get previous row's value and calculate new column pandas python

The way to get the previous is using the shift method:

In [11]: df1.change.shift(1)
Out[11]:
0          NaT
1   2014-03-08
2   2014-04-08
3   2014-05-08
4   2014-06-08
Name: change, dtype: datetime64[ns]

Now you can subtract these columns. Note: This is with 0.13.1 (datetime stuff has had a lot of work recently, so YMMV with older versions).

In [12]: df1.change.shift(1) - df1.change
Out[12]:
0        NaT
1   -31 days
2   -30 days
3   -31 days
4     0 days
Name: change, dtype: timedelta64[ns]

You can just apply this to each case/group:

In [13]: df.groupby('case')['change'].apply(lambda x: x.shift(1) - x)
Out[13]:
0        NaT
1   -31 days
2   -30 days
3   -31 days
4        NaT
dtype: timedelta64[ns]