Paper Type

Master's Thesis


College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)


Mathematics & Statistics

First Advisor

Dr. Pali Sen

Second Advisor

Dr. Denis Bell

Third Advisor

Dr. James Gleaton


In this paper, we present and implement a method to assess the mathematical synergy of two-drug combinations based on a stochastic model. The drugs in question are two isomers that are applied to the human eye via a liquid eye drop. Techniques applied to the data in this paper can be applied to other two-drug combination studies.

We derive the mean and the variance terms of the drug combination "effects" in closed form using Ito's method of stochastic differential equations. The model fit of the data to the individual subject is examined by both statistical and graphical methods. Two estimation methods in SAS, PROC NUN and PROC NLMIXED, are used to estimate model parameters. We perform simulation and power studies using R software to show the strengths of the proposed approach in estimating the model parameters.

From this research, we find that the combination of drugs under study is synergistic in nature. We also confirm that the proposed stochastic model is appropriate.

Included in

Mathematics Commons