Relative risk regression for current status data in case‐cohort studies

We propose using the weighted likelihood method to fit a general relative risk regression model for the current status data with missing data as arise, for example, in case‐cohort studies. The missingness probability is either known or can be reasonably estimated. Asymptotic properties of the weighted likelihood estimators are established. For the case of using estimated weights, we construct a general theorem that guarantees the asymptotic normality of the M‐estimator of a finite dimensional parameter in a class of semiparametric models, where the infinite dimensional parameter is allowed to converge at a slower than parametric rate, and some other parameters in the objective function are estimated a priori. The weighted bootstrap method is employed to estimate the variances. Simulations show that the proposed method works well for finite sample sizes. A motivating example of the case‐cohort study from an HIV vaccine trial is used to demonstrate the proposed method. The Canadian Journal of Statistics 39: 557–577; 2011. © 2011 Statistical Society of Canada     

Additive hazards regression of current status data with auxiliary covariates

This paper discusses the regression analysis of current status failure time data arising from the additive hazards model with auxiliary covariates. As often occurs in practice, it is impossible or impractical to measure the exact magnitude of covariates for all subjects in a study. To compensate the missing information, some auxiliary covariates are utilized instead. We propose two easy-to-implement procedures for estimation of regression parameters by making use of auxiliary information. The asymptotic properties of the resulting estimators are established and extensive numerical studies indicate that both procedures work well in practice.     

Efficient estimation for the proportional hazards model with competing risks and current status data

The proportional hazards model is the most commonly used model in regression analysis of failure time data and has been discussed by many authors under various situations (Kalbfleisch & Prentice, 2002. The Statistical Analysis of Failure Time Data, Wiley, New York). This paper considers the fitting of the model to current status data when there exist competing risks, which often occurs in, for example, medical studies. The maximum likelihood estimates of the unknown parameters are derived and their consistency and convergence rate are established. Also we show that the estimates of regression coefficients are efficient and have asymptotically normal distributions. Simulation studies are conducted to assess the finite sample properties of the estimates and an illustrative example is provided. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

Proportional hazards regression with interval-censored and left-truncated data

This paper considers the estimation of the regression coefficients in the Cox proportional hazards model with left-truncated and interval-censored data. Using the approaches of Pan [A multiple imputation approach to Cox regression with interval-censored data, Biometrics 56 (2000), pp. 199–203] and Heller [Proportional hazards regression with interval censored data using an inverse probability weight, Lifetime Data Anal. 17 (2011), pp. 373–385], we propose two estimates of the regression coefficients. The first estimate is based on a multiple imputation methodology. The second estimate uses an inverse probability weight to select event time pairs where the ordering is unambiguous. A simulation study is conducted to investigate the performance of the proposed estimators. The proposed methods are illustrated using the Centers for Disease Control and Prevention (CDC) acquired immunodeficiency syndrome (AIDS) Blood Transfusion Data.     

Nonparametric tests for stratified additive hazards model based on current status data

Stratified regression models are commonly employed when study subjects may come from possibly different strata such as different medical centers, and for the situation, one common question of interest is to test the existence of the stratum effect. To address this, there exists some literature on the testing of the stratum effects under the framework of the proportional hazards model when one observes right-censored data or interval-censored data. In this paper, we consider the situation under the additive hazards model when one faces current status data, for which there does not seem to exist an established test procedure. The asymptotic distributions of the proposed test procedure are provided. Also a simulation study is performed to evaluate the performance of the proposed method and indicates that it works well for practical situations. The approach is applied to a set of real current status data from a tumorigenicity study.     

Jointly modeling skew longitudinal survival data with missingness and mismeasured covariates

Jointly modeling longitudinal and survival data has been an active research area. Most researches focus on improving the estimating efficiency but ignore many data features frequently encountered in practice. In the current study, we develop the joint models that concurrently accounting for longitudinal and survival data with multiple features. Specifically, the proposed model handles skewness, missingness and measurement errors in covariates which are typically observed in the collection of longitudinal survival data from many studies. We employ a Bayesian inferential method to make inference on the proposed model. We applied the proposed model to an real data study. A few alternative models under different conditions are compared. We conduct extensive simulations in order to evaluate how the method works.     

Regression analysis of interval-censored failure time data with cured subgroup and mismeasured covariates

Abstract

Failure time data occur in many areas and also in various forms and in particular, many authors have discussed regression analysis of failure time data in the presence of interval censoring, a cured subgroup or mismeasured covariates. However, it does not seem to exist an established procedure that can deal with all three issues together. Corresponding to this, we propose a sieve maximum likelihood estimation procedure that takes into account all three issues with the use of the SIMEX algorithm. The asymptotic properties of the proposed estimators are established, and an extensive simulation study is also conducted and suggests that the proposed method works well for practical situations.     

Asymptotic properties of nonparametric M-estimation for mixing functional data

We investigate the asymptotic behavior of a nonparametric M-estimator of a regression function for stationary dependent processes, where the explanatory variables take values in some abstract functional space. Under some regularity conditions, we give the weak and strong consistency of the estimator as well as its asymptotic normality. We also give two examples of functional processes that satisfy the mixing conditions assumed in this paper. Furthermore, a simulated example is presented to examine the finite sample performance of the proposed estimator.     

Semiparametric inference for survival models with step process covariates

The authors consider Bayesian methods for fitting three semiparametric survival models, incorporating time‐dependent covariates that are step functions. In particular, these are models due to Cox [Cox ( 1972 ) Journal of the Royal Statistical Society, Series B, 34, 187–208], Prentice & Kalbfleisch and Cox & Oakes [Cox & Oakes ( 1984 ) Analysis of Survival Data, Chapman and Hall, London]. The model due to Prentice & Kalbfleisch [Prentice & Kalbfleisch ( 1979 ) Biometrics, 35, 25–39], which has seen very limited use, is given particular consideration. The prior for the baseline distribution in each model is taken to be a mixture of Polya trees and posterior inference is obtained through standard Markov chain Monte Carlo methods. They demonstrate the implementation and comparison of these three models on the celebrated Stanford heart transplant data and the study of the timing of cerebral edema diagnosis during emergency room treatment of diabetic ketoacidosis in children. An important feature of their overall discussion is the comparison of semi‐parametric families, and ultimate criterion based selection of a family within the context of a given data set. The Canadian Journal of Statistics 37: 60–79; © 2009 Statistical Society of Canada     

Additive hazards regression with censoring indicators missing at random

In this article, the authors consider a semiparametric additive hazards regression model for right‐censored data that allows some censoring indicators to be missing at random. They develop a class of estimating equations and use an inverse probability weighted approach to estimate the regression parameters. Nonparametric smoothing techniques are employed to estimate the probability of non‐missingness and the conditional probability of an uncensored observation. The asymptotic properties of the resulting estimators are derived. Simulation studies show that the proposed estimators perform well. They motivate and illustrate their methods with data from a brain cancer clinical trial. The Canadian Journal of Statistics 38: 333–351; 2010 © 2010 Statistical Society of Canada     

Semiparametric regression of clustered current status data

This paper discusses regression analysis of clustered current status data under semiparametric additive hazards models. In particular, we consider the situation when cluster sizes can be informative about correlated failure times from the same cluster. To address the problem, we present estimating equation-based estimation procedures and establish asymptotic properties of the resulting estimates. Finite sample performance of the proposed method is assessed through an extensive simulation study, which indicates the procedure works well. The method is applied to a motivating data set from a lung tumorigenicity study.     

A linear transformation model for multivariate interval‐censored failure time data

This paper discusses multivariate interval‐censored failure time data observed when several correlated survival times of interest exist and only interval censoring is available for each survival time. Such data occur in many fields, for instance, studies of the development of physical symptoms or diseases in several organ systems. A marginal inference approach was used to create a linear transformation model and applied to bivariate interval‐censored data arising from a diabetic retinopathy study and an AIDS study. The results of simulation studies that were conducted to evaluate the performance of the presented approach suggest that it performs well. The Canadian Journal of Statistics 41: 275–290; 2013 © 2013 Statistical Society of Canada     

Multiple imputation for competing risks regression with interval-censored data

ABSTRACT

We present here an extension of Pan's multiple imputation approach to Cox regression in the setting of interval-censored competing risks data. The idea is to convert interval-censored data into multiple sets of complete or right-censored data and to use partial likelihood methods to analyse them. The process is iterated, and at each step, the coefficient of interest, its variance–covariance matrix, and the baseline cumulative incidence function are updated from multiple posterior estimates derived from the Fine and Gray sub-distribution hazards regression given augmented data. Through simulation of patients at risks of failure from two causes, and following a prescheduled programme allowing for informative interval-censoring mechanisms, we show that the proposed method results in more accurate coefficient estimates as compared to the simple imputation approach. We have implemented the method in the MIICD R package, available on the CRAN website.