Partially Linear Single-Index Models with Current Status Data
Date
2015-01-21
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Abstract
In the field of survival analysis, there are mainly three types of censoring, (i) right censoring,
(ii) left censoring, and (iii) interval censoring. In my research, we focus on case I interval
censoring, which is more challenging than right censoring, and for such data the methods developed for right censoring do not generally apply. Case I interval-censored or current status data arise in such areas as demography, economics, epidemiology and medical science. For example, events such as time to develop tumors (i.e. time to tumor onset) or time to develop HIV cannot be known exactly; only the occurrence in a time interval is known on examination. As another example, in laboratory studies, the relationship between the distribution of time to develop a specific disease of mice or rats and covariates of interest of these animals is of interest. The presence (or absence) of the disease is detectable only at death or sacrifice; we do not observe the exact onset time. In this dissertation, we propose three parsimonious regression models for analysis of current status
data and overcome a phenomenon named "curse of dimensionality" by using partially linear single-index models which are well-known among dimension reduction methods. We use B-splines to approximate nonparametric functions and the sieve maximum likelihood method to obtain efficient estimators of the regression parameters. We derive large sample properties of the resulting estimators using martingale and counting process theory, conduct simulation
studies to assess the proposed methods, and apply them to a real data set in analyzing
probability of renal recovery of patients with acute kidney injury disease.
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Citation
Pordeli, P. (2015). Partially Linear Single-Index Models with Current Status Data (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/27259