Конвертируйте оба столбца в дату, затем вычтите ее
import pandas as pd
df['date_of_admission'] = pd.to_datetime(df['date_of_admission']).dt.date
df['DOB'] = pd.to_datetime(df['DOB']).dt.date
df['age'] = ((df['date_of_admission']-df['DOB']).dt.days) //365
ВТОРОЙ ТЕСТ
#Now I have use DOB AND date_of_admission data from the question and it is working fine
df = pd.DataFrame(data={"DOB":['2000-05-07','1965-01-30','NaT'],
"date_of_admission":["2019-01-19 12:26:00","2019-03-21 02:23:12", "2018-11-02 18:30:10"]})
df['DOB'] = pd.to_datetime(df['DOB']).dt.date
df['date_of_admission'] = pd.to_datetime(df['date_of_admission']).dt.date
df['age'] = ((df['date_of_admission']-df['DOB']).dt.days) //365
РЕЗУЛЬТАТ:
DOB date_of_admission age
2000-05-07 2019-01-19 18.0
1965-01-30 2019-03-21 54.0
NaT 2018-11-02 NaN