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.