Liuquan Sun

Semiparametric Regression Analysis of Longitudinal Data With Informative Observation Times

Statistical analysis of longitudinal data has been discussed by many authors, and a number of methods have been proposed. Most of the research have focused on situations where observation times are independent of or carry no information about the response variable and therefore rely on conditional inference procedures given the observation times. This article considers a different situation, where the independence assumption may not hold; that is, the observation times may carry information about the response variable. For inference, estimating equation approaches are proposed, and both large-sample and final-sample properties of the proposed methods are established. The methodology is applied to a bladder cancer study that motivated this investigation.

Regression Analysis of Longitudinal Data in the Presence of Informative Observation and Censoring Times

Longitudinal data frequently occur in many studies, such as longitudinal follow-up studies. To develop statistical methods and theory for the analysis of these data, independent or noninformative observation and censoring times are typically assumed, which naturally leads to inference procedures conditional on observation and censoring times. But in many situations this may not be true or realistic; that is, longitudinal responses may be correlated with observation times as well as censoring times. This article considers the analysis of longitudinal data where these correlations may exist and proposes a joint modeling approach that uses some latent variables to characterize the correlations. For inference about regression parameters, estimating equation approaches are developed and both large-sample and final-sample properties of the proposed estimators are established. In addition, some graphical and numerical procedures are presented for model checking. The methodology is applied to a bladder cancer study that motivated this investigation.

Joint Analysis of Longitudinal Data With Informative Observation Times and a Dependent Terminal Event

In many longitudinal studies, repeated measures are often correlated with observation times. Also, there may exist a dependent terminal event such as death that stops the follow-up. In this article, we propose a new joint model for the analysis of longitudinal data in the presence of both informative observation times and a dependent terminal event via latent variables. Estimating equation approaches are developed for parameter estimation, and the resulting estimators are shown to be consistent and asymptotically normal. In addition, some graphical and numerical procedures are presented for model checking. Simulation studies demonstrate that the proposed method performs well for practical settings. An application to a medical cost study of chronic heart failure patients from the University of Virginia Health System is provided.

A Class of Transformed Mean Residual Life Models With Censored Survival Data

This article features online supplementary material. The mean residual life function is an attractive alternative to the survival function or the hazard function of a survival time in practice. It provides the remaining life expectancy of a subject surviving up to time t. In this study, we propose a class of transformed mean residual life models for fitting survival data under right censoring. To estimate the model parameters, we make use of the inverse probability of censoring weighting approach and develop a system of estimating equations. Efficiency and robustness of the estimators are also studied. Both asymptotic and finite sample properties of the proposed estimators are established and the approach is applied to two real-life datasets collected from clinical trials.

Additive Hazards Model for Competing Risks Analysis of the Case-Cohort Design

Abstract Competing risks analysis of the case-cohort design is often required in epidemiological studies and for this, some methods have been proposed under the proportional hazards model. It is known that the proportional hazards model may not fit survival data well sometimes. This paper considers the analysis under the additive hazards model. Methods are proposed for estimating regression parameters and cumulative baseline hazard functions as well as cumulative incidence functions. The proposed estimators are shown to be consistent and asymptotically normal using the martingale central limit theory. Simulation studies are conducted and suggest that the proposed methods perform well.

Semiparametric Transformation Models with Time-Varying Coefficients for Recurrent and Terminal Events

In this article, we propose a family of semiparametric transformation models with time-varying coefficients for recurrent event data in the presence of a terminal event such as death. The new model offers great flexibility in formulating the effects of covariates on the mean functions of the recurrent events among survivors at a given time. For the inference on the proposed models, a class of estimating equations is developed and asymptotic properties of the resulting estimators are established. In addition, a lack-of-fit test is provided for assessing the adequacy of the model, and some tests are presented for investigating whether or not covariate effects vary with time. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies, and an application to a bladder cancer study is also illustrated.

A class of Box-Cox transformation models for recurrent event data

In this article, we propose a class of Box-Cox transformation models for recurrent event data, which includes the proportional means models as special cases. The new model offers great flexibility in formulating the effects of covariates on the mean functions of counting processes while leaving the stochastic structure completely unspecified. For the inference on the proposed models, we apply a profile pseudo-partial likelihood method to estimate the model parameters via estimating equation approaches and establish large sample properties of the estimators and examine its performance in moderate-sized samples through simulation studies. In addition, some graphical and numerical procedures are presented for model checking. An example of application on a set of multiple-infection data taken from a clinic study on chronic granulomatous disease (CGD) is also illustrated.

A class of accelerated means regression models for recurrent event data

In this article, we propose a general class of accelerated means regression models for recurrent event data. The class includes the proportional means model, the accelerated failure time model and the accelerated rates model as special cases. The new model offers great flexibility in formulating the effects of covariates on the mean functions of counting processes while leaving the stochastic structure completely unspecified. For the inference on the model parameters, estimating equation approaches are developed and both large and final sample properties of the proposed estimators are established. In addition, some graphical and numerical procedures are presented for model checking. An illustration with multiple-infection data from a clinic study on chronic granulomatous disease is also provided.

Regression Analysis of Additive Hazards Model With Latent Variables

We propose an additive hazards model with latent variables to investigate the observed and latent risk factors of the failure time of interest. Each latent risk factor is characterized by correlated observed variables through a confirmatory factor analysis model. We develop a hybrid procedure that combines the expectation–maximization (EM) algorithm and the borrow-strength estimation approach to estimate the model parameters. We establish the consistency and asymptotic normality of the parameter estimators. Various nice features, including finite sample performance of the proposed methodology, are demonstrated by simulation studies. Our model is applied to a study concerning the risk factors of chronic kidney disease for Type 2 diabetic patients. Supplementary materials for this article are available online.

Survival function and density estimation for truncated dependent data

In some long-term studies, a series of dependent and possibly truncated lifetimes may be observed. Suppose that the lifetimes have a common marginal distribution function. Under some regularity conditions, we provide a strong representation of the product-limit estimator in the form of an average of random variables plus a remainder term. In addition, we also give asymptotic representations for the kernel estimators of the density and the hazard rate. These representations enable us to obtain the asymptotic normality and the uniform consistency of the estimators.