2014
DOI: 10.1515/jci-2013-0002
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Causal Inference for a Population of Causally Connected Units

Abstract: Suppose that we observe a population of causally connected units. On each unit at each time-point on a grid we observe a set of other units the unit is potentially connected with, and a unit-specific longitudinal data structure consisting of baseline and time-dependent covariates, a time-dependent treatment, and a final outcome of interest. The target quantity of interest is defined as the mean outcome for this group of units if the exposures of the units would be probabilistically assigned according to a know… Show more

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Cited by 56 publications
(35 citation statements)
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“…For further discussion of the impact of spatial dependence in cluster randomized trials, we refer the reader to [5660]. Recent work, relaxing these assumptions and considering a network of interacting units, is elaborated in van der Laan [61]. Under these assumptions, the conditional distribution of the observed data, given the baseline covariates of the candidate units, factorizes as rightP0(O1,,OnW1,,WN)=leftj=1n2{P0(Aj1,Aj2WN)P0(Yj1Aj1,Wj1)P0(Yj2Aj2,Wj2)}right=left0.5j=1n2{P0(Yj1Aj1,Wj1)P0(Yj2Aj2,Wj2)}right=leftP0(O1,,OnW1,,Wn)=P0n(OnWn) Throughout, P0n denotes the true conditional distribution of the observed data, given the baseline covariates of the n study units W n = ( W 1 , .…”
Section: The Estimation Problemmentioning
confidence: 99%
“…For further discussion of the impact of spatial dependence in cluster randomized trials, we refer the reader to [5660]. Recent work, relaxing these assumptions and considering a network of interacting units, is elaborated in van der Laan [61]. Under these assumptions, the conditional distribution of the observed data, given the baseline covariates of the candidate units, factorizes as rightP0(O1,,OnW1,,WN)=leftj=1n2{P0(Aj1,Aj2WN)P0(Yj1Aj1,Wj1)P0(Yj2Aj2,Wj2)}right=left0.5j=1n2{P0(Yj1Aj1,Wj1)P0(Yj2Aj2,Wj2)}right=leftP0(O1,,OnW1,,Wn)=P0n(OnWn) Throughout, P0n denotes the true conditional distribution of the observed data, given the baseline covariates of the n study units W n = ( W 1 , .…”
Section: The Estimation Problemmentioning
confidence: 99%
“…Basse and Feller (2018) study two-stage experiments in which households with multiple students are assigned to treatment or control. Other works that propose methods of handling interference include Ogburn and VanderWeele (2014), which maps out causal diagrams for interference; van der Laan (2014), which studies a targeted maximum likelihood estimator for the case where network connections and treatments possibly change over time; Choi (2017), which shows how confidence intervals can be constructed in the presence of monotone treatment effects; and Jagadeesan et al (2017), which studies designs for estimating the direct effect that strive to balance the network degrees of treated and control units.…”
Section: Introductionmentioning
confidence: 99%
“…These methods tend to rely on the number of distinct groups being relatively large, rather than relying on the sample sizes of the groups themselves being large (one exception is discussed in Liu and Hudgens ()). One general approach for relaxing the partial interference assumption uses data on the underlying network connecting the subjects (Toulis and Kao, ; van der Laan, ; Aronow and Samii, ; Ogburn et al, ; Sofrygin et al, ). The network is assumed to characterize the structure of the interference by specifying that only subjects who are connected in the network may interfere with one another.…”
Section: Introductionmentioning
confidence: 99%