Table 1.

Example extensions to the Hussey and Hughes model for stepped wedge cluster randomized trials in cross-sectional and closed-cohort designs; all models assume a continuous outcome and an identity link function.

Design	Extension	Feature	Example references
Cross-sectional	Nested Exchangeable*	Distinguish between within-period and between-period ICCs	Hooper et al.;56 Girling and Hemming38
	Exponential Decay*	Allow the between-period ICC to decay at an exponential rate over time	Kasza et al.57 Kasza and Forbes61
	Random Intervention	Include random cluster-specific intervention effects, and ICC depends on intervention status	Hughes et al.55 Hemming et al.47
	Random Coefficient	Include random cluster-specific time slopes; ICC tends to be an increasing function of distance in time	Murray et al.58
Closed-cohort	Basic	Include cluster-level and subject-level random effects to separate between-individual ICC and within-individual ICC	Baio et al.65
	Block Exchangeable*	Include three random effects to distinguish between within-period ICC, between-period ICC, and within-individual ICC	Hooper et al.56 Girling and Hemming38
	Proportional Decay*	Allow the between-period ICC and within-individual ICC to decay over time at the same exponential rate	Li60
	Random Intervention	Include random cluster-specific intervention effects, and ICC depends on intervention status	Kasza et al.27

Note: The choice of terminology with the ‘*’ symbol is based on the following. The nested exchangeable correlation model was defined in Teerenstra et al.⁵⁹ and Li et al.⁶⁰ in the context of three-level CRTs and crossover CRTs. Li et al.³⁴ introduced the block exchangeable correlation model for closed-cohort design and pointed out the nested exchangeable correlation model is a special case. The exponential decay correlation model is proposed in Kasza et al. and Kasza and Forbes.^57,61 The proportional decay correlation model is introduced in Li⁶⁰ and dates back to the earlier work of Liu et al.⁷² in the context of longitudinal parallel CRTs.