Monte Carlo methods are used to evaluate the operating characteristics of several trend tests for comparing incidence rates of occult tumours. The candidate tests are applicable in long-term animal experiments that have just one sacrifice time and no information on cause of death. When survival decreases with dose and the tumour is lethal, the tests that do not adjust for survival or that assume tumours are non-lethal behave conservatively, whereas the test that assumes tumours are rapidly lethal rejects the hypothesis of equal incidence rates too frequently. The only test which consistently operates at the correct level is one that specifies a constant difference between the death rates for animals with and without the tumour. Surprisingly, the test that specifies a constant ratio of these death rates often is conservative. Finally, a test based on a simple modification of the unadjusted test, which accounts for differential mortality by scaling down the size of the risk set, performs reasonably well in many cases. Among the tests that operate at the proper level, the constant risk difference test consistently exhibits high power across a wide range of situations.