# Explainable Machine Learning for Lung Cancer Screening Models
## 4 Results  
In this study, explaining the methodology is used in order to interpret and understand machine learning model predictions. We focus on model-agnostic explainable machine learning methods that could be applied to any model. This solution enables the comparison of the models of different structures. This methodology may be divided into local (individual-level explanations) and global (dataset-level explanations) categories [33]. Global-level explanations concern model structure and behavior, whereas local-level explanations relate to model behaviors for a single observation. The vast majority of explaining methods (also those presented in this article) demonstrate the effect of each variable separately (variable by variable), and they do not consider the correlation or multilinearity of the variables. The lack of the XAI methods that would take into account the correlation of the variables is beginning to be seen. The new methods are being introduced, such \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Description** & **Frequencies** \\ \hline female & being a female & No 0: 22,219 (64.6\%) \\  & & Yes 1: 12174 (35.4\%) \\ \hline race & ethnicity & White 0: 34,393 (100.0\%) \\ \hline emp & emphysema & No 0: 34,284 (99.7\%) \\  & & Yes 1: 109 (0.3\%) \\ \hline fam.lung.trend & number of first degree relatives & No relatives 0: 33,332 (96.9\%) \\  & with lung cancer & 1 or more 1: 1061 (3.1\%) \\ \hline asb & asbestos exposure & No 0: 34,223 (99.5\%) \\  & & Yes 1: 170 (0.5\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Descriptive statistics of categorical predictors available in the Domestic Lung Cancer Database. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Description** & **Mean** & **sd** & **Median** \\ \hline age & age at diagnosis & 63.02 & 8.66 & 63 \\ smkyears & smoking years & 21.59 & 18.90 & 25 \\ qtyears & quit smoking time & 1.70 & 5.03 & 0 \\ cpd & cigarettes per day & 13.02 & 11.84 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Descriptive statistics of continuous predictors available in the Domestic Lung Cancer Database. as triplot [34] that explain the contribution of the group of the variables or ALEplot that visualize the effect of the predictor and its interaction effect [35]. Detailed descriptions and mathematical formalism of the methods used in the article are presented in the Appendix A. In this section, we present how explainable machine learning techniques behave on real lung cancer patient data in the Polish population. In the following subsections, we show how good the models are, which variables are the most important for each model, and how model response depends on particular variables. The aim of the study is neither to compare model performance nor their accuracy but to understand how the models behave for different patients. Since our cohort consists only of patients with lung cancer detected, the performance measures would not be informative. Moreover, the performance of those models has been thoroughly investigated by other researchers on other populations [31]. We present techniques other than performance measures, which enables comparison of the models. Moreover, we would like to show that the machine learning models should be compared and analyzed not only by one number, which is, for example, AUC or ACC (accuracy). The comparison of the models should be also evaluated by the XAI techniques, which allow us to compare models from different perspectives. The choice of threshold to qualify a particular population to a screening procedure is a challenge and depends on specific model. Figure 1 shows the distributions of predictions across three screening models on panel (A) and cumulative percentage of predictions lower or equal to a certain prediction on panel (B).