How to best estimate the coefficients of a confusion matrix in case of strong class imbalance?
There are many useful metrics which were introduced for evaluating the performance of classification methods for imbalanced data-sets. Some of them are Kappa, CEN, MCEN, MCC, DP, etc.

Disclaimer:

If you use python, PyCM module can help you to find and calculate these metrics.

Here is a simple code to get the recommended parameters from this module:

&gt;&gt;&gt; from pycm import *

&gt;&gt;&gt; cm = ConfusionMatrix(matrix={"Class1": {"Class1": 1, "Class2":2}, "Class2": {"Class1": 0, "Class2": 5}})  

&gt;&gt;&gt; print(cm.recommended_list)
["Kappa", "SOA1(Landis &amp; Koch)", "SOA2(Fleiss)", "SOA3(Altman)", "SOA4(Cicchetti)", "CEN", "MCEN", "MCC", "J", "Overall J", "Overall MCC", "Overall CEN", "Overall MCEN", "AUC", "AUCI", "G", "DP", "DPI", "GI"]

&gt;&gt;&gt; score = cm.Kappa