Sergey Lvin, Lecturer of Mathematics and Statistics STATISTICAL INFERENCE FOR THE RISK RATIO IN 2 X 2 BINOMIAL TRIALS WITH STRUCTURAL ZERO

In some statistical analyses, researchers may encounter the problem of analyzing correlated 2x2 table with a structural zero in one of the off diagonal cells. Structural zeros arise in situation where i t is theoretically impossible for a particular cell to be observed. For instance, Agresti (1990) provided an example involving a sample of 156 calves born in Okeechobee County, Florida. Calves are first classified according to whether they get a pneumonia infection within certain time. They are then classified again according to whether they get a secondary infection within a period after the first infection clears up. Because subjects cannot, by definition, have a secondary infection without first having a primary infection, a structural void in the cell of the summary table that corresponds with no primary infection and has secondary infection is introduced. For discussion of this phenomenon, see Tang and Tang (2002), and Liu ( 1 998). The risk ratio (RR) between the secondary infection, given the primary infection, and the pr~mary infection may be a useful measure of change in the pneumonia infection rates of the primary infection and the secondary infection. In this thesis, we will first develop and evaluate the large sample confidence intervals of RR. Then we will investigate the tests for RR and the power of these tests. An example from the literature will be provided to illustrate these procedures. Simulation studies will be carried out to examine the performance of these procedures