Stability analysis of mixtures of mutagenetic trees

Mixture models of mutagenetic trees are evolutionary models that capture several pathways of ordered accumulation of genetic events observed in different subsets of patients. They were used to model HIV progression by accumulation of resistance mutations in the viral genome under drug pressure and cancer progression by accumulation of chromosomal aberrations in tumor cells. From the mixture models a genetic progression score (GPS) can be derived that estimates the genetic status of single patients according to the corresponding progression along the tree models. GPS values were shown to have predictive power for estimating drug resistance in HIV or the survival time in cancer. Still, the reliability of the exact values of such complex markers derived from graphical models can be questioned.

In a simulation study, we analyzed various aspects of the stability of estimated mutagenetic trees mixture models. It turned out that the induced probabilistic distributions and the tree topologies are recovered with high precision by an EM-like learning algorithm. However, only for models with just one major model component, also GPS values of single patients can be reliably estimated.

It is encouraging that the estimation process of mutagenetic trees mixture models can be performed with high confidence regarding induced probability distributions and the general shape of the tree topologies. For a model with only one major disease progression process, even genetic progression scores for single patients can be reliably estimated. However, for models with more than one relevant component, alternative measures should be introduced for estimating the stage of disease progression.