# Explainable Machine Learning for Lung Cancer Screening Models
## 4 Results
### Dataset-Level Explanations  
The purpose of the dataset-level explanation is to understand how the model usually behaves. We are not interested in one particular patient. The two key questions are (1) which variables are the most important and (2) how the risk prediction changes with the variable.  
Figure 2 shows the importance of variables [36] in each model. First, we see that the models use different variables. For example, asbestos exposure is important for the BACH model, whereas other models do not include this factor. On the other hand, three variables (family lung trend, race, and emphysema) that are important for the LCRAT and PLCO\({}_{m2012}\) models are not included in the BACH model. The importance of variables from the common set is similar. The most important ones are age, number of years of smoking, cigarette count per day, and quit time. Age is the most important variable for the LCRAT  
Figure 1: (**A**) Distribution of predictions for the lung cancer risk models. (**B**) Cumulative distribution for three lung cancer risk models presenting the cumulative percentage of predictions. Vertical dotted lines indicate 2% threshold.  
and PLCO\({}_{m2012}\) models, but for the BACH model, it takes the fourth position. Similarly, the difference concerns years of smoking. It is the most important variable for the BACH model, whereas in the PLCO\({}_{m2012}\) model, it takes a lower position. According to the LCRAT model's variable importance, years of smoking are considered the second most important (after age). However, the relative importance of these variables differs.  
Figure 3 shows Partial Dependence Profiles [37,38] for the four most important variables. They summarize how the model prediction changes within the selected variable change. The greatest differences between the average models' predictions are shown for two variables: age and smoking quit time. It is worth noticing that the considered models predict lung cancer risks for different time periods. Nevertheless, we compare the shapes of the curves rather than the absolute values of the predictions.  
The PLCO\({}_{m2012}\) model prediction regarding age differs significantly from other models. The BACH model for the oldest people indicates counter-intuitive dependency, whereas the PLCO\({}_{m2012}\) model predictions increase dramatically for people more than 75 years old. For the LCRAT model, the prediction increases with age but only up to the age of 77 years. For the oldest people, the predictions remain unchanged.  
Plots indicate similar dependencies between years of smoking (smkeyears) and predictions for 2 models: LCRAT and PLCO\({}_{m2012}\). For quitting time (qtyears), the BACH model again shows counter-intuitive dependency for the highest values. A very similar  
Figure 2: Variable importance for the three considered risk models. The longer the bar is, the more important the corresponding variable. Note that _asb_ stands for asbestos exposure, _cpd_ stands for cigarettes per day, while _islander_ stands for Pacific Islander ethnicity.  
curve was also introduced in Figure 1 in the study [26]. The most similar dependencies' partial dependence plots demonstrate for cigarettes per day variable (cpd). The BACH model prediction increases for those who smoked more than 20 years in a more radical manner than other models. Those changes among the models indicate that models exploit particular variables in different ways. It seems that some of these dependencies could be corrected.