In the main article groups of patients are compared. For each patient a linear regression model is used to characterize the change in urinary oestriol excretion from the 26th week of pregnancy.
Expressed in statistical terms the model is
where ij is the logarithm of the value of the urinary oestriol excretion and xij the number of weeks for patient number i measurement number j. αi and βi are constants and εij are random variables with the same variance σ2.
The α's and β's are found to vary significantly from patient to patient within the groups to be compared. The question then arises: How should the β's in the different groups be compared?
For each patient an estimate bi of βi is calculated as
The group is characterised by the weighted average of the bi's
If the β's are supposed to vary at random