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. © 1997 by John Wiley & Sons, Ltd.