Sampling in a cross-sectional stepped-wedge

Hi all,

I am aiming to simulate stepped-wedged data for a cross-sectional design (new set of individuals are sampled from each cluster at each step or cross-over point) according to the following model with a continuous outcome:

Y_{ijk =} b₀ + b_j + dX_ijk + u_i + e_ijk

Let Y_ijk denote the continuous outcome with clusters i = 1,…,I containing individual j = 1,...J. Define X_ijk as the intervention indicator wherein X_ijk = 1 if cluster k is receiving the intervention and X_ijk = 0 if cluster k is in the control condition. b₀ is defined as the fixed effect intercept, b_j fixed effect for time as a covariate, and dfixed intervention effect. Cluster-level random intercepts were assumed to follow a normal distribution with a mean of zero and known variance u_i ~ N (0, sd). Finally, residuals are normally distributed as well e_ijk ∼ N(0, sd).

How would I sample a new set of individuals from each cluster at each timepoint?

Any help is much appreciated.

Jack.

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