Cross random effects negative binomial model

[BayzidurRahman]

Hi,

I have data from Stepped wedge cluster RCT with 2 level clustering. The outcome is error rate per patients (number of error/total number of orders). Patients are clustered withing wards and measurements are clustered within patients. one patient can readmit into different wards during the study period which makes the patient level random effects cross-classified.  With the following variables, can anyone suggest me the correct model specification with cross-random effects?

ward: unique ward id (level 3)

mrn: unique patient id (levl 2)

error: total number of error (level 1)

totalorder: total number of orders (the offset)

int: intervention (binary variable)

time: time of entering the cluster into the intervention group