival function for successive duration times under double-truncation and right-censoring

ABSTRACT

In incident cohort studies, survival data often include subjects who have had an initiate event at recruitment and may potentially experience two successive events (first and second) during the follow-up period. When disease registries or surveillance systems collect data based on incidence occurring within a specific calendar time interval, the initial event is usually subject to double truncation. Furthermore, since the second duration process is observable only if the first event has occurred, double truncation and dependent censoring arise. In this article, under the two sampling biases with an unspecified distribution of truncation variables, we propose a nonparametric estimator of the joint survival function of two successive duration times using the inverse-probability-weighted (IPW) approach. The consistency of the proposed estimator is established. Based on the estimated marginal survival functions, we also propose a two-stage estimation procedure for estimating the parameters of copula model. The bootstrap method is used to construct confidence interval. Numerical studies demonstrate that the proposed estimation approaches perform well with moderate sample sizes.     

Clustered Survival Data with Left‐truncation

Left‐truncation occurs frequently in survival studies, and it is well known how to deal with this for univariate survival times. However, there are few results on how to estimate dependence parameters and regression effects in semiparametric models for clustered survival data with delayed entry. Surprisingly, existing methods only deal with special cases. In this paper, we clarify different kinds of left‐truncation and suggest estimators for semiparametric survival models under specific truncation schemes. The large‐sample properties of the estimators are established. Small‐sample properties are investigated via simulation studies, and the suggested estimators are used in a study of prostate cancer based on the Finnish twin cohort where a twin pair is included only if both twins were alive in 1974.     

Estimation of the joint survival function for three successive duration times under double truncation and right censoring

In incident cohort studies, it is common to include subjects who have experienced a certain event within a calendar time window. For all the included individuals, the time of the previous events is retrospectively confirmed and the occurrence of subsequent events is observed during the follow-up periods. During the follow-up periods, subjects may undergo three successive events. Since the second/third duration process becomes observable only if the first/second event has occurred, the data is subject to double truncation and right censoring. We consider two cases: the case when the first event time is subject to double truncation and the case when the second event time is subject to double truncation. Using the inverse-probability-weighted approach, we propose nonparametric and semiparametric estimators for the estimation of the joint survival function of three successive duration times. We establish the asymptotic properties of the proposed estimators and conduct a simulation study to investigate the finite sample properties of the proposed estimators.     

On estimation and diagnostics analysis in log-generalized gamma regression model for interval-censored data

The interval-censored survival data appear very frequently, where the event of interest is not observed exactly but it is only known to occur within some time interval. In this paper, we propose a location-scale regression model based on the log-generalized gamma distribution for modelling interval-censored data. We shall be concerned only with parametric forms. The proposed model for interval-censored data represents a parametric family of models that has, as special submodels, other regression models which are broadly used in lifetime data analysis. Assuming interval-censored data, we consider a frequentist analysis, a Jackknife estimator and a non-parametric bootstrap for the model parameters. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some techniques to perform global influence.     

Frequentist and Bayesian approaches for interval-censored data

Interval censoring appears when the event of interest is only known to have occurred within a random time interval. Estimation and hypothesis testing procedures for interval-censored data are surveyed. We distinguish between frequentist and Bayesian approaches. Computational aspects for every proposed method are described and solutions with S-Plus, whenever are feasible, are mentioned. Three real data sets are analyzed.     

Self-Consistency Estimation of Distributions Based on Truncated and Doubly Censored Survival Data with Applications to AIDS Cohort Studies

Gomez and Lagakos (1994) propose a nonparametric method for estimating the distribution of a survival time when the origin and end points defining the survival time suffer interval-censoring and right-censoring, respectively. In some situations, the end point also suffers interval-censoring as well as truncation. In this paper, we consider this general situation and propose a two-step estimation procedure for the estimation of the distribution of a survival time based on doubly interval-censored and truncated data. The proposed method generalizes the methods proposed by DeGruttola and Lagakos (1989) and Sun (1995) and is more efficient than that given in Gomez and Lagakos (1994). The approach is based on self-consistency equations. The method is illustrated by an analysis of an AIDS cohort study.     

Nonparametric Estimation of Sojourn Time Distributions for Truncated Serial Event Data—a Weight-adjusted Approach

In follow-up studies, survival data often include subjects who have had a certain event at recruitment and may potentially experience a series of subsequent events during the follow-up period. This kind of survival data collected under a cross-sectional sampling criterion is called truncated serial event data. The outcome variables of interest in this paper are serial sojourn times between successive events. To analyze the sojourn times in truncated serial event data, we need to confront two potential sampling biases arising simultaneously from a sampling criterion and induced informative censoring. In this study, nonparametric estimation of the joint probability function of serial sojourn times is developed by using inverse probabilities of the truncation and censoring times as weight functions to accommodate these two sampling biases under various situations of truncation and censoring. Relevant statistical properties of the proposed estimators are also discussed. Simulation studies and two real data are presented to illustrate the proposed methods.     

Regression analysis of recurrent events data with incomplete observation gaps

For analyzing recurrent event data, either total time scale or gap time scale is adopted according to research interest. In particular, gap time scale is known to be more appropriate for modeling a renewal process. In this paper, we adopt gap time scale to analyze recurrent event data with repeated observation gaps which cannot be observed completely because of unknown termination times of observation gaps. In order to estimate termination times, interval-censored mechanism is applied. Simulation studies are done to compare the suggested methods with the unadjusted method ignoring incomplete observation gaps. As a real example, conviction data set with suspensions is analyzed with suggested methods.     

Non-parametric estimation with doubly censored data

Data from longitudinal studies in which an initiating event and a subsequent event occur in sequence are called 'doubly censored' data if the time of both events is interval-censored. This paper is concerned with using doubly censored data to estimate the distribution function of the so-called 'duration time', i.e. the elapsed time between the originating event and the subsequent event. The paper proposes a generalization of the Gomez and Lagakos two-step method for the case where both the time to the initiating event and the duration time are continuous. This approach is applied to estimate the AIDS-latency time from a haemophiliacs cohort.     

A semiparametric regression cure model for interval-censored and left-truncated data

Medical advancements have made it possible for patients to be cured of certain types of diseases. In follow-up studies, the disease event time can be subject to left truncation and interval censoring. In this article, we propose a semiparametric nonmixture cure model for the regression analysis of left-truncated and interval-censored (LTIC) data. We develop semiparametric maximum likelihood estimation for the nonmixture cure model with LTIC data. A simulation study is conducted to investigate the performance of the proposed estimators.     

Joint modelling of event counts and survival times

Summary.  In studies of recurrent events, such as epileptic seizures, there can be a large amount of information about a cohort over a period of time, but current methods for these data are often unable to utilize all of the available information. The paper considers data which include post-treatment survival times for individuals experiencing recurring events, as well as a measure of the base-line event rate, in the form of a pre-randomization event count. Standard survival analysis may treat this pre-randomization count as a covariate, but the paper proposes a parametric joint model based on an underlying Poisson process, which will give a more precise estimate of the treatment effect.     

Estimating age-specific incidence of dementia using prevalent cohort data

In prospective cohort studies, individuals are usually recruited according to a certain cross-sectional sampling criterion. The prevalent cohort is defined as a group of individuals who are alive but possibly with disease at the beginning of the study. It is appealing to incorporate the prevalent cases to estimate the incidence rate of disease before the enrollment. The method of back calculation of incidence rate has been used to estimate the incubation time from human immunodeficiency virus (HIV) infection to AIDS. The time origin is defined as the time of HIV infection. In aging cohort studies, the primary time scale is age of disease onset, subjects have to survive certain years to be enrolled into the study, thus creating left truncation (delay entry). The current methods usually assume that either the disease incidence is rare or the excess mortality due to disease is small compared with the healthy subjects. So far the validity of the results based on these assumptions has not been examined. In this paper, a simple alternative method is proposed to estimate dementia incidence rate before enrollment using prevalent cohort data with left truncation. Furthermore, simulations are used to examine the performance of the estimation of disease incidence under different assumptions of disease incidence rates and excess mortality hazards due to disease. As application, the method is applied to the prevalent cases of dementia from the Honolulu-Asia Aging Study to estimate the dementia incidence rate and to assess the effect of hypertension, Apoe 4 and education on dementia onset.     

Estimating age-specific incidence of dementia using prevalent cohort data

In prospective cohort studies individuals are usually recruited according to a certain cross-sectional sampling criterion. The prevalent cohort is defined as a group of individuals who are alive but possibly with disease at the beginning of the study. It is appealing to incorporate the prevalent cases to estimate the incidence rate of disease before the enrollment. The method of back calculation of incidence rate has been used to estimate the incubation time from HIV infection to AIDS. The time origin is defined as the time of HIV infection. In aging cohort studies, the primary time scale is age of disease onset, subjects have to survive certain years to be enrolled into the study, thus creating left truncation (delay entry). The current methods usually assume that either the disease incidence is rare or the excess mortality due to disease is small compared to the healthy subjects. By far the validity of the results based on these assumptions has not been examined. In this paper, a simple alternative method is proposed to estimate dementia incidence rate before enrollment using prevalent cohort data with left truncation. Furthermore simulations are used to examine the performance of the estimation of disease incidence under different assumptions of disease incidence rates and excess mortality hazards due to disease. As application, the method is applied to the prevalent cases of dementia from the Honolulu Asia Aging Study to estimate dementia incidence rate and to assess the effect of hypertension, Apoe 4 and education on dementia onset.     

Longitudinal perspectives on event history analysis

We discuss event histories from the point of view of longitudinal data analysis, comparing several possible inferential objectives. We show that the Nelson–Aalen estimate of a cumulative intensity may be derived as a limiting solution to a sequence of generalized estimating equations for intermittently observed longitudinal count data. We outline a potential use for the theory in interval-censored recurrent-event models, and demonstrate its applicability using data from a Toronto arthritis clinic. We also discuss connections with rate models, along with some implications for the longitudinal analyst.     

A case-study in the clinical epidemiology of psoriatic arthritis: multistate models and causal arguments

In psoriatic arthritis, permanent joint damage characterizes disease progression and represents a major debilitating aspect of the disease. Understanding the process of joint damage will assist in the treatment and disease management of patients. Multistate models provide a means to examine patterns of disease, such as symmetric joint damage. Additionally, the link between damage and the dynamic course of disease activity (represented by joint swelling and stress pain) at both the individual joint level and otherwise can be represented within a correlated multistate model framework. Correlation is reflected through the use of random effects for progressive models and robust variance estimation for non-progressive models. Such analyses, undertaken with data from a large psoriatic arthritis cohort, are discussed and the extent to which they permit causal reasoning is considered. For this, emphasis is given to the use of the Bradford Hill criteria for causation in observational studies and the concept of local (in)dependence to capture the dynamic nature of the relationships.     

Bayesian statistical inference of the loglogistic model with interval-censored lifetime data

Interval-censored data arise when a failure time say, T cannot be observed directly but can only be determined to lie in an interval obtained from a series of inspection times. The frequentist approach for analysing interval-censored data has been developed for some time now. It is very common due to unavailability of software in the field of biological, medical and reliability studies to simplify the interval censoring structure of the data into that of a more standard right censoring situation by imputing the midpoints of the censoring intervals. In this research paper, we apply the Bayesian approach by employing Lindley's 1980, and Tierney and Kadane 1986 numerical approximation procedures when the survival data under consideration are interval-censored. The Bayesian approach to interval-censored data has barely been discussed in literature. The essence of this study is to explore and promote the Bayesian methods when the survival data been analysed are is interval-censored. We have considered only a parametric approach by assuming that the survival data follow a loglogistic distribution model. We illustrate the proposed methods with two real data sets. A simulation study is also carried out to compare the performances of the methods.     

The analysis of mixed interval-censored and complete data

The article focuses mainly on a conditional imputation algorithm of quantile-filling to analyze a new kind of censored data, mixed interval-censored and complete data related to interval-censored sample. With the algorithm, the imputed failure times, which are the conditional quantiles, are obtained within the censoring intervals in which some exact failure times are. The algorithm is viable and feasible for the parameter estimation with general distributions, for instance, a case of Weibull distribution that has a moment estimation of closed form by log-transformation. Furthermore, interval-censored sample is a special case of the new censored sample, and the conditional imputation algorithm can also be used to deal with the failure data of interval censored. By comparing the interval-censored data and the new censored data, using the imputation algorithm, in the view of the bias of estimation, we find that the performance of new censored data is better than that of interval censored.     

Likelihood estimation for a longitudinal negative binomial regression model with missing outcomes

Joint damage in psoriatic arthritis can be measured by clinical and radiological methods, the former being done more frequently during longitudinal follow-up of patients. Motivated by the need to compare findings based on the different methods with different observation patterns, we consider longitudinal data where the outcome variable is a cumulative total of counts that can be unobserved when other, informative, explanatory variables are recorded. We demonstrate how to calculate the likelihood for such data when it is assumed that the increment in the cumulative total follows a discrete distribution with a location parameter that depends on a linear function of explanatory variables. An approach to the incorporation of informative observation is suggested. We present analyses based on an observational database from a psoriatic arthritis clinic. Although the use of the new statistical methodology has relatively little effect in this example, simulation studies indicate that the method can provide substantial improvements in bias and coverage in some situations where there is an important time varying explanatory variable.     

Nested exposure case-control sampling: a sampling scheme to analyze rare time-dependent exposures

For large cohort studies with rare outcomes, the nested case-control design only requires data collection of small subsets of the individuals at risk. These are typically randomly sampled at the observed event times and a weighted, stratified analysis takes over the role of the full cohort analysis. Motivated by observational studies on the impact of hospital-acquired infection on hospital stay outcome, we are interested in situations, where not necessarily the outcome is rare, but time-dependent exposure such as the occurrence of an adverse event or disease progression is. Using the counting process formulation of general nested case-control designs, we propose three sampling schemes where not all commonly observed outcomes need to be included in the analysis. Rather, inclusion probabilities may be time-dependent and may even depend on the past sampling and exposure history. A bootstrap analysis of a full cohort data set from hospital epidemiology allows us to investigate the practical utility of the proposed sampling schemes in comparison to a full cohort analysis and a too simple application of the nested case-control design, if the outcome is not rare.