Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department (Legacy)

Department of Physics

Committee Chair

Datta, Somnath

Author's Keywords

Multistate models; R package; Interval censored data; Nonparametric estimation; State occupation probability


Nonparametric statistics; Estimation theory; Distribution (Probability theory)


Multistate models are a type of multi-variate survival data which provide a framework for describing a complex system where individuals transition through a series of distinct states. This research focuses on nonparametric inference for general multistate models with directed tree topology. In this dissertation, we developed an R package, msSurv, which calculates the marginal stage occupation probabilities and stage entry and exit time distributions for a general, possibly non-Markov, multistage system under left-truncation and right censoring. Dependent censoring is handled via modeling the censoring hazard through observable covariates. Pointwise confidence intervals for the above mentioned quantities are obtained and returned for independent censoring from closed-form variance estimators and for dependent censoring using the bootstrap. We also develop novel nonparametric estimators of state occupation probabilities, state entry time distributions and state exit time distributions for interval censored data using a combination of weighted isotonic regression and kernel smoothing with product limit estimation. Structural assumptions about the multistate system are avoided when possible. We evaluate the performance of our estimators through simulation studies and real data analysis of a UNOS (United Network for Organ Sharing) data set.