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. Author manuscript; available in PMC: 2023 May 1.
Published in final edited form as: World Neurosurg. 2022 May;161:323–330. doi: 10.1016/j.wneu.2021.10.136

Table 1.

Select summary of conditional and marginal model variants and associated statistical software for estimating model parameters.

CONDITIONAL MODELS
Model (random-effects structure) Feature SAS and R Software Package Reference
Random intercept model One common ICC PROC MIXED (SAS)
PROC GLIMMIX (SAS)
nlme (R)
lme4 (R)
Hussey and Hughes18
Random cluster-by-time interaction model Allows for different within-period and between-period ICCs PROC MIXED (SAS)
PROC GLIMMIX (SAS)
nlme (R)
lme4 (R)
Hooper et al.22
Girling and Hemming24
Random cluster-by-time interaction model (cohort designs) Allows for different within-period, between-period and repeated measures ICCs PROC MIXED (SAS)
PROC GLIMMIX (SAS)
nlme (R)
lme4 (R)
Hooper et al.22
Girling and Hemming24
Exponential decay model Between-period ICC decays exponentially over time PROC MIXED (SAS)
PROC HPMIXED (SAS)
Kasza et al.21
Kasza and Forbes73
Random intervention model Allows for heterogeneous treatment effect by clusters PROC MIXED (SAS)
PROC GLIMMIX (SAS)
nlme (R)
lme4 (R)
Hughes et al.26
Hemming et al.27
MARGINAL MODELS
Model (working correlation structure) Feature SAS and R Software Package Reference
Simple exchangeable structure One common ICC PROC GEE (SAS)
PROC GLIMMIX (SAS)
gee (R)
geepack (R)
geesmv (R)
Hussey and Hughes18
Thompson et al.46
Ford and Westgate47
Nested exchangeable structure Allows for within-period and between-period ICCs %GEECORR (SAS macro)
geepack (R)
geeCRT (R)
Li et al.36,37
Block exchangeable structure (cohort designs) Allows for within-period, between-period and repeated measures ICCs %GEECORR (SAS macro)
geepack (R)
geeCRT (R)
Li et al.36,37
Exponential decay structure Between-period ICC decays exponentially over time geeCRT (R) Li et al.37
Proportional decay structure (cohort designs) Both the between-period ICC and the repeated measured ICC decay exponentially over time Available on GitHub and Journal Website Li41
a

The code for implementing the proportional decay GEE model is available at https://github.com/lifanfrank/Li_Quasi-least-squares_SWD and https://onlinelibrary.wiley.com/doi/10.1002/sim.8415.