When tables contain missing values, statistical models that allow the non-response probability to be a function of the intended response have been proposed by several researchers. We investigate the properties of these methods in the context of a survey of the sexual behaviour of university students. Profile likelihoods can be computed, even when models are not identified and saturated profile likelihoods (making no assumptions about the non-response mechanism) are derived. Bayesian approaches are investigated and it is shown that their results may be highly sensitive to the prior specification. The proportion of responders answering ‘yes’ to the question ‘have you ever had sexual intercourse?’ was 73%. However, different assumptions about the non-responders gave proportions as low as 46% or as high as 83%. Our preferred estimate, derived from the response-saturated profile likelihood, is 67% with a 95% confidence interval of 58–74%. This is in line with other studies on response bias in the reports of young people's sexual behaviour that suggest that the respondents overrepresent the sexually active.