For time-to-event data, the study sample is commonly selected using the nested case–control design in which controls are selected at the event time of each case. An alternative sampling strategy is to sample all controls at the same (pre-specified) time, which can either be at the last event time or further out in time. Such controls are the long-term survivors and may therefore constitute a more ‘extreme’ comparison group and be more informative than controls from the nested case–control design. We investigate this potential information gain by comparing the power of various ‘extreme’ case–control designs with that of the nested case–control design using simulation studies. We derive an expression for the theoretical average information in a nested and extreme case–control pair for the situation of a single binary exposure. Comparisons reveal that the efficiency of the extreme case–control design increases when the controls are sampled further out in time. In an application to a study of dementia, we identified Apolipoprotein E as a risk factor using a 1:1 extreme case–control design, which provided a hazard ratio estimate with a smaller standard error than that of a 2:1 nested case–control design.