In many studies, there is a suspicion that non-response is related to the value of the possibly missing values. This happens, for example, in clinical studies which evaluate a treatment, where the side effects of the treatment may have an impact on the participation of patients, and also in environmental studies, where geographical location and certain environmental factors may influence the response. When the non-response is related to the values of missing variables, the non-response is non-ignorable. When there is non-ignorable non-response, bias in the estimates of the parameters may arise if the distribution of the missing data is not considered. The purpose of this article is to approach data from clustered samples with non-ignorable non-responses using generalized estimating equations. It will be seen that it is possible to use the estimating equation to deal with the data in a unified way when the outcome is time to an event. Because censoring is a missing data mechanism which depends on the missing value in a tractable manner, the analysis of data from a censored sample is discussed and a general procedure is shown for dealing with this kind of data based on estimating equations.