Diseases are usually defined by a set of phenotypes that are associated with various pathobiological processes and their mutual interactions. Recently, there has been impressive progress in the understanding of various types of relations between disease phenotypes on the basis of common underlying molecular processes [1]. For example, two diseases can be related if there are genes that are associated to both of them [2–5]. It was shown that genes associated with the same disorder encode proteins that have a strong tendency to interact with each other [2]. Alternatively, one can think of two diseases being linked and related if their metabolic reactions within a cell share common enzymes [6]. Networks of protein–protein interactions [7, 8] have also been studied in the context of disease interactions [9, 10]. Such interaction networks for seemingly unrelated gene products were shown to be involved in a group of different diseases that share clinical and pathological phenotypes [10].

The large number of relations between myriads of cellular components implies that diseases are not a clearcut concept, but merely act as some sort of a 'discretization' in a vast and complicated phenotype space [1]. The structure of this space is typically studied through phenotypic comorbidity relations between human diseases. A comorbidity relation means that two diseases occur more frequently within a patient than what would be expected from the frequency of the individual diseases alone. This means that the joint probability for suffering two diseases i and j together is larger than the product of the probabilities of the individual diseases (prevalences), . A phenotypic human disease network (PHDN) consists of nodes representing the diseases and links that indicate comorbidity relations [11]. PHDNs have opened a novel way for doing medicine on a population-wide scale. For example it has been shown that there exist pronounced ethnic differences in the PHDNs of black and white males [11], and that PHDNs may be used to predict future sites of cancer metastasis [12]. Note that only a limited number of comorbidities can be explained by common genes, proteins, or metabolites [4, 13]. These differences with respect to the clinical reality of disease not only reflect our limited knowledge of cellular processes, they also underscore the role of environmental and epigenetic factors in disease progression. Another class of highly relevant networks in medicine are physiological networks that describe interactions of organ systems in the human organism [14, 15]. Changes in physiological function can be understood as topological transitions of such physiological networks [14, 15].

The age-dependence of PHDNs is hitherto unknown. Up to now, studies on US Medicare data have uncovered comorbidity relations in patients aged 65 and older [11, 13]. In this work we use a complete medical claims data set that contains information on all of the 8.3 million Austrians who received medical treatments in the years 2006 and 2007. The data set has been studied before to show a strong relationship between hunger in early life and the development of metabolic diseases in later life [16, 17]. Further, the nationwide age and gender dependence of diabetic complications was studied on the same data set [18].

For the first time, here we obtain a specific age-dependent PHDN of all statistically significant comorbidity relations that pose a substantial risk to male or female patients. We do so by proposing a new statistical method that leads to an age- and genderspecific disease–disease network. This network is obtained by combining the layers of a disease–disease multiplex network that consists of two layers that encode different phenomenological statistical measures for disease–disease relations. In the first layer links quantify the statistical significance of a comorbidity relation between two diseases through their correlation coefficient for binary data. The technical challenge here is that the prevalences of individual diseases can vary over several orders of magnitude, from affecting a few dozens to ten thousands of patients in the database [11]. This variability leads to biases in the correlations [19]. In particular, correlations between highly frequent and rare diseases tend to be underestimated [11, 19]. We therefore employ a multi-scale correction that accounts for this bias [20]. Links between nodes i and j in the second layer represent the risk of obtaining disease i, given that the patient already suffers from disease j. The first layer encodes information whether there exists a significant relation between two diseases; the second layer quantifies the risk that a disease relation poses to the patient.

We quantify the topological network properties of the so-obtained PHDN and show that they undergo massive structural and gender-specific changes across lifetime. We show that this analysis allows us to understand the progression of the health state of a population on a new level. Various stages of life are characterized by a unique combination of tightly interrelated disease clusters. With changing patient age, these clusters of diseases emerge, vanish, merge, or form local hubs. To a certain degree the concept of individual diseases becomes meaningless; what determines disease risks and the health state of a population more effectively is the strongly age-dependent mesoscopic organization of the PHDN in disease clusters.

Finally, we develop a simple network diffusion model for the population-wide dynamics of disease progressions. The model is based on the empirical age- and gender-specific comorbidity relations recorded in the PHDN. In particular, we show that using (i) the prevalence of all diseases within a specific age group and (ii) the age-dependent network structure of diseases for a given age, we can explain more than 85% of the variance of the appearances of new diseases within the next eight years in the total population. These results might provide important information for estimating the future burden of diseases in an aging society. The fraction of the EU population aged 65 or older will almost double by the year 2060 to 29.6% of the population, from 17.5% in 2011. The average age of the EU-27 citizen is estimated to be 47.6 years, compared to 41.2 years in 2011 [21]. However, quality of life is not determined by mere life expectancy per se, but by the number of years that are spent in healthy conditions. Healthy-life years differ greatly between men and women and across member states of the EU. Whereas life expectancy for women is 6.4y higher than for men, the number of healthy-life years for women is only 1.2y higher [22]. Aging of the population has severe implications for economic growth. Estimates suggest that by 2030 the EU-27 will experience a 14% decrease in workforce and a 7% decrease in consumer population due to aging [23]. It is therefore one of the big societal challenges to understand and anticipate to what extent the aging of the population will affect the future health state of a population.