#### Date of Award

2002

#### Level of Access Assigned by Author

Open-Access Thesis

#### Degree Name

Master of Arts (MA)

#### Department

Mathematics

#### Advisor

Ramesh C. Gupta

#### Second Committee Member

Pushpa L. Gupta

#### Third Committee Member

David M. Bradley

#### Abstract

In epidemiological studies, we are often interested in comparing the mortality rate of a certain cohort to that of a standard population. A standard computational statistic in this regard is the Standardized Mortality Ratio (SMR) @reslow and Day, 1987), given by where 0 is the number of deaths observed in the study cohort from a specified cause, E is the expected number calculated from that population. In occupational epidemiology, the SMR is the most common measure of risk. It is a comparative statistic. It is frequently based on a comparison of the number0 in the cohort with the expected value E in a standard population. Our goal is to estimate the value of SMR. Since the expected value E is assumed to be fixed for a certain standard population, what we need to do is to estimate the observed number 0 , which is -. traditionally assumed to be Poisson distributed. We are primarily interested in confidence limits for the Poisson parameter. Many authors have discussed methods for constructing confidence intervals for the Sh4R. These confidence intervals amount to obtaining more accurate confidence intervals for the Poisson parameter. In this thesis, by using classic normal approximations, exact confidence intervals based on the chi-square distribution, binomial approximations and shortcut methods, we investigate more accurate methods for the statistical analysis of Poisson distributed data and carry out some simulation studies in order to obtain and compare better estimates of the Sh4R. These methods will be employed to develop an improved analysis of the Sh4R with missing death certificates.

#### Recommended Citation

Wang, Bingxia, "Estimation of Standardized Mortality Ratio in Epidemiological Studies" (2002). *Electronic Theses and Dissertations*. 406.

https://digitalcommons.library.umaine.edu/etd/406