In our platform, we focus specifically on a subset of clinically relevant variables to enhance the interpretability and predictive performance of survival models. The variables considered include:
Aneuploidy score: Quantifies chromosomal instability within the tumor.
Birth from initial pathologic diagnosis date: Measures time from birth to diagnosis, relevant for age-related risk assessment.
Buffa hypoxia score: Assesses tumor hypoxia based on gene expression signatures.
Diagnosis age: Patient age at initial cancer diagnosis.
Disease-free (months): Duration of disease-free survival following treatment.
Fraction genome altered: Proportion of the genome affected by copy number alterations.
Last communication contact from initial pathologic diagnosis date: Captures follow-up duration.
MSI mantis score: Microsatellite instability assessment using MANTIS methodology.
TMB (nonsynonymous): Tumor mutational burden considering only nonsynonymous mutations.
Tumor break load: Measures chromosomal breakage events within tumor cells.
Winter hypoxia score: Further hypoxia scoring from an alternative validated gene signature.
These variables were carefully selected for their biological relevance and prognostic value, allowing our platform to generate robust survival analyses while ensuring interpretability for clinical research applications.
We applied our platform's analysis to the dataset described above and generated the following report.
Weibull Survival Model Interpretation
This model predicts survival time using multiple clinical and molecular covariates, based on a parametric Weibull distribution.
Variables in the Model
The model includes the following covariates related to patient survival:
Aneuploidy score
Birth from initial pathologic diagnosis date
Buffa hypoxia score
Diagnosis age
Disease free (months)
Fraction genome altered
Last communication contact from initial pathologic diagnosis date
MSI mantis score
MSIsensor score
Months of disease-specific survival
Mutation count
Progress free survival (months)
Ragnum hypoxia score
TMB (nonsynonymous)
Tumor break load
Winter hypoxia score
Additionally, intercept terms for lambda_ (scale) and rho_ (shape) parameters define the Weibull distribution.
Coefficients (β) and Hazard Ratios (HR)
Interpretation:
Coefficients (β): Effect size on the log-scale parameter (lambda). Negative β implies longer survival (lower hazard), positive implies higher hazard.
Hazard Ratios (HR = exp(β)): Multiplicative effect on hazard per unit increase in covariate.
Each unit increase lowers hazard by ~0.27%, protective effect
TMB (nonsynonymous)
0.076
1.079
1.032 to 1.128
0.0008
Each unit increase raises hazard by 7.9%, increased risk
Last communication contact
0.000366
1.00037
1.00023 to 1.00050
< 1.5e-07
Later contact associated with slightly increased hazard
Months of disease-specific survival
Positive (small)
~>1
Does not include 1
~0.0014
Small but significant increase in hazard
Progress free survival (months)
Positive (small)
~>1
Does not include 1
~0.0010
Small but significant increase in hazard
Most other variables have coefficients near zero, HR near 1, and are not statistically significant.
Statistical Significance & Confidence Intervals
Significance threshold: α = 0.05
Significant variables have p < 0.05 and HR 95% CI excluding 1.
Non-significant variables have 95% CI including 1, indicating no clear effect.
Weibull Shape and Scale Parameters
Parameter
Coefficient (β)
exp(β)
Std. Error
p-value
Interpretation
rho_ (shape)
1.618
5.04
0.0905
<< 0.001
Shape > 1 indicates increasing hazard over time
lambda_ (scale)
3.15
23.34
0.275
<< 0.001
Controls timing/spread of survival; higher means longer survival
Model Fit Metrics
Log-likelihood ratio test: 258.19 (p ≈ 1.08 × 10-45, df=16) — model fits significantly better than null.
AIC: 937.96
BIC: 915.49
Lower AIC/BIC indicates better fit; useful for model comparison.
Residuals & Model Diagnostics
No residual analyses (e.g., Cox-Snell, Martingale, Schoenfeld residuals) or proportional hazards tests are reported, limiting assessment of model assumptions and fit quality.
Concordance Index (C-index)
Value: 0.787 (Good)
This indicates good predictive accuracy; model discriminates poorly between patients by survival risk (note: c-index ranges 0.5 [random] to 1.0 [perfect]).
Proportional Hazards Assumption
Not directly applicable to Weibull parametric models as in Cox models; no tests available.
Linearity & Time-Dependent Effects
No information or tests provided for linearity of covariates or time-dependent effects.
Median and Mean Survival Times
Mean survival time: 53.06 months
Median survival time: 53.71 months
Survival & Hazard Functions
The Weibull distribution defines:
Survival function S(t): Probability of survival beyond time t
Hazard function h(t): Instantaneous risk of event at time t
Cumulative hazard H(t): Total accumulated risk up to time t
Survival function S(t) over timeHazard function h(t) over time
Using the Model for Prediction on New Data
To estimate survival probabilities or hazard for a new patient:
Collect covariate values matching the model variables.
Calculate the linear predictor: LP = β1x1 + β2x2 + ... + βkxk
Compute the scale parameter for Weibull: λ = exp(LP + intercept_lambda)
Use the shape parameter ρ = exp(intercept_rho) (assumed constant)
Derive survival probability at time t: S(t) = exp[-(λ × t)ρ]
Hazard at time t is h(t) = λ × ρ × (λ × t)ρ - 1
These calculations allow prediction of survival and hazard curves personalized by patient covariates.
Summary Interpretation
The model integrates clinical and molecular features to predict survival time with a Weibull parametric approach.
Significant protective effect of mutation count, and increased risk with higher TMB, last communication contact time, and survival durations.
Shape parameter >1 indicates hazard increases over time.
Model fit is statistically strong and predictive discrimination is good (c-index 0.787).
Most variables show no significant effect, supported by confidence intervals and p-values.
Survival and hazard functions are visualized externally.
Lack of residual diagnostics and assumption tests limits comprehensive model evaluation.
Median and mean survival times are approximately 53–54 months under this model.
For deeper interpretation of specific variables or further analyses, additional data or diagnostics would be needed.
