## Mathematics Ph.D. Dissertations

#### Title

Inference of Attributable Risk for Multiple ExposureLevels Under Cross-sectional Sampling Design

#### Date of Award

2006

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (Ph.D.)

#### Department

Mathematics

#### First Advisor

Truc Nguyen

#### Abstract

Attributable risk (AR) plays an important role in assessing the relationship between the risk factor and the disease in public health and biomedical sciences. This research is intended to develop point and interval estimation procedures for the inference of the attributable risk when the data set is obtained by means of a cross-sectional sampling design. In this thesis, we develop a novel approach for estimating the variance of the Maximum Likelihood Estimate of AR for a dichotomous risk factor by using the Delta method. The new method is computationally much easier than the existing method using the Fisher Information Matrix. This method has also been extended for a risk factor with multiple exposure levels without and with confounders. The performance of the new method has been justified with real life examples and by the Monte Carlo simulation. The simulation shows that the confidence interval estimator performs very well in terms of the coverage probability and the average length of the interval estimated. For small sample case where large sample approximation theory can not be applied, we develop inference procedure for a dichotomous risk factor using exact test regarding positive association between the risk factor and disease outcome which has never been considered before for attributable risk. This procedure has been extended for a risk factor with multiple exposure levels. The attributable risk has also been studied for intermediate base-level which is useful for detecting the significance of a particular level of risk factor with multiple exposure levels. This technique can be used to amalgamate some of the insignificant exposure levels and hence reduce the exposure levels of the undertaken risk factor. Statistical properties of attributable risk have been explored under certain conditions on the cell probabilities. The behavior of the test of positive dependence using the test statistics based on the estimate of AR and logarithm of the odds ratio, log OR has been studied. It has been shown that in some subsets of the alternative, the test using the test statistic based on the estimate of AR is better than the test using the test statistic based on the estimate of log OR, and in some other subsets, the conclusion is in converse direction. In an exact test for small sample, it has been shown that the two statistics based on the estimates of AR and log OR are equivalent.

#### Recommended Citation

Shapla, Tanweer, "Inference of Attributable Risk for Multiple ExposureLevels Under Cross-sectional Sampling Design" (2006). *Mathematics Ph.D. Dissertations*. 1.

https://scholarworks.bgsu.edu/math_diss/1