Goodness-of-fit Tests For Logistic Regression Models In Stratified Case-control Studies

Logistic regression is widely used in the biology research, specially in the research ofinvestigating the relationship between exposure and disease. In this paper, we talk about thegoodness-of-fit tests for logistic regression in the stratified case-control studies.The first chapter describes the background of the Logistic regression model and the re-search status all around the world. And then this chapter shows the semiparametric modelwhich is derivated by the logistic regression in the stratified case-control studies. At the last ofthis chapter, we briefly introduce the ideas and the structure of this paper.The second, third and the fourth chapter are the key chapters of this paper. In the threechapters, three statistics of goodness-of-fit are presented. They are the statistic of Kolmogorov-Smirnov, the statistic constructed via two kernel density estimators, and the Pearson’s chi-squared statistic. All of them are improved from the statistics in the non-stratified case-controlstudies, after they are constructed, we prove their asymptotic properties.At the last chapter, the simulation for the statistics of the goodness-of-fit are presented.Through the Bootstrap simulation, we get the powers of the three statistics, and compare witheach other. At last, the method for goodness-of-fit is applied in an example and runs well.