Three topics motivated by practical problems where the response variable is binary are described and illustrated. When a number of di!erent explanatory variables are measured on each individual, a parsimonious model may be needed to predict the response of a future patient, or in selecting the variables that any treatment e!ect must be adjusted for. Some variable selection procedures used in conjunction with "tting logistic regression models are summarized and their performance investigated using a simulation study. A study to compare two devices for delivering anaesthetic gas to patients during surgery is then described, in which the response variable is the incidence of post-operative sore throat. In this study, the allocation of patient to device was non-random and a method for analysing these data that takes account of this aspect of the data is illustrated. In studies to compare di!erent forms of contraceptive, the extent of regularity in the menstrual bleeding cycle is an important consideration for the acceptability of a contraceptive. Diary data on the menstrual bleeding pattern are therefore routinely collected. A method of summarizing the cyclic behaviour in the diary data for a particular woman is described, and extended to allow comparisons to be made between groups of women on di!erent types of contraceptive. The approach is illustrated using a database made available by the World Health Organization.