Proefschrift

APPENDIX A. SUPPLEMENT TO CHAPTER 5 bang-bang treatment schedule is said to be quite sensitive to the variation of its structure. The ranges and ratio Ω are shown in Table A.4. Figure A.1: Visual representation of quantitative metric used for measure of robustness to jitter. Objective Function Range of minimum 100 Range of all 53130 Ω Best Case Volume 1 . 957 · 10 5 3 . 684 · 10 7 0 . 53% Responder Volume 7 . 806 · 10 3 5 . 699 · 10 6 0 . 18% Non-Responder Volume 1 . 600 · 10 2 4 . 858 · 10 6 0 . 04% Best Case Variance 4 . 304 · 10 4 2 . 210 · 10 7 0 . 19% Best Case T − 9 . 000 · 10 − 3 1 . 027 · 10 1 0 . 09% Responder T − 7 . 352 · 10 6 2 . 663 · 10 7 27 . 68% Non-Responder T − 5 . 010 · 10 6 1 . 773 · 10 7 28 . 24% Table A.4: Range analysis. Ω for minimizing tumor volume, minimizing tumor variance, and minimizing the density of T − in the best-responder patient are all < 1%. This signifies that jittering the administration of the 5 doses from the optimal treatment schedule does not affect the objective value significantly. On the other hand, Ω for minimizing the density of T − in the responder and non-responder patient are 27 . 68% and 28 . 24% respectively. This indicates that jittering the administration of the 5 doses even a little from the optimal treatment schedule drastically increases the objective value. Figures A.2 - A.8 show the treatment schedules associated with the 100 minimum objective values for each case study to better explore the meaning of the robustness measure Ω. In these figures, the treatment schedules are shown in the left panel. The optimal treatment schedule is shown in the bottom row in red where each of the five blocks in the row correspond to the control point at which treatment is given. In the rows above, the treatment schedules corresponding to the minimum 100 objective values are shown. The panel on the right shows the corresponding Ω for these minimum 100 objective value treatment schedules. The bottom row in red always shows an Ω of zero as this is the optimized minimum objective value. As the treatment schedule is jittered, the value of Ω is shown increasing away from zero. Note the values of the x-axis as they are different for each image. 128