Nonparametric analysis of interval-censored failure time data

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 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.

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.

It has attracted a great deal of interest in randomized survival studies to assess the causal treatment effect under non-compliance with time-to-event outcomes. In this paper, the problem when one faces case–cohort studies for which covariates are usually too expensive to be measured or obtained for the full cohort and also the disease rate is generally low is considered. Furthermore, only interval-censored data may be available for the failure event of interest, a situation for which there does not seem to exist an established estimation procedure. To address the problem, a sieve inverse probability weighting estimation procedure is proposed, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is conducted to evaluate the finite sample performance of the proposed approach and suggests that it works well in practice. In addition, the method is applied to a breast cancer screening study.

<abstract><p>Interval-censored failure time data as a general type of survival data often arises in medicine and other applied fields. Survival tree is a flexible predictive method for survival data because no specific assumptions are required.</p> <p>Generalized Log-Rank Test have good power with parameters for interval-censored failure time data. We construct a special test statistic of Generalized Log-Rank Tests, and propose a new survival tree with hyper-parameter by combining the test statistic with Conditional Inference Framework for interval-censored failure time data. The effect of tuning hyper-parameter are discussed and hyper-parameter tuning allows the tree method to be more general and flexible. Thus the tree method either improve upon or remain competitive with existing tree method for interval-censored failure time data-ICtree, which is a special case of ours. An extensive simulation is executed to assess the predictive performance of our tree methods. Finally, the tree methods are applied to a tooth emergence data.</p></abstract>

Several tests for comparing k groups of interval-censored data based on Turnbull's estimator of a survival function are compared by a Monte Carlo simulation study. The tests under consideration include the IWD test proposed by Petroni and Wolfe, the score test derived by Finkelstein, and a logrank type test suggested by Sun. With a large sample size and in a two-sample comparison, simulation results suggest that the IWD test is applicable for early and crossing hazard difference alternatives, whereas Finkelstein's score test, Sun's test and the logrank test are slightly more powerful than the IWD tests under late hazard difference alternatives. The IWD test is designed for the two-sample testing problem. With a large sample size and in a k-sample comparison, Finkelstein's score test is slightly better than the other tests under a proportional hazards model, while Sun's test and the logrank test are slightly better than the score test under early and crossing hazard difference alternatives. However, none of the test statistics is uniformly better than the others for the alternatives considered in this paper with both non-overlapping and overlapping interval-censored data.

We propose a two-stage outcome-dependent sampling design and inference procedure for studies that concern interval-censored failure time outcomes. This design enhances the study efficiency by allowing the selection probabilities of the second-stage sample, for which the expensive exposure variable is ascertained, to depend on the first-stage observed interval-censored failure time outcomes. In particular, the second-stage sample is enriched by selectively including subjects who are known or observed to experience the failure at an early or late time. We develop a sieve semiparametric maximum pseudo likelihood procedure that makes use of all available data from the proposed two-stage design. The resulting regression parameter estimator is shown to be consistent and asymptotically normal, and a consistent estimator for its asymptotic variance is derived. Simulation results demonstrate that the proposed design and inference procedure performs well in practical situations and is more efficient than the existing designs and methods. An application to a phase 3 HIV vaccine trial is provided.

This paper discusses the fitting of the proportional hazards model to interval-censored failure time data with missing covariates. Many authors have discussed the problem when complete covariate information is available or the missing is completely at random. In contrast to this, we will focus on the situation where the missing is at random. For the problem, a sieve maximum likelihood estimation approach is proposed with the use of I-spline functions to approximate the unknown cumulative baseline hazard function in the model. For the implementation of the proposed method, we develop an EM algorithm based on a two-stage data augmentation. Furthermore, we show that the proposed estimators of regression parameters are consistent and asymptotically normal. The proposed approach is then applied to a set of the data concerning Alzheimer Disease that motivated this study.

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

NK Cells Display Poor Anti Lymphoma and AML Function At Early Times Following Allogenic HLA-Identical SCT for Leukemia and Lymphomas.

. Several non-parametric test procedures have been proposed for incomplete survival data: interval-censored failure time data. However, most of them have unknown asymptotic properties with heuristically derived and/or complicated variance estimation. This article presents a class of generalized log-rank tests for this type of survival data and establishes their asymptotics. The methods are evaluated using simulation studies and illustrated by a set of real data from a cancer study.

In this study, we extended a two-parameter bathtub hazard model that exhibits either an increasing or a bathtub-shaped failure rate depending on its shape parameter. The model was expanded to include covariates in the presence of right- and interval-censored data. To handle interval-censored data, we employed two imputation techniques: midpoint and random imputation. A simulation study was conducted to evaluate and compare the performance of these imputation methods using standard error (SE) and root mean square error (RMSE) values. The findings indicated that random imputation outperforms midpoint imputation in most instances, achieving lower SE and RMSE across different censoring proportions and sample sizes. To demonstrate the practical applicability of the extended model, a real dataset on the occurrence of oral lesions in children after liver transplantation was used for illustrative purposes.

The research explores several imputation techniques, namely left, right, midpoint and random imputations for the MLE of the Weibull regression model with covariate for uncensored, right, and interval-censored data. A simulation study is conducted to obtain the parameter estimates of the model with different imputation techniques, sample sizes, and censoring proportions and its performance are evaluated using bias, standard error (SE), and root mean square error (RMSE). The simulation result indicates that midpoint imputation technique outperformed other techniques based on the lowest RMSE values. Finally, the model was fit to diabetic nephropathy data were fitted to the model using selected imputation techniques. The result concluded that the Weibull regression model may provide a good fit to the data and that the covariate, gender has a significant effect on the survival time of patient kidneys.

We show that under reasonable conditions the nonparametric maximum likelihood estimate (NPMLE) of the distribution function from left-truncated and case 1 interval-censored data is inconsistent, in contrast to the consistency properties of the NPMLE from only left-truncated data or only interval-censored data. However, the conditional NPMLE is shown to be consistent. Numerical examples are provided to illustrate their finite sample properties.

PASS is the Power Analysis and Sample Size program. It analyzes t-tests (one mean; two means), F-tests of several means, chi-square tests (goodness of fit; contingency table), tests of proportions (one; two), log-rank survival tests, correlations (single; two correlations), ANOVA (fixed effects; randomized block; repeated measures), log-rank tests, regression (multiple; logistic), and bioequiva- lence procedures. It then produces AScii and graphics files reporting power levels. It can also be used for determination of needed sample size to achieve a given power level with a given procedure. Rank- and-file social scientists who merely want to estimate sample size during the design process will find PASS too sophisticated and non- user-friendly for their needs. Methodologists who understand power analysis, however, will find PAss an extremely useful and effective tool.