A summary of the conventional biostatistical theory of survival analysis is presented by means of an example from the literature. This is followed by a review of the historical background leading to the development of the Hardin Jones-Pauling biostatistical theory of survival analysis for cancer patients. Then, the salient details of this theory are given, along with the application of the theory to the literature example. The Hardin Jones Principle, which describes the temporal behavior of survival for terminal cancer patients, is elucidated. Three criteria for the validity of clinical trials of treatments of cancer patients based on the Hardin Jones Principle are discussed. Some of the advantages of the Hardin Jones-Pauling theory over the conventional theory are outlined.