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