name: bio-machine-learning-survival-analysis description: Builds and validates predictive time-to-event models on clinical and omics data with penalized Cox, random survival forests, gradient-boosted and deep survival models, and prediction-grade evaluation (Uno's C, time-dependent AUC, integrated Brier, calibration, competing risks). Use when building an individualized risk predictor or prognostic omics signature, choosing a survival model, or evaluating one beyond the C-index. For Kaplan-Meier, log-rank, and classical Cox hazard-ratio inference in a trial see clinical-biostatistics/survival-analysis. origin: openai4s category: bioskills/machine-learning metadata: tool_type: python primary_tool: scikit-survival third_party: name: GPTomics/bioSkills repository: https://github.com/GPTomics/bioSkills commit: d91ed3d563019e649dc854c56ccd62551359488a license: MIT
Reference examples tested with: scikit-survival 0.22+, lifelines 0.30+, numpy 1.26+, pandas 2.2+ (pycox 0.3+ for deep models).
Before using code patterns, verify installed versions match. If versions differ:
- Python: pip show <package> then help(module.function) to check signatures
scikit-survival requires the target y to be a structured array with a boolean event field and a float time field; its IPCW metrics need the training y first. lifelines concordance_index expects higher-score = longer-survival (negate the partial hazard). If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.
"Build a validated risk model from time-to-event data" -> Fit a penalized Cox or ensemble survival model, then evaluate with censoring-robust discrimination AND calibration, not the C-index alone.
- Penalized Cox / RSF / boosting: sksurv.linear_model.CoxnetSurvivalAnalysis, sksurv.ensemble.RandomSurvivalForest
- Evaluation: concordance_index_ipcw, cumulative_dynamic_auc, integrated_brier_score
- Deep survival (large n): pycox DeepSurv / DeepHit
The C-index is necessary but radically insufficient, for three reasons most papers miss. It is censoring-distribution-dependent: Harrell's C is biased upward under heavy censoring and gives different values on cohorts that differ only in follow-up -- report Uno's IPCW C with an explicit truncation tau instead (Uno 2011). It is invariant to any monotone transform of the risk score, so a model can have an excellent C and be wildly miscalibrated and clinically harmful -- C measures ranking, not the correctness of the predicted probabilities. And it is insensitive: adding a genuinely useful marker barely moves it, which is exactly why reclassification metrics (NRI/IDI) were invented. Decision-grade evaluation is Uno's C(tau) + time-dependent AUC(t) + integrated Brier vs a Kaplan-Meier baseline + calibration curves, all on honestly held-out or external data.
Two survival cultures, two skills; mixing them is the most common authoring error. Resolve every overlap by one question: is the goal to estimate and test a treatment effect in a (pre-specified) study, or to build and validate a risk-prediction model?
| This skill (machine-learning) -- prediction | clinical-biostatistics/survival-analysis -- inference |
|---|---|
| Estimand is an individualized risk (survival curve, risk score, CIF) | Estimand is a treatment effect (hazard ratio with CI, p-value) |
| Penalized Cox, RSF, boosting, DeepSurv/DeepHit | Kaplan-Meier, log-rank, classical low-dimensional Cox |
| p>>n omics signatures; feature selection inside the resampling loop | Pre-specified analysis plan, FWER control, regulated trial |
| Judged by out-of-sample prediction (Uno's C, IBS, calibration) | Judged by validity of the HR and PH diagnostics (cox.zph) |
| PH is an assumption to relax (RSF/DeepHit do not assume it) | PH is a hypothesis whose violation invalidates the reported HR |
PH concepts, censoring definitions, and the Cox partial likelihood are foundational to both -- stated in clinical-biostatistics and referenced here. This skill's value begins at "I want a validated predictor."
| Model | Assumes PH? | Handles p>>n? | Competing risks? | Best when |
|---|---|---|---|---|
| Penalized Cox (elastic-net, coxnet) | Yes | Yes -- the omics workhorse; elastic-net handles correlated genes | Cause-specific by recoding | Sparse, interpretable, reproducible risk score; the default |
| Random Survival Forest | No | Yes (tune mtry/nodesize) | Yes (per-cause CIF) | Nonlinear/interaction effects, non-PH, moderate n |
| Gradient-boosted survival | Componentwise: yes (sparse); tree base: no | Yes (componentwise selects) | Via cause-specific | Boosting accuracy + sparsity, or relaxing PH with trees |
| Survival SVM | No (optimizes concordance) | Yes (kernel) | No | Pure ranking goals; gives a score, not a survival function |
| DeepSurv (pycox CoxPH) | Yes (NN replaces the linear predictor) | Needs large n | No | Large n, nonlinear main effects, PH plausible |
| DeepHit | No (discrete-time PMF) | Needs large n | Yes -- purpose-built | Large n + competing risks + non-PH |
| Cox-Time | No (time-dependent NN) | Needs large n | Discrete-hazard extensions | Large n, non-PH, flexible survival function |
Load-bearing empirical fact: on typical clinical-omics n, penalized Cox and RSF are very hard to beat; deep survival models usually only pull ahead at large n and/or with genuine non-PH or competing-risk structure. Start with elastic-net Cox and RSF baselines; escalate to deep models only if they demonstrably beat those on a held-out set.
| Scenario | Recommended approach | Why |
|---|---|---|
| Prognostic omics signature, p>>n | Elastic-net Cox (coxnet), selection inside nested CV | Sparse + correlated-gene grouping; the workhorse |
| Nonlinear/interaction effects, non-PH suspected | Random survival forest | Assumes no PH; captures interactions |
| Large n, suspected nonlinear main effects | DeepSurv, benchmarked against coxnet/RSF | Deep only earns its keep at large n |
| Competing events (death from other causes) | Fine-Gray (CIF) or DeepHit; report cause-specific too | 1-KM overestimates incidence; sHR is not the rate effect |
| Dynamic prediction with updating biomarkers | Landmarking | Internal time-varying covariates cannot be plugged into the future |
| Evaluating any survival model | Uno's C(tau) + AUC(t) + IBS-vs-KM + calibration | C-index alone is insufficient |
| KM curve, log-rank, or a trial hazard ratio | -> clinical-biostatistics/survival-analysis | Confirmatory inference, not prediction |
| Selecting the prognostic genes | -> machine-learning/biomarker-discovery (same irreproducibility) | Selection is its own discipline, inside the loop |
Goal: Fit a penalized Cox and an RSF baseline with the correct target format.
Approach: Build the structured y (boolean event, float time), fit coxnet with an elastic-net mix and a baseline model for survival functions, and an RSF for nonlinear structure.
from sksurv.util import Surv
from sksurv.linear_model import CoxnetSurvivalAnalysis
from sksurv.ensemble import RandomSurvivalForest
# event MUST be bool, time float. Field order in from_arrays is (event, time).
y = Surv.from_arrays(event=df['status'].astype(bool), time=df['time'].astype(float))
# Elastic-net Cox: l1_ratio in (0,1]; fit_baseline_model=True enables predict_survival_function.
coxnet = CoxnetSurvivalAnalysis(l1_ratio=0.9, alpha_min_ratio=0.01, fit_baseline_model=True)
coxnet.fit(X_train, y_train)
rsf = RandomSurvivalForest(n_estimators=500, min_samples_leaf=15, max_features='sqrt', n_jobs=-1)
rsf.fit(X_train, y_train)
risk = coxnet.predict(X_test) # a risk score (higher = higher risk), NOT a probability
Goal: Report discrimination AND calibration on out-of-sample data, not the C-index alone.
Approach: Use Uno's IPCW C (truncated at tau), time-dependent AUC over a horizon grid, integrated Brier vs the KM baseline, and a calibration check at clinical horizons. IPCW metrics take the training y first to estimate the censoring distribution.
import numpy as np
from sksurv.metrics import concordance_index_ipcw, cumulative_dynamic_auc, integrated_brier_score
c_uno = concordance_index_ipcw(y_train, y_test, risk, tau=t_horizon)[0] # censoring-robust
times = np.percentile(y_test['time'][y_test['event']], np.linspace(10, 80, 15)) # inside follow-up
auc_t, mean_auc = cumulative_dynamic_auc(y_train, y_test, risk, times)
surv_fns = coxnet.predict_survival_function(X_test) # needs fit_baseline_model=True
surv_prob = np.vstack([[fn(t) for t in times] for fn in surv_fns])
ibs = integrated_brier_score(y_train, y_test, surv_prob, times) # compare against the KM-only IBS
print(f"Uno C: {c_uno:.3f} mean AUC(t): {mean_auc:.3f} IBS: {ibs:.3f}")
Calibration (the most decision-relevant, most-ignored axis): at a clinical horizon, plot predicted P(event by t) against the observed event probability (KM within risk groups, or a smooth calibration curve), and summarize with ICI/E50/E90 (Austin 2020) -- never Hosmer-Lemeshow. Calibration is what usually breaks on external validation even when discrimination is preserved.
A competing event precludes the event of interest (death from another cause precludes cause-specific death). Treating competing events as ordinary censoring is wrong: Kaplan-Meier overestimates cumulative incidence (1-KM >= the cumulative incidence function), so report the CIF (Aalen-Johansen), not 1-KM. Two hazards answer two questions: the cause-specific hazard (Cox censoring competing events) is the etiologic rate; the Fine-Gray subdistribution hazard maps to the CIF and is the prognostic/absolute-risk target -- but a Fine-Gray sHR is NOT the cause-specific HR and not an effect on the event rate (a covariate can raise a CIF purely by lowering the competing hazard). Since this skill is the prediction regime, the CIF is usually the target; report both models for a complete picture. DeepHit is purpose-built for competing risks at large n; evaluate with competing-risks-aware concordance (Wolbers 2009) and CIF-based Brier.
In p>>n, elastic-net Cox beats LASSO for stability with correlated genes (LASSO arbitrarily keeps one of a correlated group). The same irreproducibility as biomarker discovery applies: different cohorts select near-disjoint gene sets at similar performance, so the deliverable is the prediction, not the gene list. Feature selection and tuning MUST live inside the resampling loop -- nested CV with survival metrics (Uno's C, IBS) as the objective; selecting genes on the full data then CV-ing the final model is leakage producing grossly optimistic signatures. Optimism-correct internal validation via Harrell's bootstrap, validate externally, and report per TRIPOD+AI (Collins 2024).
| Threshold | Source | Rationale |
|---|---|---|
| Report Uno's C with explicit tau | Uno 2011 | Harrell's C is censoring-dependent and biased upward |
| Evaluate beyond C: AUC(t), IBS-vs-KM, calibration | Graf 1999; Austin 2020 | C is monotone-invariant and insensitive |
| CIF (not 1-KM) under competing risks | Putter 2007 | 1-KM overestimates incidence |
| Selection inside nested CV with survival metrics | field standard | Selection-before-CV leaks in p>>n |
| Start with penalized Cox / RSF baselines | neutral benchmarks | Deep models rarely beat them at clinical n |
| Error / symptom | Cause | Solution |
|---|---|---|
sksurv crash / silent misbehavior on y |
y not a structured (bool event, float time) array | Use Surv.from_arrays(event=..bool, time=..float) |
| IPCW metric wrong | Training y not passed first |
concordance_index_ipcw(y_train, y_test, risk, tau=) |
predict_survival_function errors |
coxnet without baseline | CoxnetSurvivalAnalysis(fit_baseline_model=True) |
| lifelines C reported as 1-C | partial hazard not negated | concordance_index(time, -predict_partial_hazard(df), event) |
| pycox survival nonsense | baseline hazard not computed | model.compute_baseline_hazards() before predict_surv_df |
times for AUC/IBS out of range |
beyond largest uncensored test time | Clip times to the observed follow-up |