Indiana University-Purdue University Indianapolis (IUPUI) / Context. Prediction models for dementia are crucial for informing clinical decision making in older adults. Previous models have used genotype and age to obtain risk scores to determine risk of Alzheimer’s Disease, one of the most common forms of dementia (Desikan et al., 2017). However, previous prediction models do not account for the fact that the time to dementia onset is unknown, lying between the last negative and the first positive dementia diagnosis time (interval censoring). Instead, these models use time to diagnosis, which is greater than or equal to the true dementia onset time. Furthermore, these models do not account for the competing risk of death which is quite frequent among elder adults. Objectives. To develop a prediction model for dementia that accounts for interval censoring and the competing risk of death. To compare the predictions from this model with the predictions from a naïve analysis that ignores interval censoring and the competing risk of death. Methods. We apply the semiparametric sieve maximum likelihood (SML) approach to simultaneously model the cumulative incidence function (CIF) of dementia and death while accounting for interval censoring (Bakoyannis, Yu, & Yiannoutsos, 2017). The SML is implemented using the R package intccr. The CIF curves of dementia are compared for the SML and the naïve approach using a dataset from the Indianapolis Ibadan Dementia Project. Results. The CIF from the SML and the naïve approach illustrated that for healthier individuals at baseline, the naïve approach underestimated the incidence of dementia compared to the SML, as a result of interval censoring. Individuals with a poorer health condition at baseline have a CIF that appears to be overestimated in the naïve approach. This is due to older individuals with poor health conditions having an elevated risk of death. Conclusions. The SML method that accounts for the competing risk of death along with interval censoring should be used for fitting prediction/prognostic models of dementia to inform clinical decision making in older adults. Without controlling for the competing risk of death and interval censoring, the current models can provide invalid predictions of the CIF of dementia.

No description available.

The serial interval (SI), defined as the symptom time between an infector and an infectee, is widely used to better understand transmission patterns of an infectious disease. Estimating the SI for tuberculosis (TB) is complicated by the slow progression from asymptomatic infection to active, symptomatic disease, and the fact that there is only a 5-10% lifetime risk of developing active TB disease. Furthermore, the time of symptom onset for infectors and infectees is rarely observed accurately. In this dissertation, we first conduct a systematic literature review to demonstrate the limited methods currently available to estimate the serial interval for TB as well as the few estimates that have been published. Secondly, under the assumption of an ideal scenario where all SIs are observed with precision, we evaluate the effect of prior information on estimating the SI in a Bayesian framework. Thirdly, we apply cure models, proposed by Boag in 1949, to estimate the SI for TB in a Bayesian framework. We show that the cure models perform better in the presence of credible prior information on the proportion of the study population that develop active TB disease, and should be chosen over traditional survival models which assume that all of the study population will eventually have the event of interest—active TB disease. Next, we modify the method by Reich et al. in 2009 by using a Riemann sum to approximate the likelihood function that involves a double integral. In doing so, we are able to reduce the computing time of the approximation method by around 50%. We are also able to relax the assumption of uniformity on the censoring intervals. We show that when using weights that are consistent with the underlying skewness of the intervals, the proposed approaches consistently produce more accurate estimates than the existing approaches. We provide SI estimates for TB using empirical datasets from Brazil and USA/Canada.

Indiana University-Purdue University Indianapolis (IUPUI) / In many longitudinal studies, the time scales upon which we assess the primary outcomes are anchored by pre-specified events. However, these anchoring events are often not observable and they are randomly distributed with unknown distribution. Without direct observations of the anchoring events, the time scale used for analysis are not available, and analysts will not be able to use the traditional longitudinal models to describe the temporal changes as desired. Existing methods often make either ad hoc or strong assumptions on the anchoring events, which are unveri able and prone to biased estimation and invalid inference. Although not able to directly observe, researchers can often ascertain an interval that includes the unobserved anchoring events, i.e., the anchoring events are interval censored. In this research, we proposed a two-stage method to fit commonly used longitudinal models with interval censored anchoring events. In the first stage, we obtain an estimate of the anchoring events distribution by nonparametric method using the interval censored data; in the second stage, we obtain the parameter estimates as stochastic functionals of the estimated distribution. The construction of the stochastic functional depends on model settings. In this research, we considered two types of models. The first model was a distribution-free model, in which no parametric assumption was made on the distribution of the error term. The second model was likelihood based, which extended the classic mixed-effects models to the situation that the origin of the time scale for analysis was interval censored. For the purpose of large-sample statistical inference in both models, we studied the asymptotic properties of the proposed functional estimator using empirical process theory. Theoretically, our method provided a general approach to study semiparametric maximum pseudo-likelihood estimators in similar data situations. Finite sample performance of the proposed method were examined through simulation study. Algorithmically eff- cient algorithms for computing the parameter estimates were provided. We applied the proposed method to a real data analysis and obtained new findings that were incapable using traditional mixed-effects models. / 2 years

Continuous-time multi-state models are widely used in modeling longitudinal data of disease processes with multiple transient states, yet the analysis is complex when subjects are observed periodically, resulting in interval censored data. Recently, most studies focused on modeling the true disease progression as a discrete time stationary Markov chain, and only a few studies have been carried out regarding non-homogenous multi-state models in the presence of interval-censored data. In this dissertation, several likelihood-based methodologies were proposed to deal with interval censored data in multi-state models. Firstly, a continuous time version of a homogenous Markov multi-state model with backward transitions was proposed to handle uneven follow-up assessments or skipped visits, resulting in the interval censored data. Simulations were used to compare the performance of the proposed model with the traditional discrete time stationary Markov chain under different types of observation schemes. We applied these two methods to the well-known Nun study, a longitudinal study of 672 participants aged ≥ 75 years at baseline and followed longitudinally with up to ten cognitive assessments per participant. Secondly, we constructed a non-homogenous Markov model for this type of panel data. The baseline intensity was assumed to be Weibull distributed to accommodate the non-homogenous property. The proportional hazards method was used to incorporate risk factors into the transition intensities. Simulation studies showed that the Weibull assumption does not affect the accuracy of the parameter estimates for the risk factors. We applied our model to data from the BRAiNS study, a longitudinal cohort of 531 subjects each cognitively intact at baseline. Last, we presented a parametric method of fitting semi-Markov models based on Weibull transition intensities with interval censored cognitive data with death as a competing risk. We relaxed the Markov assumption and took interval censoring into account by integrating out all possible unobserved transitions. The proposed model also allowed for incorporating time-dependent covariates. We provided a goodness-of-fit assessment for the proposed model by the means of prevalence counts. To illustrate the methods, we applied our model to the BRAiNS study.

Consideramos um modelo de regressão linear simples, em que tanto a variável resposta como a independente estão sujeitas a censura intervalar. Como motivação utilizamos um estudo em que o objetivo é avaliar a possibilidade de previsão dos resultados de um exame audiológico comportamental a partir dos resultados de um exame audiológico eletrofisiológico. Calculamos intervalos de previsão para a variável resposta, analisamos o comportamento dos estimadores de máxima verossimilhança obtidos sob o modelo proposto e comparamos seu desempenho com aquele de estimadores obtidos de um modelo de regressão linear simples usual, no qual a censura dos dados é desconsiderada. / We consider a simple linear regression model in which both variables are interval censored. To motivate the problem we use data from an audiometric study designed to evaluate the possibility of prediction of behavioral thresholds from physiological thresholds. We develop prediction intervals for the response variable, obtain the maximum likelihood estimators of the proposed model and compare their performance with that of estimators obtained under ordinary linear regression models.

Being able to explore a relationship between two life events is of great interest to scientists from different disciplines. Some issues of particular concern are, for example, the connection between smoking cessation and pregnancy (Thompson and Pantoja-Galicia 2003), the interrelation between entry into marriage for individuals in a consensual union and first pregnancy (Blossfeld and Mills 2003), and the association between job loss and divorce (Charles and Stephens 2004, Huang 2003 and Yeung and Hofferth 1998). Establishing causation in observational studies is seldom possible. Nevertheless, if one of two events tends to precede the other closely in time, a causal interpretation of an association between these events can be more plausible. The role of longitudinal surveys is crucial, then, since they allow sequences of events for individuals to be observed. Thompson and Pantoja-Galicia (2003) discuss in this context several notions of temporal association and ordering, and propose an approach to investigate a possible relationship between two lifetime events. In longitudinal surveys individuals might be asked questions of particular interest about two specific lifetime events. Therefore the joint distribution might be advantageous for answering questions of particular importance. In follow-up studies, however, it is possible that interval censored data may arise due to several reasons. For example, actual dates of events might not have been recorded, or are missing, for a subset of (or all) the sampled population, and can be established only to within specified intervals. Along with the notions of temporal association and ordering, Thompson and Pantoja-Galicia (2003) also discuss the concept of one type of event "triggering" another. In addition they outline the construction of tests for these temporal relationships. The aim of this thesis is to implement some of these notions using interval censored data from longitudinal complex surveys. Therefore, we present some proposed tools that may be used for this purpose. This dissertation is divided in five chapters, the first chapter presents a notion of a temporal relationship along with a formal nonparametric test. The mechanisms of right censoring, interval censoring and left truncation are also overviewed. Issues on complex surveys designs are discussed at the end of this chapter. For the remaining chapters of the thesis, we note that the corresponding formal nonparametric test requires estimation of a joint density, therefore in the second chapter a nonparametric approach for bivariate density estimation with interval censored survey data is provided. The third chapter is devoted to model shorter term triggering using complex survey bivariate data. The semiparametric models in Chapter 3 consider both noncensoring and interval censoring situations. The fourth chapter presents some applications using data from the National Population Health Survey and the Survey of Labour and Income Dynamics from Statistics Canada. An overall discussion is included in the fifth chapter and topics for future research are also addressed in this last chapter.

Being able to explore a relationship between two life events is of great interest to scientists from different disciplines. Some issues of particular concern are, for example, the connection between smoking cessation and pregnancy (Thompson and Pantoja-Galicia 2003), the interrelation between entry into marriage for individuals in a consensual union and first pregnancy (Blossfeld and Mills 2003), and the association between job loss and divorce (Charles and Stephens 2004, Huang 2003 and Yeung and Hofferth 1998). Establishing causation in observational studies is seldom possible. Nevertheless, if one of two events tends to precede the other closely in time, a causal interpretation of an association between these events can be more plausible. The role of longitudinal surveys is crucial, then, since they allow sequences of events for individuals to be observed. Thompson and Pantoja-Galicia (2003) discuss in this context several notions of temporal association and ordering, and propose an approach to investigate a possible relationship between two lifetime events. In longitudinal surveys individuals might be asked questions of particular interest about two specific lifetime events. Therefore the joint distribution might be advantageous for answering questions of particular importance. In follow-up studies, however, it is possible that interval censored data may arise due to several reasons. For example, actual dates of events might not have been recorded, or are missing, for a subset of (or all) the sampled population, and can be established only to within specified intervals. Along with the notions of temporal association and ordering, Thompson and Pantoja-Galicia (2003) also discuss the concept of one type of event "triggering" another. In addition they outline the construction of tests for these temporal relationships. The aim of this thesis is to implement some of these notions using interval censored data from longitudinal complex surveys. Therefore, we present some proposed tools that may be used for this purpose. This dissertation is divided in five chapters, the first chapter presents a notion of a temporal relationship along with a formal nonparametric test. The mechanisms of right censoring, interval censoring and left truncation are also overviewed. Issues on complex surveys designs are discussed at the end of this chapter. For the remaining chapters of the thesis, we note that the corresponding formal nonparametric test requires estimation of a joint density, therefore in the second chapter a nonparametric approach for bivariate density estimation with interval censored survey data is provided. The third chapter is devoted to model shorter term triggering using complex survey bivariate data. The semiparametric models in Chapter 3 consider both noncensoring and interval censoring situations. The fourth chapter presents some applications using data from the National Population Health Survey and the Survey of Labour and Income Dynamics from Statistics Canada. An overall discussion is included in the fifth chapter and topics for future research are also addressed in this last chapter.

Use of progression-free survival in the evaluation of clinical interventions is hampered by a variety of issues, including censoring patterns not addressed in the usual methods for survival analysis. Progression can be right-censored before survival or interval-censored between inspection times. Current practice calls for imputing events to their time of detection. Such an approach is prone to bias, underestimates standard errors and makes inefficient use of the data at hand. Moreover a composite outcome prevents inference about the actual treatment effect on the risk of progression. This thesis develops semiparametric and sieve maximum likelihood estimators to more formally analyze progression-related endpoints. For the special case where death rarely precedes progression, a Cox-Aalen model is proposed for regression analysis of time-to-progression under intermittent inspection. The general setting considering both progression and survival is examined with a Markov Cox-type illness-death model under various censoring schemes. All of the resulting estimators globally converge to the truth slower than the parametric rate, but their finite-dimensional components are asymptotically efficient. Numerical studies suggest that the new methods perform better than their imputation-based alternatives under moderate to large samples having higher rates of censoring.

Consideramos um modelo de regressão linear simples, em que tanto a variável resposta como a independente estão sujeitas a censura intervalar. Como motivação utilizamos um estudo em que o objetivo é avaliar a possibilidade de previsão dos resultados de um exame audiológico comportamental a partir dos resultados de um exame audiológico eletrofisiológico. Calculamos intervalos de previsão para a variável resposta, analisamos o comportamento dos estimadores de máxima verossimilhança obtidos sob o modelo proposto e comparamos seu desempenho com aquele de estimadores obtidos de um modelo de regressão linear simples usual, no qual a censura dos dados é desconsiderada. / We consider a simple linear regression model in which both variables are interval censored. To motivate the problem we use data from an audiometric study designed to evaluate the possibility of prediction of behavioral thresholds from physiological thresholds. We develop prediction intervals for the response variable, obtain the maximum likelihood estimators of the proposed model and compare their performance with that of estimators obtained under ordinary linear regression models.