Interpreting the Cox PH model

Survival Analysis in Python

Shae Wang

Senior Data Scientist

The baseline hazards

Hazard ratio: how much hazard increases or decreases relative to baseline hazards.
Baseline hazards: the risk for individuals at the baseline levels of covariates.
- Baseline $\neq$ setting covariates to 0
- Baseline means setting covariates to their averages (median for lifelines)

The baseline functions

Baseline hazard function

model.baseline_hazard_.plot()
plt.show()

baseline_hazard

Baseline survival function

model.baseline_survival_.plot()
plt.show()

baseline_survival

Interpret the hazard ratio

Hazard ratio: $e^{coef}$, how much hazard changes relative to the average individual when covariates change.

	Calculation	Example
Coefficient	$x$	$0.405$
Hazard ratio	$e^x$	$e^{0.405}=1.5$
Hazards interpretation	$e^x-1$	$1.5-1 = 0.5$ -> 50% increase in hazards
Survival time interpretation	$\frac{1}{e^x}-1$	$\frac{1}{1.5}-1 = 0.67-1 = -0.23$ -> 23% decrease in survival time

Visualize the hazard ratio

.plot_partial_effects_on_outcome()

covariates (string or list): name(s) of the covariate(s) in the original dataset that we wish to vary.
- If there are multiple covariates, pass them in as a list.
values (1d or 2d iterable): values we wish the covariate to take on.
- If there are multiple covariates, pass the values as pairs/tuples of values.

Visualize the hazard ratio

The model has covariates A, B, C, and we wish to vary

A over 1, 2

B over 3, 4

model.plot_partial_effects_on_outcome(
    covariates=["A","B"],
    values=[[1,2],
            [3,4]]
)
plt.show()

wrong_plot_partial_effects_on_outcome

Wrong...

Visualize the hazard ratio

The model has covariates A, B, C, and we wish to vary

A over 1, 2

B over 3, 4

model.plot_partial_effects_on_outcome(
    covariates=["A","B"],
    values=[[1,3],
            [1,4],
            [2,3],
            [2,4]]
)
plt.show()

correct_plot_partial_effects_on_outcome

Correct!

Let's practice!

Survival Analysis in Python