Mortality statistics are useful tools for public-health statisticians, actuaries and policy makers

to study health status of populations in communities and to make plans in health care systems. Several statistical models and methods of

parameter estimation have been proposed. In this thesis, we review some benchmark mortality models and propose three alternative statistical models for both epidemiologic data and survival data.

For epidemiologic data, we propose two statistical models,

a Smoothed Segmented Lee-Carter model and a Smoothed

Segmented Poisson Log-bilinear model. The models are modifications of the Lee-Carter (1992) model which combine an age segmented Lee-Carter

parameterization with spline smoothed period effects within each age segment. With different period effects across age groups, the two models are fitted by maximizing

respectively a penalized least squares criterion and

a penalized Poisson likelihood.

The new methods are applied to the 1971-2006 public-use mortality data sets released

by the National Center for Health Statistics (NCHS). Mortality rates

for three leading causes of death, heart diseases, cancer and accidents,

are studied.

For survival data, we propose a phase type model having features of mixtures,

multiple stages or hits and a trapping state. Two parameter estimation techniques studied are a direct numerical method and an EM algorithm. Since phase type model parameters are known to be

difficult to estimate, we study in detail the performance of our parameter estimation techniques by reference to the Fisher

Information matrix. An alternative way to produce a Fisher Information matrix for an EM parameter estimation is also provided. The proposed model and the

best available parameter estimation techniques are

applied to a large SEER 1992-2002 breast cancer dataset.