The Markov model
In non-static situations, such as in chronic diseases or malignancies, health states of the patients may alter depending on imaging and treatment options. In such situations, a Markov model can be used to reflect alterations in health states during the period of CEA. In a Markov model, the clinical situation is described in terms of the conditions that patients can be in (‘health states’), how they can move in such states (‘transitions’), and how likely such moves are (‘transition probabilities’) [25]. The time frame of the analysis can be chosen as suitable for the underlying medical question with respect to the available literature. For CEA of screening imaging tests and follow-up imaging in cancer, a long frame over several years or lifetime may be adequate. For example, in a Markov model used for the decision problem on optimal follow-up imaging after treated NSCLC, patients can be in the health states “no evidence of disease”, “progressive disease” or “dead” (Fig. 3). Progressive disease can be detected (i.e., the true positive test results) or not (the false negative test results). No evidence of disease represents the paths in the decision tree with true negatives and the false positives test results. At each time point of follow-up imaging, patients stay in the state they are, or move to different states, e.g., from no evidence of disease to progressive disease (and vice versa) or from no evidence of disease or progressive disease to dead. Please note that in this example, the Markov model directly follows on the health outcomes in the decision tree. It is common practice in imaging studies to combine a decision tree for the short-term diagnostic accuracy and treatment decision with a Markov model for the longer-term consequences of the disease.
Fig. 3 Schematic example of a Markov model