In this paper, we attempt to find the most efficient trial design to determine the optimal dose of cancer treatment. The two trial designs being evaluated are a standard trial design and intra-patient dose-switching trial. The optimal dose is the lowest dose that still causes a decrease in the tumor size. The most efficient trial is defined as the trial in which the distribution of parameters from the data set mostly closely matches the distribution from a simulated trial. We developed an ordinary differential equation to model the change in the sum of the length of tumor diameters over time. This equation takes into account resistance of the tumor to the drug, the carrying capacity of the tumor, the growth rate of the the tumor and the decay rate of the tumor due to the drug dose. This equation was used to fit the parameters and run simulations. We determined that the intra-patients dose switching trial had a parameter distribution that mostly closely matched the original data in comparison to the standard trial.

Publication Date


Document Type

Senior Project

Student Type


Department, Program, or Center

School of Mathematical Sciences (COS)


Michael Cromer

Advisor/Committee Member

Kara L. Maki


RIT – Main Campus