Stereotype Logistic Regression Model Of Case-control Study

Recently, case-control study has been paid more and more attention by re-searchers both at home and aboard, since it plays an irreplaceable role in the study of rare diseases, especially in the domain of epidemiology and sociology.Firstly, we introduce the background of this paper:based on the incidence trends of prostatic cancer, categorical variables and common models used to deal with cat-egorical response variables are introduced in this paper, such as logistic regression models, cumulative logit models, continuation ratio models, partial proportional odds models, adjacent-category logit models, multinomial logistic regression models and stereotype logistic regression models. And we can select proper model based on its own applicable case.In the case-control study, samples of are often chosen from the components made up of both the illness group and the control group, and then the values of indepen-dent variable X are observed. Here, X is random, and the probability that whether the individual is selected or not is different. Therefore, we introduce a new vari-able Z, where Z=1 represents that the individual is selected and Z=0 is the opposite,and the probabilities ?1= P(Z=1|the individual in cases),?0= P(Z= 1|the individual in controls). Combined with stereotype regression model, the con-ditional probability P(y= k|Z= 1, X) is computed. And then the conditional logistic regression and the non-conditional logistic regression in layered case-control study are considered, this is the first innovation of this paper; we calculate the maximum likelihood estimation for these two regression which is the second innovation of this paper and the third innovation is the Bayesian estimation for them. Results show that the mean square errors and the biases are smaller in such case.Finally, we illustrate our theoretical results by a simulation example. The results show that the estimators under the same matching ratio and different matching ratios are similar, but the results considering the probability that whether an individual is selected or not are better than those without considering the probability. So the method in this paper has statistical significance to some extent.