  Large observational clinical datasets become increasingly available for
mining associations between various disease traits and administered therapy.
These datasets can be considered as representations of the landscape of all
possible disease conditions, in which a concrete pathology develops through a
number of stereotypical routes, characterized by `points of no return' and
`final states' (such as lethal or recovery states). Extracting this information
directly from the data remains challenging, especially in the case of
synchronic (with a short-term follow up) observations. Here we suggest a
semi-supervised methodology for the analysis of large clinical datasets,
characterized by mixed data types and missing values, through modeling the
geometrical data structure as a bouquet of bifurcating clinical trajectories.
The methodology is based on application of elastic principal graphs which can
address simultaneously the tasks of dimensionality reduction, data
visualization, clustering, feature selection and quantifying the geodesic
distances (pseudotime) in partially ordered sequences of observations. The
methodology allows positioning a patient on a particular clinical trajectory
(pathological scenario) and characterizing the degree of progression along it
with a qualitative estimate of the uncertainty of the prognosis. Overall, our
pseudo-time quantification-based approach gives a possibility to apply the
methods developed for dynamical disease phenotyping and illness trajectory
analysis (diachronic data analysis) to synchronic observational data. We
developed a tool $ClinTrajan$ for clinical trajectory analysis implemented in
Python programming language. We test the methodology in two large publicly
available datasets: myocardial infarction complications and readmission of
diabetic patients data.
