## 4 Discussion  
The intracellular levels of ROS, CA, Ki-67\({}^{+}\) count, and cell cycle activity can independently help indicate whether cell proliferation or cell death is occurring for cells treated with CHCP. This study thus aimed to pinpoint which variables affect cell proliferation and cell death in a Granger causal manner. The Granger causal model is a prediction-based statistical concept of causality in which empirical data is used to find patterns of correlation. Granger causality is also known as a \"bottom-up\" procedure because it assumes two time-series variables are independent of one another. The variables are then subsequently analyzed for correlation. This is different from \"top-down\" procedures which initially assume a link between the time series variables [21]. Prior to model generation, it was hypothesized that ROS would act as the main proxy of causality due to the widespread effects of oxidation on the cell cycle. Intracellular ROS measurements indicated that after CHCP treatment, all breast cancer cell lines underwent oxidative stress, which gradually increased with post-treatment incubation time. For both cell proliferation and cell death, while not all ROS models indicated Granger causality, as seen by \(p\)-values > 0.05, this does not mean that ROS did not heavily influence upstream actions. The effects of oxidative species may have affected other cellular processes in a more direct manner. For the 3 min CHCP treatment cell proliferation models, it was seen that only BT-474 and SK-BR-3 displayed ROS Granger causality. Both of these cell lines are HER2\({}^{+}\), with ER/PR receptors present in BT-474 cancer cells and no ER/PR receptors present in SK-BR-3. The cell lines that did not display ROS causality, MCF-7 and MDA-MB-231, are both HER2\({}^{-}\). Ligand-mediated stimulation of HER2 receptors causes auto-phosphorylation of key tyrosine residues that serve as docking sites for downstream signaling cascades that regulate normal cell function by promoting growth and survival. However, when disrupted, HER2 can spur on the growth of cancer [4]. Given this, HER2\({}^{+}\) cell lines are more likely to respond to treatment that directly targets the HER2 protein itself. The results of this study may suggest that CHCP does directly affect the HER2 transmembrane protein in a way that would signal Granger causality. It was also seen that the coefficient of regression for the SK-BR-3 3 min ROS model was significantly smaller than that of the BT-474 ROS model. This may be due to the fact that SK-BR-3 has no hormone receptor, while BT-474 is both ER+ and PR+ [1]. Based on the results, CAP-induced ROS may have a greater impact on cells with a greater number of different receptors. A lack of hormone receptors may cause cells to have a certain degree of tolerance to different oncological therapies, including CAP. CA showed consistent causality for all of the 3 min cell proliferation models, except that of the BT-474 cell line. This is because BT-474 treated by CHCP at 120 p for 3 min did not induce activation of caspase (data shown in [14]). When treated for 5 min, CA of all four cell lines showed causality towards proliferation, but BT-474's coefficient being the smallest also confirmed lower CHCP-induced caspase activation in this cell line. It was also found that the Ki-67 variable had a clear causal relationship to cancer cell proliferation for all cell lines except MDA-MB-231. The Ki-67 count increased as cells prepared to divide, and with the generalized uncontrolled growth exhibited by cancer cells, a large Ki-67 count indicates significant cancer growth [17]. Thus, tumor suppression goes hand-in-hand with a decrease in Ki-67 due to its vital role in the continuance of the cell cycle itself [17; 29]. The reason MDA-MB-231 did not display Ki-67 causality with cell proliferation may be due to the cell line's inherent level of resistance to CAP and its low levels of Ki-67 already present within the cells [2; 5].