# Recommendation Algorithm Based on Survival Action Rules
## 4 Experiments and Results
It is noteworthy that the vast majority of rules (more than 95% on average) are statistically significant at both the 0.05 and 0.01 significance levels. The exception here is the zinc set, where only half of the induced rules are significant at the 0.01 level and 67% at the 0.05 level. Table 4 shows the predictive capacity of the recommendation algorithm. To measure this feature, an arbiter model is used to test whether performing the actions suggested by the recommendation algorithm for a given example causes a significant change in the estimated survival time. The arbiter model chosen is the XGBoost algorithm, which is suitable for the analysis of censored data. In the literature, the XGBoost algorithm is reported to have high predictive performance in solving classification and regression problems and in survival analysis [73]. The model in our study is based on gradient-boosted Cox proportional hazard loss, with regression trees as base learners, and is available in the scikit-survival Python package. The validation procedure is as follows:  
1. The XGBoost model is trained on the training data. 2. For each test example \(x\), the survival curve \(KM_{T}\) is determined, which represents the conclusion of the recommendation. \begin{table}
\begin{tabular}{l r r r r r r r r} \hline \hline
**Dataset** & \(n_{r}\) & \(\overline{n}_{a}\) & \(\overline{n}_{\text{ANY}}\) & \(P_{0,05}\) & \(P_{0,01}\) & \(\overline{\text{Cov}}_{\text{S}}\) & \(\overline{\text{Cov}}_{\text{T}}\) & \(n_{\text{BETTER}}\) & \(n_{\text{WORSE}}\) \\ \hline FD001 & 2.0 & 2.45 & 0.15 & 100 & 100 & 34.72 & 36.44 & 1.0 & 1.0 \\ FD002 & 6.8 & 3.05 & 0.39 & 91 & 86 & 24.43 & 26.13 & 3.6 & 3.1 \\ FD003 & 2.0 & 4.00 & 1.30 & 100 & 100 & 35.06 & 41.50 & 1.0 & 1.0 \\ FD004 & 6.5 & 3.49 & 0.79 & 100 & 100 & 28.48 & 29.94 & 3.4 & 3.1 \\ GBSG2 & 13.8 & 3.31 & 0.47 & 100 & 100 & 27.41 & 33.16 & 11.5 & 2.3 \\ melanoma & 3.9 & 2.62 & 0.63 & 100 & 100 & 32.62 & 38.82 & 2.6 & 1.3 \\ actg320 & 18.4 & 4.00 & 1.96 & 99 & 99 & 22.48 & 39.29 & 16.1 & 2.2 \\ bmt-ch & 4.7 & 2.50 & 0.60 & 100 & 100 & 30.63 & 40.34 & 2.9 & 1.8 \\ follicle & 7.2 & 1.86 & 0.45 & 98 & 98 & 33.26 & 22.61 & 4.2 & 3.0 \\ hd & 10.1 & 1.22 & 0.21 & 87 & 81 & 22.10 & 40.01 & 8.0 & 2.1 \\ lung & 7.1 & 2.79 & 0.71 & 100 & 100 & 35.59 & 36.49 & 3.5 & 3.6 \\ maintenance & 20.8 & 2.56 & 0.03 & 98 & 91 & 22.27 & 12.10 & 12.7 & 8.1 \\ mgus & 4.1 & 3.27 & 0.91 & 100 & 100 & 31.00 & 21.63 & 2.8 & 1.3 \\ pbc & 6.8 & 2.73 & 0.49 & 100 & 100 & 29.88 & 45.10 & 5.7 & 1.1 \\ std & 15.1 & 4.18 & 2.10 & 100 & 100 & 23.72 & 28.36 & 7.4 & 7.7 \\ uis & 8.0 & 3.49 & 1.55 & 100 & 100 & 26.80 & 45.86 & 7.0 & 1.0 \\ whas1 & 6.9 & 2.52 & 0.07 & 100 & 100 & 27.58 & 34.88 & 4.9 & 2.0 \\ whas500 & 7.9 & 4.33 & 0.43 & 100 & 100 & 29.33 & 33.44 & 6.6 & 1.3 \\ zinc & 6.9 & 2.59 & 0.90 & 67 & 53 & 21.61 & 39.53 & 4.9 & 2.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Rules statistics. The columns represent the average values of the following parameters: the number of rules (\(n_{r}\)); the number of actions in a rule (\(\overline{n}_{a}\)); the number of ANY actions in a rule (\(\overline{n}_{\text{ANY}}\)); the percentage of rules with a \(p\)-value less than 0.01 (\(P_{0,01}\)); the percentage of examples covered by the source rule (\(\overline{\text{Cov}}_{\text{S}}\)); the percentage of examples covered by the target rule (\(\overline{\text{Cov}}_{\text{T}}\)); the number of BETTER rules (\(n_{\text{BETTER}}\)); the number of WORSE rules (\(n_{\text{WORSE}}\)). The example \(x^{\prime}\) is passed to the trained XGBoost model with attribute values modified according to the recommendation algorithm. 4. The XGBoost model assigns the survival curve \(KM_{x^{\prime}}\) to the example \(x^{\prime}\). 5. The difference between the curves \(KM_{T}\) and \(KM_{x^{\prime}}\) is examined; if the curves are not significantly different, then the rule action model is assumed to be working correctly. The validation process presented above is called the consistency score (column \(Cs\) in Table 4).