Table 3.

Description of variables used in simulation study 1

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
$X_{e{p}_{\mathit{ij}}}$	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
$X_{E{L}_{\mathit{ij}}}$	Unobserved episode-level binary covariate, which can vary across episodes	Bernoulli random variable with probability of 0.5
μi	Random intercept for patient i	$\sim N\left(0,,,{\mathrm{\sigma }}_{\mathrm{\mu }}^2\right)$
εij	Random error term for episode j in patient i	$\sim N\left(0,,,{\mathrm{\sigma }}_{\mathrm{\epsilon }}^2\right)$