Characteristic Estimator of Interval-Censored Binomial Data and Its Application

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.

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.

It is known that various types of location privacy attacks can be carried out using a personalized transition matrix that is learned for each target user, or a population transition matrix that is common to all target users. However, since many users disclose only a small amount of location information in their daily lives, the training data can be extremely sparse. The aim of this paper is to clarify the risk of location privacy attacks in this realistic situation. To achieve this aim, we propose a learning method that uses tensor factorization (or matrix factorization) to accurately estimate personalized transition matrices (or a population transition matrix) from a small amount of training data. To avoid the difficulty in directly factorizing the personalized transition matrices (or population transition matrix), our learning method first factorizes a transition count tensor (or matrix), whose elements are the number of transition counts that the user has made, and then normalizes counts to probabilities. We focus on a localization attack, which derives an actual location of a user at a given time instant from an obfuscated trace, and compare our learning method with the maximum likelihood (ML) estimation method in both the personalized matrix mode and the population matrix mode. The experimental results using four real data sets show that the ML estimation method performs only as well as a random guess in many cases, while our learning method significantly outperforms the ML estimation method in all of the four data sets.

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.

When analyzing censored datasets, where one or more measurements are below the limit of detection (LOD), the maximum likelihood estimation (MLE) method is often considered the gold standard for estimating the GM and GSD of the underlying exposure profile. A new and relatively simple substitution method, called β -substitution, is presented and compared with the MLE method and the common substitution methods (LOD/2 and LOD/√2 substitution) when analyzing a left-censored dataset with either single or multiple censoring points. A computer program was used to generate censored exposure datasets for various combinations of true geometric standard deviation (1.2 to 4), percent censoring (1% to 50%), and sample size (5 to 19 and 20 to 100). Each method was used to estimate four parameters of the lognormal distribution: (1) the geometric mean, GM; (2) geometric standard deviation, GSD; (3) 95th percentile, and (4) Mean for the censored datasets. When estimating the GM and GSD, the bias and root mean square error (rMSE) for the β -substitution method closely matched those for the MLE method, differing by only a small amount, which decreased with increasing sample size. When estimating the Mean and 95th percentile the β -substitution method bias results closely matched or bettered those for the MLE method. In addition, the overall imprecision, as indicated by the rMSE, was similar to that of the MLE method when estimating the GM, GSD, 95th percentile, and Mean. The bias for the common substitution methods was highly variable, depending strongly on the range of GSD values. The β-substitution method produced results comparable to the MLE method and is considerably easier to calculate, making it an attractive alternative. In terms of bias it is clearly superior to the commonly used LOD/2 and LOD/√2 substitution methods. The rMSE results for the two substitution methods were often comparable to rMSE results for the MLE method, but the substitution methods were often considerably biased.

Monotone function, such as growth function and cumulative distribution function, is often a study of interest in statistical literature. In this dissertation, we propose a nonparametric least-squares method for estimating monotone functions induced from stochastic processes in which the starting time of the process is subject to interval censoring. We apply this method to estimate the mean function of tumor growth with the data from either animal experiments or tumor screening programs to investigate tumor progression. In this type of application, the tumor onset time is observed within an interval. The proposed method can also be used to estimate the cumulative distribution function of the elapsed time between two related events in human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) studies, such as HIV transmission time between two partners and AIDS incubation time from HIV infection to AIDS onset. In these applications, both the initial event and the subsequent event are only known to occur within some intervals. Such data are called doubly interval-censored data. The common property of these stochastic processes is that the starting time of the process is subject to interval censoring. A unified two-step nonparametric estimation procedure is proposed for these problems. In the first step of this method, the nonparametric maximum likelihood estimate (NPMLE) of the cumulative distribution function for the starting time of the stochastic process is estimated with the framework of interval-censored data. In the second step, a specially designed least-squares objective function is constructed with the above NPMLE plugged in and the nonparametric least-squares estimate (NPLSE) of the mean function of tumor growth or the cumulative distribution function of the elapsed time is obtained by minimizing the aforementioned objective function. The theory of modern empirical process is applied to prove the consistency

구간중도절단은 중도절단의 가장 일반적인 개념으로 구간중도절단자료는 의학 및 역학분야의 연구에서 흔히 관찰된다. 본 연구에서는 구간중도절단의 상황에서 생존함수와 중간생존시간을 추정하는 방법으로 평균대치법과 자기일치법을 비교 연구하고, 실제 자료로 혈우병환자에서 선천성면역결핍바이러스 감염시점을 추정하였다. 또한 구간중도절단자료를 생성하는 새로운 방법을 제시하였으며, 생성된 구간중도절단자료를 이용한 모의실험을 통하여 두 추정치에 대한 다양한 비교연구를 시행하였다. 구간중도절단자료에서 생존함수와 중간생존시간을 추정할 경우 중도절단율이 크지 않다면 평균대치법이 자기일치법보다 더 우수한 추정치로 판명되었다. Interval-censored observations are common in medical and epidemiologic studies; however, limited studies exist due to the complexity and special structure of interval-censoring. This paper introduces the imputation method and the self consistency method in the interval-censored data. We propose a new method of generating random numbers under an interval-censoring set-up. Through simulation studies we compare two methods under various simulation schemes in the sense of the mean squared error for estimating the median survival time and the mean integrated squared error for estimating the survival function. Under a moderate censoring percentage, the mean imputation method showed a better performance than the self-consistency method in estimating the median survival time and the survival function.

Travel Time Reliability Estimation Model Using Observed Link Flows in a Road Network

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.

In weak GNSS signal environments, extending integration time is paramount to improving the GNSS receiver's sensitivity. Furthermore, sufficient coherent integration can help to separate the line-of-sight (LOS) and non LOS (NLOS) signals — primarily in the Doppler domain — for multipath mitigation. However, extending integration time is limited by the presence of the navigation message data bits. The Maximum-Likelihood (ML) estimation method has been shown as the most effective way to estimate the navigation bit boundary locations (i.e., bit synchronization) and subsequently estimate the data bit values (i.e., bit decoding) in the presence of noise alone. This paper further analyzes the performance of ML estimation method as a function of various other parameters by using the successful synchronization rate (SSR) and successful decoding rate (SDR) as the criteria. The parameters considered include the number of data bits required (i.e., integration time) and the Doppler frequency error, and both are evaluated under different signal strength scenarios. The requirements for bit synchronization are analyzed under three SSRs, which are 85%, 90% and 95%. Results indicate that, under the SSR of 90% and the SDR of 90%, bit synchronization and bit decoding are valid for signal strengths of 15 dB-Hz and 20 dB-Hz respectively, and the Doppler frequency errors should not be larger than 24 Hz and 11 Hz respectively.

Recent catastrophic failures of the rocket motor on a US missile caused concern in the US Navy that the missile might not be serviceable past its estimated service life of 20 years. This paper analyzes nearly 2000 firings of the motor under field conditions using classical maximum likelihood estimation (MLE) methods and Bayesian methods. MLE methods indicate that there could be less than a 1% chance that the motor will survive past 20 years of life and are not considered credible. Bayesian methods indicate that there is better than a 99% chance that the motors will survive past 20 years of life. The authors present reasons for preferring the Bayesian analysis and discuss testing schemes for more precise estimates. They comment on the lack of data to perform degradation analysis as a function of temperature cycling for the motor and make recommendations for future missile system data collection.

The statistical problem considered in this article is the parametric treatment comparison when partly interval-censored failure time data exist. Partly interval-censored failure time data are composed of exact observations and interval-censored observations. This phenomenon often occurs in clinical trials and health studies that require periodic following up with patients. The authors constructed a score test and likelihood ratio test for this type of failure time data under Weibull distributions using multiple imputation technique. A simulation study and a modified secondary data set from breast cancer study are used to assess the proposed test and illustrate the differences between the two tests. The results indicate that the presented procedure works well for both tests, but the likelihood ratio test is better than the score test in certain situations.

Survival analysis methods make better use of temporal information, accommodate multiple levels of explanatory variables, and are meant to deal with interval-censored data. In a context of harvest modeling, this approach could improve some known limitations. In this study, we used data from a network of permanent plots in the province of Quebec, Canada, as a real-world case study. We tested the potential of survival analysis to predict plot-level harvest probabilities from plot- and regional-level variables. The approach also included random effects to account for spatial correlations. The results showed the potential of survival analysis to provide annual predictions of harvest occurrence. Both regional and time-varying variables, as well as spatial patterns, had important effects on the probability of a plot to be harvested. Respectively, reductions in the annual allowable cut volumes led to a decrease in the harvest probabilities. Greater harvest probabilities were associated with the broadleaved dynamics class and higher values of basal area. In contrast, they were decreased by stem density and slope classes. The spatial random effect resulted in an improvement of the model fit. Our plot-level model improved some limitations reported in previous studies by taking the effect of a time-varying regional variable into account.

Population density is an important state variable in ecology and monitoring of wildlife populations. In the study of large carnivores, traditional density estimation methods have relied on camera trapping to collect capture–recapture data using sampling designs suited to a single target species and ad hoc methods to calculate the effective trapping area. We describe an application of spatially explicit capture–recapture analysis to estimate density for four sympatric carnivore species using a standard spatial sampling grid, camera trap sampling, and maximum-likelihood estimation methods. We used camera traps deployed in four adjacent, sequential camera arrays to construct capture histories for leopard, aardwolf, spotted hyena, and striped hyena in an African savanna/scrub ecosystem. We considered two methods of constructing trapping histories: (1) a simultaneous layout in which all cameras are deployed and active for 21 trapping intervals of 24 h each; and (2) an incomplete layout in which cameras are considered deployed for 84 sampling intervals, but with only a fraction of traps active for a given sampling interval. We estimated density and confidence or profile likelihood intervals for each species using a mean maximum distance moved method and maximum-likelihood estimation procedures with model averaging. Maximum-likelihood densities ranged from 4.93/100 km2 for spotted hyena to 12.03/100 km2 for leopard. Estimates did not differ between simultaneous and incomplete trap layouts. Our approach demonstrates the utility and cost effectiveness of using maximum-likelihood density estimation methods in studies of sympatric species that are individually recognizable.