BACKGROUND: In many clinical trials, data are collected longitudinally over time. In such studies, missingness, in particular dropout, is an often encountered phenomenon. METHODS: We discuss commonly used but often problematic methods such as complete case analysis and last observation carried forward and contrast them with broadly valid and easy to implement direct-likelihood methods. We comment on alternatives such as multiple imputation and the expectation-maximization algorithm. RESULTS: We apply these methods in particular to data from a study with continuous outcomes. The outcomes are modelled using a general linear mixed-effects model. The bias with CC and LOCF is established in the case study and the advantages of the direct-likelihood approach shown. CONCLUSIONS: We have established formal but easy to understand arguments for a shift towards a direct-likelihood paradigm when analysing incomplete data from longitudinal clinical trials, necessitating neither imputation nor deletion.