This book collects and unifies statistical models and methods that have been proposed for analyzing interval-censored failure time data. It provides the first comprehensive coverage of the topic of interval-censored data and complements the books on right-censored data. The focus of the book is on nonparametric and semiparametric inferences, but it also describes parametric and imputation approaches. This book provides an up-to-date reference for people who are conducting research on the analysis of interval-censored failure time data as well as for those who need to analyze interval-censored data to answer substantive questions.

Cost-effectiveness analysis is widely conducted in the economic evaluation of new treatments, due to skyrocketing health care costs and limited resource available. Censored costs data poses a unique problem for cost estimation due to "induced informative censoring" problem. Thus, many standard approaches for survival analysis are not valid for the analysis of cost data. We first derive the confidence interval for the incremental cost-effectiveness ratio for a special case, when terminating events are different for survival time and costs. Then we study how to intuitively explain some existing estimators for costs, based on the generalized redistribute-to-the-right algorithm. Motivated by that idea, we also propose two improved survival estimators of costs, based on generalized redistribute-to-the-right algorithm and kernel method. We first consider one special situation in conducting cost-effectiveness analysis, when the terminating events for survival time and costs are different. Traditional methods for statistical inference cannot deal with such data. We propose a new method for deriving the confidence interval for the incremental cost-effectiveness ratio under this situation, based on the counting process theory and the general theory for missing data process. The simulation studies and real data example show that our method performs very well for some practical settings. In addition, we provide intuitive explanation to a mean cost estimator and a survival estimator for costs, based on generalized redistribute-to-the-right algorithm. Since those estimators are derived based on the inverse probability weighting principle and semiparametric efficiency theory, it is not always easy to understand how these methods work. Therefore, our work engenders a better understanding of those theoretically derived cost estimators. Motivated by the idea of generalized redistribute-to-the-right algorithm, we propose an estimator for the survival function of costs. The proposed estimator is naturally monotone, more efficient than some existing survival estimators, and has a quite small bias in many realistic settings. We further propose a kernel-based survival estimator for costs. The latter estimator, which is asymptotically unbiased, overcomes the deficiency of the former estimator, while preserving the nice properties. Our proposed estimators outperform existing estimators under various scenarios in simulation and real data example. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155096

Missing data pose challenges to real-life data analysis. Simple ad-hoc fixes, like deletion or mean imputation, only work under highly restrictive conditions, which are often not met in practice. Multiple imputation replaces each missing value by multiple plausible values. The variability between these replacements reflects our ignorance of the true (but missing) value. Each of the completed data set is then analyzed by standard methods, and the results are pooled to obtain unbiased estimates with correct confidence intervals. Multiple imputation is a general approach that also inspires novel solutions to old problems by reformulating the task at hand as a missing-data problem. This is the second edition of a popular book on multiple imputation, focused on explaining the application of methods through detailed worked examples using the MICE package as developed by the author. This new edition incorporates the recent developments in this fast-moving field. This class-tested book avoids mathematical and technical details as much as possible: formulas are accompanied by verbal statements that explain the formula in accessible terms. The book sharpens the reader’s intuition on how to think about missing data, and provides all the tools needed to execute a well-grounded quantitative analysis in the presence of missing data.

Cost-effectiveness analysis is widely conducted in the economic evaluation of new treatment options. In many clinical and observational studies of costs, data are often censored. Censoring brings challenges to both medical cost estimation and cost-effectiveness analysis. Although methods have been proposed for estimating the mean costs with censored data, they are often derived from theory and it is not always easy to understand how these methods work. We provide an alternative method for estimating the mean cost more efficiently based on a replace-from-the-right algorithm, and show that this estimator is equivalent to an existing estimator based on the inverse probability weighting principle and semiparametric efficiency theory. Therefore, we provide an intuitive explanation to a theoretically derived mean cost estimator. In many applications, it is also important to estimate the survival function of costs. We propose a generalized redistribute-to-the right algorithm for estimating the survival function of costs with censored data, and show that it is equivalent to a simple weighted survival estimator of costs based on inverse probability weighting techniques. Motivated by this redistribute-to-the-right principle, we also develop a more efficient survival estimator for costs, which has the desirable property of being monotone, and more efficient, although not always consistent. We conduct simulation to compare our method with some existing survival estimators for costs, and find the bias seems quite small. Thus, it may be considered as a candidate for survival estimator for costs in a real setting when the censoring is heavy and cost history information is available. Finally, we consider one special situation in conducting cost-effectiveness analysis, when the terminating events for survival time and costs are different. Traditional methods for statistical inference cannot deal with such data. We propose a new method for deriving the confidence interval for the incremental cost-effectiveness ratio under this situation, based on counting process and the general theory for missing data process. The simulation studies show that our method performs very well for some practical settings. Our proposed method has a great potential of being applied to a real setting when different terminating events exist for survival time and costs.

Interval-Censored Time-to-Event Data: Methods and Applications collects the most recent techniques, models, and computational tools for interval-censored time-to-event data. Top biostatisticians from academia, biopharmaceutical industries, and government agencies discuss how these advances are impacting clinical trials and biomedical research.Divid