A local likelihood method for estimating relative risk functions in case-control studies

A local likelihood method with constraints is developed for the case-control sample for estimating the unknown relative risk function and odds ratio. Our estimates can be reduced to simply solving two systems of estimating equations. One system of estimating equations is for estimating the relative risk function, and is identical to that based on the locally weighted logistic regression analysis under prospective sampling. Another system of estimating equations is for estimating the odds ratio, and is identical to that used in the traditional linear logistic regression analysis. Asymptotic properties of the estimators are presented. Two real examples and simulations are given to illustrate our method. The results confirm that our approach is useful for estimating the relative risk function and odds ratio in case-control studies.