Abstract
Consider a study in which we collect data on N units connected by a social network. For each unit i = 1, …, N, we record baseline covariate (W i ), exposure (A i ), and outcome of interest (Y i ) information. We also observe the set F i that consists of the units in {1, …, N}∖{i} that are connected to and could influence the unit i. The set F i constitutes “i’s friends”. We allow | F i |, the total number of friends of i, to vary in i. In addition, we assume that | F i | goes to zero when scaled by 1∕N. For example, F i could represent the set of all the friends of i in a social network, or the set of all of i’s sexual partners in a study of the effects of early HIV treatment initiation.
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Notes
- 1.
This assumption will be also referred to as the weak dependence of W.
- 2.
Note that we have previously defined F i ∗ as F i ∪{ i}.
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Sofrygin, O., Ogburn, E.L., van der Laan, M.J. (2018). Single Time Point Interventions in Network-Dependent Data. In: Targeted Learning in Data Science. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-65304-4_21
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