Modern medicine is supported by increasingly sophisticated algorithms. In diagnostics or screening, statistical models are commonly used to assess the risk of disease development, the severity of its course, and expected treatment outcome. The growing availability of very detailed data and increased interest in personalized medicine are leading to the development of effective but complex machine learning models. For these models to be trusted, their predictions must be understandable to both the physician and the patient, hence the growing interest in the area of Explainable Artificial Intelligence (XAI). In this paper, we present selected methods from the XAI field in the example of models applied to assess lung cancer risk in lung cancer screening through low-dose computed tomography. The use of these techniques provides a better understanding of the similarities and differences between three commonly used models in lung cancer screening, i.e., BACH, PLCO${}_{m2012}$, and LCART. For the presentation of the results, we used data from the Domestic Lung Cancer Database. The XAI techniques help to better understand (1) which variables are most important in which model, (2) how they are transformed into model predictions, and facilitate (3) the explanation of model predictions for a particular screenee.