Regression Analysis of Left-truncated and Case I Interval-censored Data with the Additive Hazards Model

In recent years the analysis of interval-censored failure time data has attracted a great deal of attention and such data arise in many fields including demographical studies, economic and financial studies, epidemiological studies, social sciences, and tumorigenicity experiments. This is especially the case in medical studies such as clinical trials. In this article, we discuss regression analysis of one type of such data, Case I interval-censored data, in the presence of left-truncation. For the problem, the additive hazards model is employed and the maximum likelihood method is applied for estimations of unknown parameters. In particular, we adopt the sieve estimation approach that approximates the baseline cumulative hazard function by linear functions. The resulting estimates of regression parameters are shown to be consistent and efficient and have an asymptotic normal distribution. An illustrative example is provided.     

Testing the proportional odds model for interval-censored data

This paper discusses the goodness-of-fit test for the proportional odds model for K-sample interval-censored failure time data, which frequently occur in, for example, periodic follow-up survival studies. The proportional odds model has a feature that allows the ratio of two hazard functions to be monotonic and converge to one and provides an important tool for the modeling of survival data. To test the model, a procedure is proposed, which is a generalization of the method given in Dauxois and Kirmani [Dauxois JY, Kirmani SNUA (2003) Biometrika 90:913–922]. The asymptotic distribution of the procedure is established and its properties are evaluated by simulation studies     

A class of linear transformation models for interval censored data with a cured proportion

Interval-censored data arise due to a sequence random examination such that the failure time of interest occurs in an interval. In some medical studies, there exist long-term survivors who can be considered as permanently cured. We consider a mixed model for the uncured group coming from linear transformation models and cured group coming from a logistic regression model. For the inference of parameters, an EM algorithm is developed for a full likelihood approach. To investigate finite sample properties of the proposed method, simulation studies are conducted. The approach is applied to the National Aeronautics and Space Administration’s hypobaric decompression sickness data.     

A Semiparametric Regression Method for Interval-Censored Data

In many medical studies, event times are recorded in an interval-censored (IC) format. For example, in numerous cancer trials, time to disease relapse is only known to have occurred between two consecutive clinic visits. Many existing modeling methods in the IC context are computationally intensive and usually require numerous assumptions that could be unrealistic or difficult to verify in practice. We propose a flexible and computationally efficient modeling strategy based on jackknife pseudo-observations (POs). The POs obtained based on nonparametric estimators of the survival function are employed as outcomes in an equivalent, yet simpler regression model that produces consistent covariate effect estimates. Hence, instead of operating in the IC context, the problem is translated into the realm of generalized linear models, where numerous options are available. Outcome transformations via appropriate link functions lead to familiar modeling contexts such as the proportional hazards and proportional odds. Moreover, the methods developed are not limited to these settings and have broader applicability. Simulations studies show that the proposed methods produce virtually unbiased covariate effect estimates, even for moderate sample sizes. An example from the International Breast Cancer Study Group (IBCSG) Trial VI further illustrates the practical advantages of this new approach.     

Additive Transformation Models for Multivariate Interval-Censored Data

ABSTRACT

We present a new estimator of extreme quantiles dedicated to Weibull tail distributions. This estimate is based on a consistent estimator of the Weibull tail coefficient. This parameter is defined as the regular variation coefficient of the inverse cumulative hazard function. We give conditions in order to obtain the weak consistency and the asymptotic distribution of the extreme quantiles estimator. Its asymptotic as well as its finite sample performances are compared to classical ones.     

Analysis of Multivariate Interval Censoring by Diabetic Retinopathy Study

Multivariate failure time data are commonly encountered in biomedical research since each study subject may experience multiple events or because there exists clustering of subjects such that failure times within the same cluster are correlated. In this article, we use the frailty approach to catch the related survival variables and assume each event is a discrete analog as an interval of clinical examinations periodically. For estimation, an Expectation–Maximization (EM) algorithm is developed and is applied to the diabetic retinopathy study (DRS).