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Table 3 Description of variables used in simulation study 1

From: Independence estimators for re-randomisation trials in multi-episode settings: a simulation study

Variable Description Method of generation
Yij Continuous outcome for patient i in episode j Generated based on model [5]
Zij Treatment allocation (0 = control, 1 = intervention) for patient i in episode j Bernoulli random variable with probability of 0.5 (implying simple randomisation
\({X}_{e{p}_{ij}}\) Indicator for episode 2 NA
\({X}_{M_i}\) Indicator for number of episodes patient experiences (0 = 1 episode, 1 = 2 episodes); equivalent to Mi NA
Zi, j − 1 Treatment allocation for patient i in episode j − 1; equal to 0 for episode 1 NA
\({X}_{P{L}_i}\) Unobserved patient-level binary covariate, which is constant across episodes Bernoulli random variable with probability of 0.5
\({X}_{E{L}_{ij}}\) Unobserved episode-level binary covariate, which can vary across episodes Bernoulli random variable with probability of 0.5
μi Random intercept for patient i \(\sim N\left(0,{\upsigma}_{\upmu}^2\right)\)
εij Random error term for episode j in patient i \(\sim N\left(0,{\upsigma}_{\upvarepsilon}^2\right)\)