MRC PhD student

Level of study: PhD

Title: Optimal designs for Drug Synergy

Brief summary of the research

Statistical modeling of the responses to drug interactions is well developed in literature, and the models are easily fitted using statistical software packages such as SAS, STATA, SPSS and GENSTAT. Modeling errors such as choosing the wrong model can be variously corrected. However, a poorly designed experiment such as a clinical trial is difficult or impossible to correct at later stages of an experiment. The results from a weakly planned experiment can be misleading. Hence, the focus of my thesis is on the construction of model oriented optimal designs for detecting drug interactions.

A lot of work on optimal designs has been done for linear models because of the ease of analyzing these models. However, very little research has been conducted on optimal designs for nonlinear and generalized linear models with more than one explanatory variable because the calculations are challenging.  Since responses to drug interactions are generally modeled using generalized linear models (e.g. Logistic and Poisson models) with at least two explanatory variables, the thesis is focused on constructing optimal designs for the two-variable logistic models with and without interaction. Once the theory is well established, generalization to models with more than two explanatory variables will be considered.

Overall objective

The main aim of the study is to develop an approach of analytically or numerically constructing D-optimal designs for the binary two-variable logistic models with and without interaction on a restricted design (dose) space.

Specific aims

1. To construct D-optimal designs for the binary two-variable logistic model without interaction in the design space [0, ∞) X [0, ∞) and establish conditions on the parameters and design space for a 3- or a 4- point optimal design.
2. To construct D-optimal designs for the binary two-variable logistic model without interaction in the rectangular design space [a, b] X [c, d] and set up  conditions on the parameters and design space for a 3-, 4-, or 6- point optimal design.
3. To construct D-optimal for the binary two-variable logistic model with interaction in the design space [a, b] X [c, d] and present conditions on the parameters and design space for a 4-, 5-, 6- , 7-, or 8- point optimal design.
4. To illustrate the theory of D-optimal designs for the binary two-variable logistic model without and with interaction using real world data.

Supervisors:
Dr Principal Ndlovu, UKZN: http://statsactsci.ukzn.ac.za/ndlovu5859.aspx
Prof Linda Haines, UCT: http://web.uct.ac.za/depts/stats/lhaines.htm
Study Institution: School of Statistics and Actuarial Science, University of KwaZulu-Natal
MRC Unit: Biostatistics Unit