Cumulative disease progression models for cross‐sectional data: A review and comparison

A better understanding of disease progression is beneficial for early diagnosis and appropriate individual therapy. Many different approaches for statistical modelling of cumulative disease progression have been proposed in the literature, including simple path models up to complex restricted Bayesian networks. Important fields of application are diseases such as cancer and HIV. Tumour progression is measured by means of chromosome aberrations, whereas people infected with HIV develop drug resistances because of genetic changes of the HI‐virus. These two very different diseases have typical courses of disease progression, which can be modelled partly by consecutive and partly by independent steps. This paper gives an overview of the different progression models and points out their advantages and drawbacks. Different models are compared via simulations to analyse how they work if some of their assumptions are violated. In a simulation study, we evaluate how models perform in terms of fitting induced multivariate probability distributions and topological relationships. We often find that the true model class used for generating data is outperformed by either a less or a more complex model class. The more flexible conjunctive Bayesian networks can be used to fit oncogenetic trees, whereas mixtures of oncogenetic trees with three tree components can be well fitted by mixture models with only two tree components.