Date of Award

Spring 2001

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computational Analysis and Modeling

First Advisor

Raja Nassar

Abstract

Some of the common measures of risk used m epidemiology today are the relative risk, the odds ratio, the attributable risk, and the chi-square goodness of fit test. All of these measures have their shortcomings. A new approach to measuring risk in case-control studies is to use the unitless measure of the coefficient of variation of incidence of disease over the risk categories, kˆ2, first proposed by Begg et al. (1998). Begg et al. (1998), also showed that the product of multiple risk factors may be compared to an overall measure of the square of the coefficient of variation of the Incidence of disease over all risk categories known and unknown, S, the standardized Incidence ratio. It is shown that [special characters omitted], where [special characters omitted] represents the square of the coefficient of variation of the incidence of disease over all risks. If the risks are independent, then an estimate of S may be calculated from a case-control study as [special characters omitted] and [special characters omitted] = [special characters omitted]. The parameter S may be available from a source such as a cancer registery. If [special characters omitted] is much smaller than S then it may be that not all risks have been considered.

The distribution and statistical properties of kˆ 2, [special characters omitted], and [special characters omitted] have not been investigated. In this study, it is shown that the distribution of kˆ2 for one risk factor with multiple levels, is [special characters omitted]. A simulation study was conducted to investigate the power of this statistic for testing Ho : kˆ 2 = 0 vs Ha : kˆ 2 ≠ 0 for one risk factor with multiple levels. The simulation study confirmed the power of he test statistic to be very good as long as the sample size was at least 200 for both cases and controls.

The measure [special characters omitted] is of interest because it may be used to compare the sum of the logarithms of risk factors used in a study to the natural log of the overall square of the coefficient of variation of the incidence of disease over all risks known and unknown, [special characters omitted]. Also, this study investigates the distribution of the statistic [special characters omitted] and the power of this statistic when used to test Ho : [special characters omitted] = 0 vs. Ha : [special characters omitted] and Ho : [special characters omitted] = [special characters omitted] vs. Ha : [special characters omitted].

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