Inference on conditional quantile residual life for censored survival data

For randomly censored data, the residual life function at a given time determines a life distribution of a subject survived up to that time point. In the situation where the data are censored, or where the underlying distribution is skewed, the quantile residual life function is preferred. A number of studies regarding the quantile residual lifetime have been conducted in the univariate settings by many professionals. However, when a pair of units are observed, i.e. a study of twins, or when patients experience two types of events, i.e. time to morbidity and time to mortality, a bivariate modelling of quantile residual lifetime subject to right censoring might be of utmost interest. In this dissertation, we develop the estimation of conditional quantile residual lifetime on semi-competing risks data. The proposed estimator is conditioning on the occurrence of the nonterminal event beyond time t. The covariate effects on specifc pairs of failure times are evaluated based on a log-linear regression on conditional quantile residual lifetime for semi-competing risks data. Numerical studies demonstrate a reasonable performance of the estimator for moderate sample sizes. The proposed method is applied to a study of breast cancer data from a phase III clinical trial. Public Health Significance: In many survival studies, bivariate correlated failure times can be observed in a pair or in the same individual experiencing multiple failure times. It is of interest to know the additional time to failure of a surviving unit, when another unit is known to have failed at an earlier time. In this dissertation, the proposed estimator of the residual lifetime given the occurrence of a failure demonstrates the importance of lifetime expectancy that patients and their family seek to know before an onset of a new treatment

The bootstrap -A review

The bootstrap, extensively studied during the last decade, has become a powerful tool in different areas of Statistical Inference. In this work, we present the main ideas of bootstrap methodology in several contexts, citing the most relevant contributions and illustrating with examples and simulation studies some interesting aspects

SEMIPARAMETRIC BIVARIATE QUANTILE-QUANTILE REGRESSION FOR ANALYZING SEMI-COMPETING RISKS DATA

In this paper, we consider estimation of the effect of a randomized treatment on time to disease progression and death, possibly adjusting for high-dimensional baseline prognostic factors. We assume that patients may or may not have a specific type of disease progression prior to death and those who have this endpoint are followed for their survival information. Progression and survival may also be censored due to loss to follow-up or study termination. We posit a semi-parametric bivariate quantile-quantile regression failure time model and show how to construct estimators of the regression parameters. The causal interpretation of the parameters depends on non-identifiable assumptions. We discuss two assumptions: the first applies to situations where it is reasonable to view disease progression as well defined after death and the second applies to situations where such a view is unreasonable. We conduct a simulation study and analyze data from a randomized trial for the treatment of brain cancer

Precautionary Motives and Portfolio Decisions

Theory predicts that under certain restrictions on preferences prudent consumers will allocate relatively more funds to riskless assets when there is uninsurable background risk. This paper analyzes empirically the relevance of precautionary motives for the structure of household wealth. To this end, a new and rich data source from the Netherlands is exploited. The question of primary concern is: what impact, if any, does the presence of income uncertainty have on the structure of Dutch households' portfolios? We employ various semi{parametric estimators, both for cross{sections and for panel data to assess the response of households' portfolios to uninsurable background risk. We find some, but not unanimous support for the view that portfolios become less risky as income uncertainty increases.precautionary saving;background risk;household saving;portfolio choice;application of LDV models

Empirical Likelihood Quantile Regression for Right-Censored Data

Quantile estimation of time-to-event data plays a key role in many medical applications, especially conditional on covariates of interest. In such settings, bias due to model misspecification is an important concern. As such, Empirical Likelihood (EL) is a particularly attractive estimation approach, making minimal parametric modeling assumptions without unduly compromising statistical efficiency. However, observed survival times are typically subject to right-censoring, in which case most EL approaches cannot be applied directly. In this thesis, we revisit a widely-applicable Expectation-Maximization (EM) algorithm for right-censored EL. As the covariate-free EL function becomes discontinuous in the conditional setting, we propose a continuity correction for which the computational properties of EM are retained. Several approaches to obtaining confidence intervals are explored. We provide an implementation of our method and related algorithms in the R package flexEL. The source code is written in C++ for high computational performance, and a straightforward interface allows users to fit arbitrary EL models with little programming effort

Empirical Likelihood Inferences in Survival Analysis

In survival analysis, different regression models are used to estimate the effects of covariates on the survival time. The proportional hazards model is commonly applied. However, the proportional hazards model does not always give good fit in the real life. Other models, such as proportional odds models, additive hazards models are useful alternative. Motivated by this limitation, we investigate empirical likelihood method and make inference for semiparametric transformation models and accelerated failure time models in this dissertation. The proposed empirical likelihood methods can solve several challenging and open problems. These interesting problems include semiparametirc transformation model with length-biased sampling, semiparametric analysis based on weighted estimating equations with missing covariates. In addition, a more computationally efficient method called jackknife empirical likelihood (JEL) is proposed, which can be applied to make statistical inference for the accelerated failure time model without computing the limiting variance. We show that under certain regularity conditions, the empirical log-likelihood ratio test statistic converges to a standard chi-squared distribution. Finally, computational algorithms are developed for utilizing the proposed empirical likelihood and jackknife empirical likelihood methods. Extensive simulation studies on coverage probabilities and average lengths of confidence intervals for the regression parameters for those topics indicate good finite samples performance under various settings. Furthermore, for each model, real data sets are analyzed for illustration of the proposed methods