# Performance

`smoothstate` is intentionally specialized for smoothing state probabilities. The secondary-Cox implementation uses the same cloglog transformation, 3-knot restricted cubic spline, Efron tie handling, and ridge-penalized Cox model used by the current `rtichoke` implementation, while avoiding the general modeling overhead of `lifelines`.

On GitHub Actions with Python 3.12 and `lifelines` 0.30.3:

| Observations | `smoothstate` | `lifelines` | Speedup |
|-------------:|--------------:|------------:|--------:|
|        1,000 |      0.0021 s |    0.0820 s |   39.0× |
|       10,000 |      0.0212 s |    0.6103 s |   28.9× |
|      100,000 |      0.2353 s |    6.0746 s |   25.8× |

After matching `lifelines` penalty scaling, standardization, and baseline cumulative-hazard interpolation, predicted curves agree to numerical noise (maximum absolute differences around 1e-8 in the benchmark).


# Reference validation

The Cox core is also checked independently against R's `survival::coxph()` on the same deterministic validation data. The current GitHub Actions reference run gives:

| Comparison           | Maximum absolute difference |
|----------------------|----------------------------:|
| Cox coefficients     |                    2.28e-08 |
| Predicted risk curve |                    3.66e-09 |

This cross-language agreement provides an independent check of the unpenalized Cox implementation. Harrell's `rms::cph(Surv(...) ~ rcs(x, 3))` comparison is retained as a manual reference validation because installing the full `rms` dependency stack is unnecessarily expensive for routine CI.

These benchmarks are development checks rather than general claims about all Cox regression workloads. `smoothstate` is faster here because it solves a deliberately narrow problem with a one-predictor, two-column spline design matrix.