Home › Survival › Survival estimators

AalenSummary.SmoothedHazards

The increments smoothed by an Epanechnikov kernel: lifelines' smoothed_hazards_.

public double[] SmoothedHazards(double bandwidth = 1)

Parameters — bandwidth is the kernel's half-width, in time; positive and finite, one by default, lifelines' default.

Returns — row-major, one row per EventTimes entry and one column per coefficient, as Hazards.

Exceptions — ArgumentOutOfRangeException when bandwidth is not positive and finite.

Example — the treatment's smoothed increment at the first event time, over three months either side.

using Lodestar.Survival;

double[] treated = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1];
double[] months = [3, 10, 5, 4, 8, 18, 12, 6, 9, 20, 7, 15];
bool[] died = [true, true, true, false, true, true, true, true, true, false, true, true];

AalenSummary fit = AalenAdditive.Fit(treated, months, died, featureCount: 1);

double[] smoothed = fit.SmoothedHazards(3.0);
double atThree = Math.Round(smoothed[0], 6);   // => -0.208333

Remarks — at each event time, the sum of every increment within bandwidth of it, weighted by 0.75 (1 − u²) with u the gap over the bandwidth. The kernel is not divided by the bandwidth, as lifelines' is not, so the result is a sum of increments rather than a hazard per unit of time. A bandwidth no wider than the gap between event times smooths nothing: each time then sees only its own increment, times 0.75, which is what the default does on durations recorded in whole months.

Applies to — net10.0, netstandard2.0.

See also — AalenSummary, AalenAdditive.