Influence of wiring cost on the large-scale architecture of human cortical connectivity

In the past two decades some fundamental properties of cortical connectivity have been discovered: small-world structure, pronounced hierarchical and modular organisation, and strong core and rich-club structures. A common assumption when interpreting results of this kind is that the observed structural properties are present to enable the brain's function. However, the brain is also embedded into the limited space of the skull and its wiring has associated developmental and metabolic costs. These basic physical and economic aspects place separate, often conflicting, constraints on the brain's connectivity, which must be characterized in order to understand the true relationship between brain structure and function. To address this challenge, here we ask which, and to what extent, aspects of the structural organisation of the brain are conserved if we preserve specific spatial and topological properties of the brain but otherwise randomise its connectivity. We perform a comparative analysis of a connectivity map of the cortical connectome both on high- and low-resolutions utilising three different types of surrogate networks: spatially unconstrained (‘random’), connection length preserving (‘spatial’), and connection length optimised (‘reduced’) surrogates. We find that unconstrained randomisation markedly diminishes all investigated architectural properties of cortical connectivity. By contrast, spatial and reduced surrogates largely preserve most properties and, interestingly, often more so in the reduced surrogates. Specifically, our results suggest that the cortical network is less tightly integrated than its spatial constraints would allow, but more strongly segregated than its spatial constraints would necessitate. We additionally find that hierarchical organisation and rich-club structure of the cortical connectivity are largely preserved in spatial and reduced surrogates and hence may be partially attributable to cortical wiring constraints. In contrast, the high modularity and strong s-core of the high-resolution cortical network are significantly stronger than in the surrogates, underlining their potential functional relevance in the brain

Estimating Treatment Effects using Multiple Surrogates: The Role of the Surrogate Score and the Surrogate Index

Estimating the long-term effects of treatments is of interest in many fields. A common challenge in estimating such treatment effects is that long-term outcomes are unobserved in the time frame needed to make policy decisions. One approach to overcome this missing data problem is to analyze treatments effects on an intermediate outcome, often called a statistical surrogate, if it satisfies the condition that treatment and outcome are independent conditional on the statistical surrogate. The validity of the surrogacy condition is often controversial. Here we exploit that fact that in modern datasets, researchers often observe a large number, possibly hundreds or thousands, of intermediate outcomes, thought to lie on or close to the causal chain between the treatment and the long-term outcome of interest. Even if none of the individual proxies satisfies the statistical surrogacy criterion by itself, using multiple proxies can be useful in causal inference. We focus primarily on a setting with two samples, an experimental sample containing data about the treatment indicator and the surrogates and an observational sample containing information about the surrogates and the primary outcome. We state assumptions under which the average treatment effect be identified and estimated with a high-dimensional vector of proxies that collectively satisfy the surrogacy assumption, and derive the bias from violations of the surrogacy assumption, and show that even if the primary outcome is also observed in the experimental sample, there is still information to be gained from using surrogates