This paper concerns the design and analysis of two-stage studies, where, at the first stage, the response and the exposure variables are available among a large group of subjects. The other covariables, however, are available in only a subset of the large group, obtained in a second-stage sample. This paper introduces a class of twelve such two-stage designs, including two-stage case-control and case-cohort designs as special cases. In analysing such two-stage data, one objective is to extract information about the relationship between the exposure variable and the response after controlling for other covariables. We discuss three statistical methods to analyse the data and report results of Monte Carlo stimulation to study the efficiency of the three methods.