Maximum Likelihood Estimation for the Pooled Repeated Partly Interval-Censored Observations Logistic Regression Model

Often in longitudinal studies, some subjects complete their follow-up visits, but others miss their visits due to various reasons. For those who miss follow-up visits, some of them might learn that the event of interest has already happened when they come back. In this case, not only are their event times interval-censored, but also their time-dependent measurements are incomplete. This problem was motivated by a national longitudinal survey of youth data. Maximum likelihood estimation (MLE) method based on expectation-maximization (EM) algorithm is used for parameter estimation. Then missing information principle is applied to estimate the variance-covariance matrix of the MLEs. Simulation studies demonstrate that the proposed method works well in terms of bias, standard error, and power for samples of moderate size. The national longitudinal survey of youth 1997 (NLSY97) data is analyzed for illustration.

Analysis of Complex Correlated Interval-Censored HIV Data from Population Based Survey

In studies of HIV, interval-censored data occur naturally. HIV infection time is not usually known exactly, only that it occurred before the survey, within some time interval or has not occurred at the time of the survey. Infections are often clustered within geographical areas such as enumerator areas (EAs) and thus inducing unobserved frailty. In this paper we consider an approach for estimating parameters when infection time is unknown and assumed correlated within an EA where dependency is modeled as frailties assuming a normal distribution for frailties and a Weibull distribution for baseline hazards. The data was from a household based population survey that used a multi-stage stratified sample design to randomly select 23,275 interviewed individuals from 10,584 households of whom 15,851 interviewed individuals were further tested for HIV (crude prevalence = 9.1%). A further test conducted among those that tested HIV positive found 181 (12.5%) recently infected. Results show high degree of heterogeneity in HIV distribution between EAs translating to a modest correlation of 0.198. Intervention strategies should target geographical areas that contribute disproportionately to the epidemic of HIV. Further research needs to identify such hot spot areas and understand what factors make these areas prone to HIV.

Nonparametric Regression with Interval-Censored Data

In many medical studies,the prevalence of interval censored data is increasing due to periodic monitoring of the progression status of a disease.In nonparametric regression model,when the response variable is subjected to interval-censoring,the regression function could not be estimated by traditional methods directly.With the censored data,we construct a new response variable which has the same conditional expectation as the original one.Based on the new variable,we get a nearest neighbor estimator of the regression function.It is established that the estimator has strong consistency and asymptotic normality.The relevant simulation reports are given.

Regression Analysis of Interval-Censored Data with Informative Observation Times Under the Accelerated Failure Time Model

This paper discusses regression analysis of interval-censored failure time data arising from the accelerated failure time model in the presence of informative censoring.For the problem,a sieve maximum likelihood estimation approach is proposed and in the method,the copula model is employed to describe the relationship between the failure time of interest and the censoring or observation process.Also I-spline functions are used to approximate the unknown functions in the model,and a simulation study is carried out to assess the finite sample performance of the proposed approach and suggests that it works well in practical situations.In addition,an illustrative example is provided.

Robust Regression Analysis for Clustered Interval-Censored Failure Time Data

Clustered interval-censored failure time data often occur in a wide variety of research and application fields such as cancer and AIDS studies. For such data, the failure times of interest are interval-censored and may be correlated for subjects coming from the same cluster. This paper presents a robust semiparametric transformation mixed effect models to analyze such data and use a U-statistic based on rank correlation to estimate the unknown parameters. The large sample properties of the estimator are also established. In addition, the authors illustrate the performance of the proposed estimate with extensive simulations and two real data examples.