Surrogate endpoint is chosen as a measure or indicator of a biological process that is obtained sooner, at less cost or less invasively than a true endpoint of health outcome, and is used to arrive at conclusions about the effect of intervention on the true endpoint. Following the work of Begg and Leung (J. R. Stat. Soc. Ser. A 2000; 163:15–28), we introduce a new motivation to analyse the surrogate and true endpoints together, to have a better estimate of the treatment difference where both the endpoints are binary. Several estimators are studied and compared. Some real data sets are analysed. Copyright © 2010 John Wiley & Sons, Ltd.