Suppose that the occurrence of spontaneously developing cancer in a group of transgenic animals is 50% (p_c = 0.5) and the investigator wishes to test an anti-cancer drug. The investigator would like to detect when the drug causes the occurrence rate to drop to 25% of animals (p_e = 0.25), with a power of 90% and a significance level of 5%. Then d = .25 and C = 10.51 (see Table A-1 for value of C), and

animals are needed in each group, which is about 85 animals in each group, for a total number of 170 animals necessary for the experiment.

The second approach is to treat time to occurrence as a continuous variable. This approach is applicable only if all animals are followed to event occurrence (for example, until death or time to exhibit a disease, such as cancer), but it cannot be used if some animals do not reach the event during the study. To compute sample size, it is necessary to obtain the estimate of the standard deviation of the variable (s) and the magnitude of the difference (d) the investigator wishes to detect, then

where C is a constant dependent on the value of a and 1-ß, as above.

Suppose that a strain of rats spontaneously develops cancer in 12 months with a standard deviation of 4 months. Assume that an investigator would like to test a drug postulated to delay the onset of cancer. If the investigator would like to be able to detect when the time to occurrence of cancer is extended to 15 months with a power of 90% and a significance level of 5%, then the difference to be detected is 3 months and 2C = 21 (C = 10.51, see Table A-1), and

animals in each group or roughly 80 animals for the whole study.