Weighted likelihood, pseudo-likelihood and maximum likelihood methods for logistic regression analysis of two-stage data.

General approaches to the fitting of binary response models to data collected in two-stage and other stratified sampling designs include weighted likelihood, pseudo-likelihood and full maximum likelihood. In previous work the authors developed the large sample theory and methodology for fitting of logistic regression models to two-stage case-control data using full maximum likelihood. The present paper describes computational algorithms that permit efficient estimation of regression coefficients using weighted, pseudo- and full maximum likelihood. It also presents results of a simulation study involving continuous covariables where maximum likelihood clearly outperformed the other two methods and discusses the analysis of data from three bona fide case-control studies that illustrate some important relationships among the three methods. A concluding section discusses the application of two-stage methods to case-control studies with validation subsampling for control of measurement error.