# Breast Cancer Survival Analysis Model
## 5 Conclusions  
In this study, the survival analysis of BC was initially studied using the chi-square test to assess the independent influence of various types of factors on survival. When the significant variables were submitted to the Kaplan-Meier survival analysis, it was discovered that the significant variables affected the survival of patients with BC when considering the univariate scenario. BC is classified by stage, treatment modality (surgery, chemotherapy, and hormone therapy), ERA, and PRA, although radiation has no bearing on survival, and patients without chemotherapy have a worse survival rate than those with chemotherapy. Next, a Cox proportional risk analysis was performed to examine survival using the treatment method under the influence of multiple variables. It was discovered that patients who received radiotherapy were significantly (\(p=0.001\)) more likely to survive than those who did not receive chemotherapy, implying that the treatment received by the patients was influenced by the various stages. The Markov chain model was built without taking the survival rate into account in the analysis of BC metastasis, and the matrix showed a steady-state prediction compared with the actual one. However, the prediction was getting closer to the actual one, and each value in each column represented the long-term stable condition. As a result, the Markov chain stage model of BC metastasis can be constructed by utilizing the probability value of each stage's survival transition, and then the semi-Markov chain model can be established by taking the survival rate into account. The risk of getting surgery for stage I and II patients with BC is lower than the risk of not receiving surgery, whereas the effect of receiving therapy (surgery, radiation, and hormone) for stage III and IV patients are mainly insignificant. The earlier the BC is detected, the better the chances of survival and the more significant the treatment's success. Conceptualization, R.-H.L. and C.-L.C. ; methodology, C.-S.L., B.K.K. and Y.-C.C. ; software, C.-L.C. ; validation, R.-H.L., C.-L.C. and Y.-C.C. ; formal analysis, C.-L.C. ; investigation, Y.-C.C. ; resources, C.-S.L. ; data curation, C.-L.C. ; writing--original draft preparation, B.K.K. and R.-H.L. ; writing--review and editing B.K.K., R.-H.L. and C.-L.C. ; All authors have read and agreed to the published version of the manuscript. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Covariate** & **Transition State** & **Parameters \(\mathbf{\beta}\)** & **Relative Risk** & \(\mathbf{p}\)**Value** \\ \hline Surgical treatment & 1\(\rightarrow\)2 & \(-\)1.47 & 0.230 & \(<\)0.001 * \\ Surgical treatment & 1\(\rightarrow\)3 & \(-\)2.40 & 0.091 & \(<\)0.001 * \\ Surgical treatment & 1\(\rightarrow\)4 & \(-\)2.74 & 0.065 & \(<\)0.001 * \\ Surgical treatment & 2\(\rightarrow\)1 & \(-\)4.22 & 0.015 & \(<\)0.001 * \\ Surgical treatment & 2\(\rightarrow\)3 & \(-\)3.105 & 0.045 & \(<\)0.001 * \\ Surgical treatment & 2\(\rightarrow\)4 & \(-\)2.46 & 0.085 & \(<\)0.001 * \\ Surgical treatment & 3\(\rightarrow\)1 & \(-\)1.33 & 0.264 & \(<\)0.001 * \\ Chemotherapy & 1\(\rightarrow\)2 & \(-\)0.44 & 0.644 & 0.007 \\ Chemotherapy & 3\(\rightarrow\)2 & 0.23 & 1.259 & 0.495 \\ Chemotherapy & 4\(\rightarrow\)3 & \(-\)3.97 & 0.019 & 0.021 \\ Hormonal therapy & 1\(\rightarrow\)3 & 0.811 & 2.250 & 0.0177 \\ Hormonal therapy & 1\(\rightarrow\)4 & \(-\)1.10 & 0.333 & 0.021 \\ Hormonal therapy & 3\(\rightarrow\)4 & \(-\)1.62 & 0.198 & \(<\)0.001 * \\ Radiotherapy & 1\(\rightarrow\)2 & \(-\)0.421 & 0.656 & 0.0393 \\ Radiotherapy & 1\(\rightarrow\)3 & \(-\)1.10 & 0.333 & 0.0439 \\ Radiotherapy & 2\(\rightarrow\)3 & 0.571 & 1.770 & \(<\)0.001 * \\ Radiotherapy & 2\(\rightarrow\)4 & \(-\)0.562 & 0.570 & \(<\)0.001 * \\ Radiotherapy & 3\(\rightarrow\)2 & 0.824 & 2.280 & \(<\)0.001 * \\ \hline \hline \end{tabular} Note: * means significant.  
\end{table} 
Table 14: Covariate parameters of the multivariate model.