# Concordance index calculation

I am trying to calculate a customized concordance index for survival analysis. Below is my code. It runs well for small input dataframe but extremely slow on a dataframe with one million rows (>30min).

import pandas as pd

def c_index1(y_pred, events, times):
df = pd.DataFrame(data={'proba':y_pred, 'event':events, 'time':times})
n_total_correct = 0
n_total_comparable = 0
df = df.sort_values(by=['time'])
for i, row in df.iterrows():
if row['event'] == 1:
comparable_rows = df[(df['event'] == 0) & (df['time'] > row['time'])]
n_correct_rows = len(comparable_rows[comparable_rows['proba'] < row['proba']])
n_total_correct += n_correct_rows
n_total_comparable += len(comparable_rows)

return n_total_correct / n_total_comparable if n_total_comparable else None

c = c_index([0.1, 0.3, 0.67, 0.45, 0.56], [1.0,0.0,1.0,0.0,1.0], [3.1,4.5,6.7,5.2,3.4])
print(c) # print 0.5


For each row （in case it matters...）:

• If the event of the row is 1: retrieve all comparable rows whose

1. index is larger (avoid duplicate calculation),
2. event is 0, and
3. time is larger than the time of the current row. Out of the comparable rows, the rows whose probability is less than the current row are correct predictions.

I guess it is slow because of the for loop. How should I speed up it?

You will not get dramatic speedups untill you can vectorize the operations, but here are some tips already

# indexing before iterating

for i, row in df.iterrows():
if row['event'] == 1:


If you do

for i, row in df[df['event'] == 1].rows():


you will iterate over less rows.

# itertuples

generally, itertuples is faster than iterrows

# comparable_rows

for comparable_rows you are only interested in the proba and the length, so you might as well make this into a Series, or even better, a numpy array.

The test (df['event'] == 0) doesn't change during the iteration, so you can define a df2 = df[df['event'] == 0] outside of the loop

# n_correct_rows

instead of len(comparable_rows[comparable_rows['proba'] < row['proba']]), you can use the fact that True == 1 do (comparable_rows['proba'] < row.proba).sum()

# result

def c_index3(y_pred, events, times):
df = pd.DataFrame(data={'proba':y_pred, 'event':events, 'time':times})
n_total_correct = 0
n_total_comparable = 0
df = df.sort_values(by=['time'])
df2 = df.loc[df['event'] == 0]
for row in df[df['event'] == 1].itertuples():
comparable_rows = df2.loc[(df2['time'] > row.time), 'proba'].values
n_correct_rows = (comparable_rows < row.proba).sum()
n_total_correct += n_correct_rows
n_total_comparable += len(comparable_rows)

return n_total_correct / n_total_comparable if n_total_comparable else N


## timings

data = ([0.1, 0.3, 0.67, 0.45, 0.56], [1.0,0.0,1.0,0.0,1.0], [3.1,4.5,6.7,5.2,3.4])
%timeit c_index1(*data)

5.17 ms ± 33.6 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

%timeit c_index3(*data)

3.77 ms ± 160 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)