Toward First Principle Medical Diagnostics: On the Importance of Disease-Disease and Sign-Sign Interactions

Abstract

A fundamental problem in medicine and biology is to assign states, e.g., healthy or diseased, to cells, organs or individuals. State assignment or making a diagnosis is often a nontrivial and challenging process and, with the advent of omics technologies, the diagnostic challenge is becoming more and more serious. The challenge lies not only in the increasing number of measured properties and dynamics of the system (e.g., cell or human body) but also in the co-evolution of multiple states and overlapping properties, and degeneracy of states. We develop, from first principles, a generic rational framework for state assignment in cell biology and medicine, and demonstrate its applicability with a few simple theoretical case studies from medical diagnostics. We show how disease-related statistical information can be used to build a comprehensive model that includes the relevant dependencies between clinical and laboratory findings (signs) and diseases. In particular, we include disease-disease and sign-sign interactions and study how one can infer the probability of a disease in a patient with given signs. We perform comparative analysis with simple benchmark models to check the performances of our models. We find that including interactions can significantly change the statistical importance of the signs and diseases. This first principles approach, as we show, facilitates the early diagnosis of disease by taking interactions into accounts, and enables the construction of consensus diagnostic flow charts. Additionally, we envision that our approach will find applications in systems biology, and in particular, in characterizing the phenome via the metabolome, the proteome, the transcriptome, and the genome.

Statistical physics of medical diagnostics: Study of a probabilistic model

“…A patient with disease pattern D and N O initial observed signs from the most probable symptoms S(D) is presented to the model for diagnosis; a disease pattern is chosen with a probability proportional to the weights W a of the present diseases in D. From [23] we know that the D1S1 and D2S1 models work well so long as the number of present diseases in D, denoted by |D|, is less than or equal to two; that is why we choose patients with a small number of diseases. As the figure shows, we obtain more accurate predictions as the parameter β increases.…”

“…Here the goal could be to reach the right diagnosis with a minimum number of the medical tests [23,24]. Thus, for the objective function we propose an increasing function of the polarizations (deviations from the neutral value) in the posterior disease probabilities.…”

“…In Refs. [23,24] we proposed probabilistic models of signs and diseases which can systematically take into account the effects of different types of sign-disease, disease-disease, and sign-sign interactions; the models are indeed graphical models of the sign and disease variables with a number of interaction factors, each one connecting a small subset of disease variables to the associated sign variables [22]. We introduced approximate inference and optimization algorithms to deal with such probabilistic models, and studied the effects of the model structure and the objective function on the performances of the diagnostic algorithms.…”

“…In Ref. [23], we showed that such interactions can significantly improve the accuracy of diagnosis without resorting to the exclusive diseases or the causal independence assumption.…”

“…We employ the mean-field approximation to study the possible changes in the (macroscopic) state of the system as the number of observed signs increases, and to estimate the sign and disease marginal probabilities [25]. For the objective function, we choose a function that favors the more polarizing tests, which result in disease probabilities that are closer to zero or one [23]. This could be useful especially when the gap between the most probable diseases and the other diseases is small.…”