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Deep understanding of (C-index) evaluation measure for better model
Lets start with three patients groups:
Group A
Group B
Group C
For each patient, we will predict risk score (higher score means higher risk of early event).
Step 1: Understanding Concordance Index
The Concordance Index (C-index) evaluate that how well the model ranks survival times.
Understand with sample data:
Group A has 3 patients with actual survival times and predicted risk scores:
Patient Actual Survival Time Predicted Risk Score
P1 5 months 0.8
P2 3 months 0.9
P3 10 months 0.2
Comparable pairs:
(P1, P2): P2 has a shorter survival time and a higher risk score → Concordant ✅
(P1, P3): P3 has a longer survival time and a lower risk score → Concordant ✅
(P2, P3): P3 has a longer survival time and a lower risk score → Concordant ✅
Total pairs = 3
Total concordant pairs = 3
C-index for Group A = Concordant pairs/Total pairs= 3/3 = 1.0
Step 2: Calculate C-index for All Groups
Repeat the process for all groups. For now we can assume:
Group A: C-index = 1.0
Group B: C-index = 0.8
Group C: C-index = 0.6
Step 3: Stratified Concordance Index
The Stratified Concordance Index combines the C-index scores of all groups and focusing on the following:
Average performance across groups (mean of C-indices).
Consistency across groups (low standard deviation of C-indices).
Formula:
Stratified C-index = Mean(C-index scores) - Standard Deviation(C-index scores)
Calculate the mean:
Mean=1.0 + 0.8 + 0.6/3 = 0.8
Calculate the standard deviation:
Standard Deviation= sqrt((1.0-0.8)^2 + (0.8-0.8)^2 + (0.6-0.8)^/3) = 0.16
Stratified C-index:
Stratified C-index = 0.8 - 0.16 = 0.64
Step 4: Interpret the Results
A high Stratified C-index means:
The model predicts well overall (high mean C-index).
Lets start with three patients groups:
Group A
Group B
Group C
For each patient, we will predict risk score (higher score means higher risk of early event).
Step 1: Understanding Concordance Index
The Concordance Index (C-index) evaluate that how well the model ranks survival times.
Understand with sample data:
Group A has 3 patients with actual survival times and predicted risk scores:
Patient Actual Survival Time Predicted Risk Score
P1 5 months 0.8
P2 3 months 0.9
P3 10 months 0.2
Comparable pairs:
(P1, P2): P2 has a shorter survival time and a higher risk score → Concordant ✅
(P1, P3): P3 has a longer survival time and a lower risk score → Concordant ✅
(P2, P3): P3 has a longer survival time and a lower risk score → Concordant ✅
Total pairs = 3
Total concordant pairs = 3
C-index for Group A = Concordant pairs/Total pairs= 3/3 = 1.0
Step 2: Calculate C-index for All Groups
Repeat the process for all groups. For now we can assume:
Group A: C-index = 1.0
Group B: C-index = 0.8
Group C: C-index = 0.6
Step 3: Stratified Concordance Index
The Stratified Concordance Index combines the C-index scores of all groups and focusing on the following:
Average performance across groups (mean of C-indices).
Consistency across groups (low standard deviation of C-indices).
Formula:
Stratified C-index = Mean(C-index scores) - Standard Deviation(C-index scores)
Calculate the mean:
Mean=1.0 + 0.8 + 0.6/3 = 0.8
Calculate the standard deviation:
Standard Deviation= sqrt((1.0-0.8)^2 + (0.8-0.8)^2 + (0.6-0.8)^/3) = 0.16
Stratified C-index:
Stratified C-index = 0.8 - 0.16 = 0.64
Step 4: Interpret the Results
A high Stratified C-index means:
The model predicts well overall (high mean C-index).
