Table 1.

Terminology for Estimation of Individual and Disseminated Effects in Network-Randomized Studies

Recommended Term	Alternative Term(s)	Definition	Parameter of Interest	Network-Randomized Design Estimator
				Aggregatea	Stratifiedb
Individual	Direct	Effect on persons directly receiving an intervention beyond being in an intervention network	$E{\left[Y_{kij}\left(1,1\right)\right]}^{\mathrm{c}}-E{\left[Y_{kij}\left(0,1\right)\right]}^{\mathrm{d}}$	${\hat{\mathrm{\gamma }}}_3$	${\hat{\mathrm{\alpha }}}_1-{\hat{\mathrm{\beta }}}_1$
Disseminated	Indirect, social diffusion, diffusion of innovation, contamination, spillover	Effect on persons who received an intervention indirectly through the index participant	$E[Y_{kij}(0,1)]-E{[Y_{kij}(0,0)]}^{\mathrm{e}}$	${\hat{\mathrm{\gamma }}}_2$	${\hat{\mathrm{\beta }}}_1$
Composite	Total	Combined individual and disseminated effects; effect among index members in intervention networks contrasted with effect among network members in control networks	$E[Y_{kij}(1,1)]-E[Y_{kij}(0,0)]$	${\hat{\mathrm{\gamma }}}_2+{\hat{\mathrm{\gamma }}}_3$	${\hat{\mathrm{\alpha }}}_1$
Overallf	Crude	Effect among members of intervention networks contrasted with effect among members of control networks	$E{\left[Y_{kij}(\cdot ,1)\right]}^{\mathrm{g}}-E{\left[Y_{kij}(\cdot ,0)\right]}^{\mathrm{h}}$	${\hat{\mathrm{\beta }}}_1^{⁎}$

Abbreviation: GEE, generalized estimating equation.

^a For a network-randomized design, rate difference parameters of the individual, disseminated, and composite effects, respectively, can be estimated from an aggregate GEE model with an identity link and binomial variance: $E\left[Y_{kij}|R_{ki},X_k,{\mathit{Z}}_{ki}\right]={\mathrm{\gamma }}_0+{\mathrm{\gamma }}_1{R}_{ki}+{\mathrm{\gamma }}_2{X}_k+{\mathrm{\gamma }}_3{X}_k{R}_{ki}+{\mathrm{\gamma }}_4{\mathit{Z}}_{ki}.$

^b For a network-randomized design, rate difference parameters of the individual, disseminated, and composite effects, respectively, can be estimated from a stratified GEE model with an identity link and binomial variance: $E\left[Y_{kij}|R_{ki},X_k,{\mathit{Z}}_{ki}\right]=I\left(R_{ki}=0\right)\times ({\mathrm{\beta }}_0+{\mathrm{\beta }}_1{X}_k+{\mathrm{\beta }}_2{\mathit{Z}}_{ki})+I\left(R_{ki}=1\right)\times ({\mathrm{\alpha }}_0+{\mathrm{\alpha }}_1{X}_k+{\mathrm{\alpha }}_2{\mathit{Z}}_{ki}).$

^c$Y_{kij}\left(1,1\right)$ is the potential outcome for participant $i$ at visit $j$ in network $k$, if, possibly contrary to fact, this participant was an index member in a network randomized to the intervention group. $E\left[X\right]$ is the expectation of the random variable $X$.

^d$Y_{kij}\left(0,1\right)$ is the potential outcome for participant $i$ at visit $j$ in network $k$, if, possibly contrary to fact, this participant was a network member in a network randomized to the intervention group.

^e$Y_{kij}\left(0,0\right)$ is the potential outcome for participant $i$ at visit $j$ in network $k$, if, possibly contrary to fact, this participant was a network member in a network randomized to the control group.

^f For a network-randomized design, the parameter of the overall effect is estimated from a GEE model with an identity link and binomial variance: $E[Y_{kij}|X_k]={\mathrm{\beta }}_0^{\ast }+{\mathrm{\beta }}_1^{\ast }{X}_k.$

^g$Y_{kij}\left(\cdot ,1\right)$ is the potential outcome for participant $i$ at visit $j$ in network $k$, if, possibly contrary to fact, this participant was in a network randomized to the intervention group.

^h$Y_{kij}\left(\cdot ,0\right)$ is the potential outcome for participant $i$ at visit $j$ in network $k$, if, possibly contrary to fact, this participant was in a network randomized to the control group.