Survival Analysis

Survival analysis evaluates whether synthetic data preserves clinically meaningful survival patterns by comparing Overall Survival (OS) and Progression-Free Survival (PFS) between treatment responders and non-responders.

C-index Score

The C-index score measures similarity based on the absolute difference between original and synthetic concordance indices from Cox proportional hazards models:

\[C_\text{score}^\text{OS} = 1 - \left|C_\text{original}^\text{OS} - C_\text{synthetic}^\text{OS}\right|\]

\[C_\text{score}^\text{PFS} = 1 - \left|C_\text{original}^\text{PFS} - C_\text{synthetic}^\text{PFS}\right|\]

\[C_\text{score}^\text{final} = \frac{C_\text{score}^\text{OS} + C_\text{score}^\text{PFS}}{2}\]

Higher values indicate greater agreement in survival discrimination. Kaplan-Meier survival curves are compared using the log-rank test.

Code Example

from synomicsbench.metrics.narrow_utility.survival_analysis import  SurvivalEvaluator

# Define dataset dictionary
survival_cols = ["OS", "OS_CNSR", "Benefit"]
original_data = pd.read_csv("original_data.csv")
synthetic_data = pd.read_csv("synthetic_data.csv")

dataset_dict = {
    "Origin": original_data[survival_cols],
    "Synthetic_data": synthetic_data[survival_cols],
}



# Define phenotype comparison
phenotype = {"Benefit": ["CB", "NCB"]}

# Define evaluator
evaluator = SurvivalEvaluator(
    datasets_dict=dataset_dict,
    phenotype=phenotype,
    time_target="OS",
    event_target="OS_CNSR",
    original_name="Origin"
)

# Compute C-index similarity scores with respect to the original data
summary_df = evaluator.compute_survival_metrics()
scored_df = evaluator.compute_cindex_scores(original_name="Origin")

# Extract the C-index score
synthetic_score = scored_df.loc[scored_df["Dataset"] == "Synthetic_data", "C-index_score"].values[0]
print(f"Synthetic Score: {synthetic_score:.4f}")

Kaplan-Meier Curve Visualization

from synomicsbench.metrics.narrow_utility.survival_analysis import  SurvivalEvaluator

# Define datasets — the key for the reference must match original_name
datasets = {
    "Origin": real_df,
    "Gaussian Copula": gc_df,
    "Avatars K5": avatars_k5_df,
    "Avatars K10": avatars_k10_df,
    "CTGAN": ctgan_df,
    "Synthpop": synthpop_df,
    "TVAE": tvae_df,
}

phenotype = {"Benefit": ["CB", "NCB"]}

evaluator = SurvivalEvaluator(
    datasets_dict=datasets,
    phenotype=phenotype,
    time_target="OS",
    event_target="OS_CNSR",
    original_name="Origin"
)
evaluator.compute_survival_metrics()
fig, summary = evaluator.plot_grid(
    save_dir="survival_analysis_results/"
)

# Each panel shows: Kaplan-Meier curves, log-rank P value, C-index

Survival signal preservation across SDG methods. Log-rank P values and C-indices are annotated in each panel.