### Book

## Proceedings of the first Workshop on Data Analysis in Medicine (WDAM-2017)

This volume contains proceedings of the first Workshop on Data Analysis in Medicine held in May 2017 at the National Research University Higher School of Economics, Moscow. The volume contains one invited paper by Dr. Svetla Boytcheva, 6 regular contributions and 2 project proposals, carefully selected and reviewed by at least two reviewers from the international program commit- tee. The papers accepted for publication report on different aspects of analysis of medical data, among them treatment of data on particular diseases (Consoli- dated mathematical growth model of Breast Cancer CoMBreC, Artificial neural networks for prediction of final height in children with growth hormone deficiency), methods of data analysis (analysis of rare diseases, methods of machine learning and Big Data, subgroup discovery for treatment optimization), and instrumental tools (explanation-oriented methods of data analysis in medicine, information support features of the medical research process, modeling frame- work for medical data semantic transformations, radiology quality management and peer-review system). Organizers of the workshop would like to thank the reviewers for their careful work and all contributors and participants of the workshop.

Clinical informatics has been undergoing radical transformation. What are the causes and the drivers of this transformation? Which task can be solved well, and which cannot? How we should implement data analysis in clinical informatics projects in new reality? What is an importance of interpretability (comprehensibility) and explanation of data analysis methods in clinical informatics? At the workshop, we will try to answer some of such questions and setup a framework for later discussion.

Modern medicine aspire to improve the effectiveness of treatment for some diseases through, so called, personalized medicine. However, totally personalized medicine or personalized treatment of even one disease is a very ambitious goal. Subgroup analysis of patients is a preliminary step to the total personalization. Several completely different views on the principles and usefulness of subgroup analysis for treatment personalization exist. This paper is limited to data-driven subgroup discovery, when collected data analyzed for significant treatment-biomarker interactions in post-hoc manner, and presents a brief overview of key methods for this type of subgroup analysis.

This paper is devoted to mathematical modelling of the progression considering stages of breast cancer. Given the relation between primary tumor (PT) and metastases (MTS), the problem of discovering breast cancer (BC) process seems to be twofold: firstly, it is im- portant to describe the whole natural history of BC to understand the process as a whole; secondly, it is necessary to predict the period of a clinical MTS manifestation. In order to understand growth processes of BC on each stage CoMBreC was proposed as a new research tool. The CoMBreC is threefold: CoMPaS (stages I-II), CoM-III (stage III) and CoM-IV (stage IV). A new model rests on exponential growth model and complementing formulas. For the first time, it allows us to calculate different growth periods of PT and MTS in patients with/without lymph nodes MTS: 1) non-visible period for PT; 2) non- visible period for MTS; 3) visible period for MTS. Calculations via CoMBreC correspond to survival data considering stage of BC. It may help to improve predicting accuracy of BC process using an original mathematical model referred to CoMBreC and corresponding software. Consequently, thesis concentrated on: 1) modelling the whole natural history of PT and MTS in patients with/without lymph nodes MTS; 2) developing adequate and precise CoMBreC that reflects relations between PT and MTS; 3) analysing the CoMBreC scope of application. The CoMBreC was implemented to iOS application as a new predictive tool: 1) is a solid foundation to develop future studies of BC models; 2) does not require any expensive diagnostic tests; 3) is the first predictor of survival in breast cancer that makes forecast using only current patient data.

An outline of a few methods in an emerging field of data analysis, “data interpretation”, is given as pertaining to medical informatics and being parts of a general interpretation issue. Specifically, the following subjects are covered: measuring correlation between categories, conceptual clustering, and generalization and interpretation of empirically derived concepts in taxonomies. It will be shown that all of these can be put as parts of the same inquiry.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

The geographic information system (GIS) is based on the first and only Russian Imperial Census of 1897 and the First All-Union Census of the Soviet Union of 1926. The GIS features vector data (shapefiles) of allprovinces of the two states. For the 1897 census, there is information about linguistic, religious, and social estate groups. The part based on the 1926 census features nationality. Both shapefiles include information on gender, rural and urban population. The GIS allows for producing any necessary maps for individual studies of the period which require the administrative boundaries and demographic information.

It is well-known that the class of sets that can be computed by polynomial size circuits is equal to the class of sets that are polynomial time reducible to a sparse set. It is widely believed, but unfortunately up to now unproven, that there are sets in EXPNP, or even in EXP that are not computable by polynomial size circuits and hence are not reducible to a sparse set. In this paper we study this question in a more restricted setting: what is the computational complexity of sparse sets that are *selfreducible*? It follows from earlier work of Lozano and Torán (in: Mathematical systems theory, 1991) that EXPNP does not have sparse selfreducible hard sets. We define a natural version of selfreduction, tree-selfreducibility, and show that NEXP does not have sparse tree-selfreducible hard sets. We also construct an oracle relative to which all of EXP is reducible to a sparse tree-selfreducible set. These lower bounds are corollaries of more general results about the computational complexity of sparse sets that are selfreducible, and can be interpreted as super-polynomial circuit lower bounds for NEXP.