Semiparametric regression analysis of failure time data with dependent interval censoring.

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 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.

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.

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.

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.

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.

Bayesian estimation of parameters for the bivariate Gompertz regression model with shared gamma frailty under random censoring

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.

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.

Interval-censored data is a common type of failure time data in survival analysis. However, in practice, there is often a dependent relationship between the failure time and the observation time, and ignoring this dependency can lead to biased inferences. To address this issue, this study describes the dependent relationship between the failure time and the observation time using the copula model and establishes a copula-based joint model. Existing research on dependent censored data has focused on cases where covariate effects take relatively simple forms, however, in practical studies, it has been observed that the effects of covariates are more complex. Consequently, this study assumes that the failure time follows an additive-multiplicative hazards model, which includes covariates with multiplicative effects as well as covariates with additive effects, providing greater flexibility. Additionally, we propose a penalized sieve maximum likelihood estimation method. Furthermore, a Newton Multiple Iteration (Newton-MI) algorithm, adept at handling parameter non-negativity constraints, is employed to estimate the model parameters. Extensive simulations validate the proposed method's favorable statistical properties. Finally, we apply the proposed model and methods to a tumor dataset.

Continuing symptoms and poor health following cancer treatments may alter meaning in life for cancer survivors. Gynecologic cancer survivors are particularly troubled with physical sequelae. In addition, for the most common sites of disease, such as breast and gynecologic cancers, the prevalence of depression is also high. This study tests meaning in life as a mechanism for the relationship between physical symptoms and depressive symptoms. Gynecologic cancer survivors (N = 260) participated. Measures of physical sequelae (nurse rated symptoms/signs, patient-reported gynecologic symptoms), meaning in life (harmony, life purpose, spirituality, and conversely, confusion and loss), and depressive symptoms were obtained at the time of a routine clinical follow-up visit 2-10 years following the completion of treatment. Latent variables were defined, and structural equation modeling tested a mediator model. Analyses support partial mediation. That is, survivors with more physical sequelae also reported lower levels of meaning in life, which was associated with higher levels of depressive symptoms. Gynecologic cancer patients have been neglected in psychosocial research, and findings highlight the importance of existential issues in their lives. While many adjust well, those with persistent physical functioning deficits may experience depressive symptoms. By appreciating the role of meaning in their experience, we may help survivors foster their own growth and perspectives important for their future.

Long-Term Outcome of Myelodysplastic Syndromes (MDS) Patients Treated with Erythropoiesis Stimulating Agents (ESAs)

Panel count data and interval-censored data are two types of incomplete data that often occur in event history studies. Almost all existing statistical methods are developed for their separate analysis. In this paper, we investigate a more general situation where a recurrent event process and an interval-censored failure event occur together. To intuitively and clearly explain the relationship between the recurrent current process and failure event, we propose a failure time-dependent mean model through a completely unspecified link function. To overcome the challenges arising from the blending of nonparametric components and parametric regression coefficients, we develop a two-stage conditional expected likelihood-based estimation procedure. We establish the consistency, the convergence rate and the asymptotic normality of the proposed two-stage estimator. Furthermore, we construct a class of two-sample tests for comparison of mean functions from different groups. The proposed methods are evaluated by extensive simulation studies and are illustrated with the skin cancer data that motivated this study.

Functional and Mental Health Outcomes of the Joint Effects of Spousal Health: The Potential Threats of “Concordant Frailty”

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.