path length between nodes j and j ′ is d$_{ijj}$ ′ , where d$_{ijj}$ ′ := ∞ when no path exists between the two nodes. The shortest path length from the closest node affected at baseline is min$_{j}$ ′ d$_{ijj}$ ′ , with inverse (min$_{j}$ ′ d$_{ijj}$ ′ ) − $^{1}$. The sum of the inverse path lengths to node j is ∑ j ′ ( d$_{ijj}$ ′ ) − $^{1}$. While some of these metrics would be difficult to determine in practice given limited knowledge about a network or process outcomes, we examine whether their inclusion in the analysis yields strong enough improvements to warrant the efforts necessary to gather the required data. Table 1 summarizes these network features. Table 1: A collection of summaries of the contact network and contagion status at baseline. 2.2 GEE-based estimation of the effect of an exposure on an outcome The generalized estimating equations (GEE) approach provides a general approach for analyzing correlated outcomes that: i) is more robust to variance structure misspecification, ii) relies less on parametric assumptions than the standard likelihood methods, and iii) provides population level conclusions on the effect of an exposure on an outcome. This section reviews a modified version of the doubly-robust augmented GEE described in 8 and describes incorporation of contact network structure in the estimation process. Consider an observational study of a contagion process that consists of i = 1 , ..., m clusters (each cluster can be represented by one large network or a collection of smaller networks) with j = 1 , ..., n$_{i}$ individuals per cluster, and $^{∑}$$_{i}$n$_{i}$ = N is the total number of individuals in the study. The binary outcome for individual j in cluster i , Y$_{ij}$ , is 1 if the individual is affected by the process by the end of the study, otherwise Y$_{ij}$ = 0 . Y$_{i}$ = ( Y$_{i}$$_{1}$, ..., Y$_{in}$$_{i}$ ) ⊤ denotes the associated vector of outcomes in cluster i . We assume there is no mixing across clusters and assume the clusters to be independent. We consider a setting where some of the clusters are exposed to a specific treatment, intervention or exposure while others are not; and we use A$_{i}$ = a to denote an exposure indicator such that a = 1 for the exposed clusters and a = 0 for the unexposed (control) 4 None: No adjustment term X $^{(1)}$: Degree k$_{ij}$ X $^{(2)}$: Mean neighbor degree ∑ j ′ A$_{ijj}$ ′ k$_{ij}$ k$_{ij}$ X $^{(3)}$: Assortativity See Text (Page 4) X $^{(4)}$: Member of connected block $_{I}$( b$_{ij}$ ∈ { 1 , 5 } ) X $^{(5)}$: Size of largest component ∑ j $_{I}$( c$_{ij}$ = 1) X $^{(6)}$: Mean component size n$_{i}$/C$_{i}$ X $^{(7)}$: Number of components C$_{i}$ X $^{(8)}$: Size of node’s component ∑ j ′ $_{I}$( c$_{ij}$ = c$_{ij}$ ′ ) X $^{(9)}$: Total neighbor infections at baseline ∑ j $_{′}$e$_{ijj}$ ′ I$_{ij}$ ′ (0) X $^{(10)}$: Total node’s component infections at baseline ∑ j ′ $_{I}$( c$_{ij}$ = c$_{ij}$ ′ ) I$_{ij}$ ′ (0) X $^{(11)}$: 1/nearest affected path length at baseline (min$_{j}$ ′ d$_{ijj}$ ′ ) − 1 X $^{(12)}$: ∑ j ′ 1/path length to affected j at baseline ∑ j ′ ( d$_{ijj}$ ′ ) − 1