Stratified initial values and change scores

A common question that is encountered in many studies is relating a change in a variable to the variable's initial value. It is well known that regressing the change on the initial value creates a spurious association and misleads the unwary. One attempt to cope with this problem has been to stratify that data based on the initial value. We show that this approach does not solve the problem. Theoretical and simulation results for independent normal and independent exponential random variables are provided.