Table 3.

Possible approaches to account for the presence of clustering and heterogeneity

Model parameter and modelling choices to account for clustering	Modelled difference between studies	Modelling approaches
Intercept term
Common effect	All clusters share a common intercept term	GLM
Random effects	Clusters might have a different intercept term. The intercept terms are assumed to be related, and assumed to follow a certain (usually normal) distribution across clusters.	GLMM153 154
Fixed effects (stratification)	Clusters might have a different intercept term. The intercept terms are unrelated, and estimated separately for each cluster. Different groups of clusters might also have a different intercept term. Clusters could be stratified by a categorical (eg, secondary versus tertiary care) or continuous (eg, inpatient capacity) variable.	GLM including the cluster membership or the cluster level variable as an additional covariate154
Baseline hazard function
Common	All clusters share a common baseline hazard function	Survival model (eg, CPH model, RP model)
Random effects	All clusters share a common shape of the baseline hazard function, but its magnitude can vary across clusters. Briefly, the baseline hazard functions are assumed to be proportional across clusters, and their magnitude are assumed to follow a certain distribution.	Frailty models for survival data151 155-157 (eg, hierarchical CPH model)
Fixed effects	All clusters share a common shape of the baseline hazard function, but its magnitude might vary across clusters. Briefly, the baseline hazard functions are assumed to be proportional across clusters. The magnitude of the baseline hazard function is then estimated separately for each cluster.	Survival model where cluster membership is included as an additional covariate151
Stratification	All clusters might have a different baseline hazard function, which is estimated separately for each cluster. No relation exists between the baseline hazard function of different clusters.	Survival model where cluster membership is included as stratum variable151
Regression coefficient
Common effect	The magnitude of the regression coefficient is identical for all clusters.	Any regression or survival model
Random effects	The magnitude of the regression coefficient might vary across clusters. The regression coefficients are assumed to be related, and assumed to follow a certain (usually normal) distribution.	GLMM,153 154 frailty model for survival data
Fixed effects (Stratification)	The magnitude of the regression coefficient might vary across clusters. The regression coefficients are unrelated, and estimated separately for each cluster.	Regression or survival model with an interaction term between the predictor and cluster membership
Variance of the residual error
Common	The variance of the residual error is common across all clusters	GLM
Random effects	The variance of the residual error might vary across clusters. The error variances are assumed to be related, and assumed to follow a certain (usually inverse gamma) distribution across clusters.	GLMM154
Fixed effects (stratification)	The residual variance is estimated separately for each cluster, and is unrelated across clusters.	GLM with heteroscedasticity

GLM=generalised linear regression model; GLMM=generalised linear mixed regression model; CPH=Cox proportional hazards; RP=Royston-Parmar. More specific details about the implementation of each approach are available from the literature, which generally focus on binary outcomes,^{154 158} continuous outcomes,¹⁵⁴ time-to-event outcomes,^{151 154 159} and other outcomes.¹⁵⁴