I have the following data:
study_id       list_value
1              ['aaa', 'bbb']
1              ['aaa']
1              ['ccc']
2              ['ddd', 'eee', 'aaa']
2              np.NaN
2              ['zzz', 'aaa', 'bbb']
How can I convert it into something like this?
study_id       list_value
1              ['aaa', 'bbb', 'ccc']
1              ['aaa', 'bbb', 'ccc']
1              ['aaa', 'bbb', 'ccc']
2              ['aaa', 'bbb', 'ddd', 'eee', 'zzz'] 
2              ['aaa', 'bbb', 'ddd', 'eee', 'zzz'] 
2              ['aaa', 'bbb', 'ddd', 'eee', 'zzz'] # order of list item doesn't matter
                itertools.chain with GroupBy.transform
First, get rid of NaNs inside your column using a list comprehension (messy, I know, but this is the fastest way to do it).
df['list_value'] = [
    [] if not isinstance(x, list) else x for x in df.list_value
]
Next, group on study_id and flatten your lists inside GroupBy.transform and extract unique values using a set.
from itertools import chain
df['list_value'] = df.groupby('study_id').list_value.transform(
    lambda x: [list(set(chain.from_iterable(x)))]
)
As a last step, if you plan to mutate individual list items, you may want to do
df['list_value'] = [x[:] for x in df['list_value']]
If not, changes in one list will be reflected across all sublists in that group.
df
   study_id                 list_value
0         1            [aaa, ccc, bbb]
1         1            [aaa, ccc, bbb]
2         1            [aaa, ccc, bbb]
3         2  [bbb, ddd, eee, aaa, zzz]
4         2  [bbb, ddd, eee, aaa, zzz]
5         2  [bbb, ddd, eee, aaa, zzz]
                        defaultdictfrom collections import defaultdict
d = defaultdict(set)
for t in df.dropna(subset=['list_value']).itertuples():
    d[t.study_id] |= set(t.list_value)
df.assign(list_value=df.study_id.map(pd.Series(d).apply(sorted)))
   study_id       list_value
0         1        [a, b, c]
1         1        [a, b, c]
2         1        [a, b, c]
3         2  [a, b, d, e, z]
4         2  [a, b, d, e, z]
5         2  [a, b, d, e, z]
np.unique and other other trickinessMind you the results are ndarray
df.assign(
    list_value=df.study_id.map(
        df.set_index('study_id').list_value.dropna().sum(level=0).apply(np.unique)
    )
)
   study_id       list_value
0         1        [a, b, c]
1         1        [a, b, c]
2         1        [a, b, c]
3         2  [a, b, d, e, z]
4         2  [a, b, d, e, z]
5         2  [a, b, d, e, z]
We need to use sorted to get all the way there
df.assign(
    list_value=df.study_id.map(
        df.set_index('study_id').list_value.dropna()
          .sum(level=0).apply(np.unique).apply(sorted)
    )
)
df.assign(
    list_value=df.study_id.map(
        df.list_value.str.join('|').groupby(df.study_id).apply(
            lambda x: sorted(set('|'.join(x.dropna()).split('|')))
        )
    )
)
   study_id       list_value
0         1        [a, b, c]
1         1        [a, b, c]
2         1        [a, b, c]
3         2  [a, b, d, e, z]
4         2  [a, b, d, e, z]
5         2  [a, b, d, e, z]
df = pd.DataFrame(dict(
    study_id=[1, 1, 1, 2, 2, 2],
    list_value=[['a', 'b'], ['a'], ['c'], ['d', 'e', 'a'], np.nan, ['z', 'a', 'b']]
), columns=['study_id', 'list_value'])
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