Semiparametric analysis of dependent interval-censored data based on the Newton-MI algorithm

Interval-censored failure time data commonly occur in many periodic follow-up studies such as epidemiological experiments, medical studies and clinical trials. By intervalcensored data, we usually mean that one cannot observe the failure time of interest and instead we know that it belongs to a time interval. Correlated failure time data commonly occur when there are multiple events on one individual or when the study subjects are clustered into some small groups. In this situation, study subjects from same subgroup or the failure events from same individuals are usually regarded as dependent, but the subjects in different clusters or failure events from different individuals are assumed to be independent. Besides the correlation between the cluster, sometimes the cluster size may be informative or carry some information about the failure time of interest. Cured subgroup is another interesting topic that has been discussed by many authors. For this situation, unlike the assumptions in traditional survival model that all study subjects would experience the failure event of interest eventually if the follow-up time is long enough, some subjects may never experience or not be susceptible to the event. Such subjects are treated as cured and assumed to belong to a cured subgroup in a study population. The research in this dissertation focuses on regression analysis of correlated intervalcensored data with a cured subgroup via different approaches based on different data structures. In the first part of this dissertation, we discuss clustered interval-censored data with a cured subgroup and informative cluster size. To address this, we present a within-cluster resampling method and in the approach, the multiple imputation procedure is applied for estimation of unknown parameters. To assess the performance of the proposed method, a simulation study is conducted and suggests that it works well in practical situations. Also, the method is applied to a set of real data that motivated this study. In the second part of this dissertation, we consider the clustered interval-censored data with a cured subgroup via a non-mixture cure model. We present a maximum likelihood estimation procedure under the semiparametric transformation nonmixture cure model. To estimate the unknown parameters, an expectation maximization (EM) algorithm based on an augmentation of Poisson variable is developed. To assess the performance of the proposed method, a simulation study is conducted and suggests that it works well in practical situations. An application to a study conducted by the National Aeronautics and Space Administration that motivated this study is also provided. In the third part of this dissertation, we investigate the bivariate interval-censored data with a cured subgroup. A sieve maximum likelihood estimation procedure under the semiparametric transformation non-mixture cure model based on Bernstein polynomials is presented. A simulation study is conducted to assess the finite sample performance of the proposed method and suggests that the proposed model works well. Also, a real data application from the study of AIDS Clinical Trial Group 181 is provided.

Regression analysis of interval-censored failure time data commonly arises in biomedical studies, particularly when the available sample size is limited. Although many methods have been proposed for the semiparametric probit model with interval-censored data, there does not appear to exist an established approach that effectively borrows information from external sources to improve estimation efficiency. Such external information may arise, for example, in clinical trials where an auxiliary dataset from a related population is available but may differ from the target population in certain aspects, leading to heterogeneity between populations. To address this issue, a sieve maximum likelihood estimation procedure is developed for the semiparametric probit model with interval-censored data, and a transfer learning method is proposed to leverage auxiliary information from a source domain to improve estimation efficiency in the target domain while accounting for population heterogeneity. The proposed approach is based on a penalized likelihood formulation and uses monotone splines to approximate the unknown baseline function, providing flexibility in both modeling and computation. Simulation studies show that the proposed estimator substantially improves estimation accuracy compared with methods that rely solely on the target data, particularly when the target sample size is small. An application to an Alzheimer’s disease dataset further illustrates the practical usefulness of the proposed approach in biomedical studies.

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.

Interval-censored failure-time data arise when subjects are examined or observed periodically such that the failure time of interest is not examined exactly but only known to be bracketed between two adjacent observation times. The commonly used approaches assume that the examination times and the failure time are independent or conditionally independent given covariates. In many practical applications, patients who are already in poor health or have a weak immune system before treatment usually tend to visit physicians more often after treatment than those with better health or immune system. In this situation, the visiting rate is positively correlated with the risk of failure due to the health status, which results in dependent interval-censored data. While some measurable factors affecting health status such as age, gender, and physical symptom can be included in the covariates, some health-related latent variables cannot be observed or measured. To deal with dependent interval censoring involving unobserved latent variable, we characterize the visiting/examination process as recurrent event process and propose a joint frailty model to account for the association of the failure time and visiting process. A shared gamma frailty is incorporated into the Cox model and proportional intensity model for the failure time and visiting process, respectively, in a multiplicative way. We propose a semiparametric maximum likelihood approach for estimating model parameters and show the asymptotic properties, including consistency and weak convergence. Extensive simulation studies are conducted and a data set of bladder cancer is analyzed for illustrative purposes. Copyright © 2017 John Wiley & Sons, Ltd.

ABSTRACTThis paper discusses regression analysis of clustered interval-censored failure time data, which often occur in medical follow-up studies among other areas. For such data, sometimes the failure time may be related to the cluster size, the number of subjects within each cluster or we have informative cluster sizes. For the problem, we present a within-cluster resampling method for the situation where the failure time of interest can be described by a class of linear transformation models. In addition to the establishment of the asymptotic properties of the proposed estimators of regression parameters, an extensive simulation study is conducted for the assessment of the finite sample properties of the proposed method and suggests that it works well in practical situations. An application to the example that motivated this study is also provided.

Interval-censored data arise frequently in medical studies of diseases that require periodic examinations for symptoms of interest, such as disease-free survival (DFS). This paper provides an introduction to the R package ICBayes which implements a set of programs for analyzing case 1 interval-censored data and case 2 interval-censored data under Bayesian semiparametric framework. The main function ICBayes fits commonly-used survival regression models: proportional hazards, proportional odds, and probit. A simulation study is conducted to compare the performance of the package with two R packages that fit Bayesian proportional hazards, proportional odds, and accelerated failure time models. The use of the package is illustrated through analyzing a case 2 interval-censored breast cosmesis data and a case 1 interval-censored animal tumorigenicity data.

This study aims to determine the estimation of interval-censored data with a special distribution, namely the binomial distribution. This research is using quantitative methods, the steps are estimating parameters on the interval-censored binomial distribution using the Maximum Likelihood Estimation method. The second step shows the properties of the estimator on the interval-censored binomial distribution. The last is to determine the parameter estimation of interval-censored data from the binomial distribution in survival analysis and provide an example of research containing interval-censored observations which will then be used as a case study. The results showed that the estimator is a sufficient statistic, meaning that it is unbiased. The case study was conducted using interval-censored data regarding the study of ninety-four breast cancer patients to see which group survived longer (survival value) of the two treatments, namely patients who underwent radiotherapy alone and patients who underwent radiotherapy followed by adjuvant chemotherapy.

The classical random censorship model assumes that we follow an individual continuously up to the time of failure or censoring, so observing this time as well as the indicator of its type. Under passive registration we only get information on the state of the individual at random observation or registration times. In this paper we assume that these registration times are the times of events in an independent Poisson process, stopped at failure or censoring; the time of failure is also observed if not censored. This problem turns up in historical demography, where the survival time of interest is the life‐length, censoring is by emigration, and the observation times are times of births of children, and other life‐events. (Church registers contain dates of births, marriages, deaths, but not emigrations.) The model is shown to be related to the problem of estimating a density known to be monotone. This leads to an explicit description of the non‐parametric maximum likelihood estimator of the survival function (based on i.i.d. observations from this model) and to an analysis of its large sample properties.

This thesis considers the problem of treatment comparisons when only interval-censored failure time data are available.This type of data occurs frequently in clinical trials and other follow-up studies.We study several nonparametric procedures developed previously and compare them under different situations.In particular, we study the situation where the difference between the groups occurs at an early or late time period.For this problem, we generalize the log-rank tests developed for interval-censored data in Zhao and Sun ( 2004) and the weighted log-rank test presented in Kalbfleisch (2002).Numerical studies are conducted to evaluate the proposed test and compare it with the unweighted log-rank test, which indicate that the proposed method works well.This thesis also considerers the problem of finding an appropriate sample size to achieve a desired power.We present a simple-to-use formula to find the sample size for a prespecified power and level of significance for the case of interval-censored data.Since many researchers use missing data techniques such as imputation along with right censored methods to analyze interval-censored data, we also compare an imputed Kaplan-Meier Estimate of the survival function to Turnbull's Self Consistent Estimate.We present a large numerical study to show that these estimates often disagree at late time points when the mean survival time is large.

Clustered interval-censored failure time data occur when the failure times of interest are clustered into small groups and known only to lie in certain intervals. A number of methods have been proposed for regression analysis of clustered failure time data, but most of them apply only to clustered right-censored data. In this paper, a sieve estimation procedure is proposed for fitting a Cox frailty model to clustered interval-censored failure time data. In particular, a two-step algorithm for parameter estimation is developed and the asymptotic properties of the resulting sieve maximum likelihood estimators are established. The finite sample properties of the proposed estimators are investigated through a simulation study and the method is illustrated by the data arising from a lymphatic filariasis study.

In survival analysis, estimating the failure time distribution is an important and difficult task, since usually the data is subject to censoring. Specifically, in this paper we consider current status data, a type of data where the failure time cannot be directly observed. The format of the data is such that the failure time is restricted to knowledge of whether or not the failure time exceeds a random monitoring time. We propose a flexible kernel machine approach for estimation of the failure time expectation as a function of the covariates, with current status data. In order to obtain the kernel machine decision function, we minimize a regularized version of the empirical risk with respect to a new loss function. Using finite sample bounds and novel oracle inequalities, we prove that the obtained estimator converges to the true conditional expectation for a large family of probability measures. Finally, we present a simulation study and an analysis of real-world data that compares the performance of the proposed approach to existing methods. We show empirically that our approach is comparable to current state of the art, and in some cases is even better.

A common feature of many failure time data in epidemiological studies or reliability studies is that they are simultaneously censored and truncated. Additionally, survival or reliability data could be truncated. There are also various types of truncation. For example right-truncated data occur in registers. An acquired immune deficiency syndrome (AIDS) register only contains AIDS cases which have already been reported, which generates right-truncated samples of induction times. The chapter defines a marginal non-parametric likelihood for interval-censored and interval-truncated data first introduced in B. W. Turnbull and later studied by A. Alioum and D. Commenges and C. Huber and F. Vonta in connection also to parametric and semi-parametric models. It formulates a complete non-parametric likelihood for interval-censored and interval-truncated data. The chapter discusses consistency in Hellinger distance of the density of survival or reliability under regularity conditions. It considers as the total interval of observation time the interval.

For the analysis of ultrahigh-dimensional data, the first step is often to perform screening and feature selection to effectively reduce the dimensionality while retaining all the active or relevant variables with high probability. For this, many methods have been developed under various frameworks but most of them only apply to complete data. In this paper, we consider an incomplete data situation, case II interval-censored failure time data, for which there seems to be no screening procedure. Basing on the idea of cumulative residual, a model-free or nonparametric method is developed and shown to have the sure independent screening property. In particular, the approach is shown to tend to rank the active variables above the inactive ones in terms of their association with the failure time of interest. A simulation study is conducted to demonstrate the usefulness of the proposed method and, in particular, indicates that it works well with general survival models and is capable of capturing the nonlinear covariates with interactions. Also the approach is applied to a childhood cancer survivor study that motivated thisinvestigation.

Regression analysis of interval-censored failure time data with time-dependent covariates

Partly interval-censored (PIC) data arise frequently in medical studies of diseases that require periodic examinations for symptoms of interest, such as progression-free survival and relapse-free survival. The proportional hazards (PH) model is the most widely used model in survival analysis. This paper introduces our new R package, PICBayes, which implements a set of functions for fitting the PH model to different complexities of partly interval-censored data under the Bayesian semiparametric framework. The main function of PICBayes is to fit (1) the PH model to PIC data; (2) the PH model with spatial frailty to areally-referenced PIC data; (3) the PH model with one random intercept to clustered PIC data; (4) the PH model with one random intercept and one random effect to clustered PIC data; and (5) general mixed effects PH model to clustered PIC data. We also included the corresponding functions for general interval-censored data. A random intercept or random effect can follow both a normal prior and a Dirichlet process mixture prior. The use of the package is illustrated by analyzing two real data sets.