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.