private static void coxProportionalHazards()
{
// Let's say we have the following survival problem. Each row in the table below
// represents a patient under care in a hospital. The first colum represents their
// age (a single feature, but there could have been many like age, height, weight,
// etc), the time until an event has happened (like, for example, unfortunatey death)
// and the event outcome (i.e. what has exactly happened after this amount of time,
// has the patient died or did he simply leave the hospital and we couldn't get more
// data about him?)
object[,] data =
{
// input time until outcome
// (features) event happened (what happened?)
{ 50, 1, SurvivalOutcome.Censored },
{ 70, 2, SurvivalOutcome.Failed },
{ 45, 3, SurvivalOutcome.Censored },
{ 35, 5, SurvivalOutcome.Censored },
{ 62, 7, SurvivalOutcome.Failed },
{ 50, 11, SurvivalOutcome.Censored },
{ 45, 4, SurvivalOutcome.Censored },
{ 57, 6, SurvivalOutcome.Censored },
{ 32, 8, SurvivalOutcome.Censored },
{ 57, 9, SurvivalOutcome.Failed },
{ 60, 10, SurvivalOutcome.Failed },
}; // Note: Censored means that we stopped recording data for that person,
// so we do not know what actually happened to them, except that things
// were going fine until the point in time appointed by "time to event"
// Parse the data above
double[][] inputs = data.GetColumn(0).ToDouble().ToJagged();
double[] time = data.GetColumn(1).ToDouble();
SurvivalOutcome[] output = data.GetColumn(2).To <SurvivalOutcome[]>();
// Create a new PH Newton-Raphson learning algorithm
var teacher = new ProportionalHazardsNewtonRaphson()
{
ComputeBaselineFunction = true,
ComputeStandardErrors = true,
MaxIterations = 100
};
// Use the learning algorithm to infer a Proportional Hazards model
ProportionalHazards regression = teacher.Learn(inputs, time, output);
// Use the regression to make predictions (problematic)
SurvivalOutcome[] prediction = regression.Decide(inputs);
// Use the regression to make score estimates
double[] score = regression.Score(inputs);
// Use the regression to make probability estimates
double[] probability = regression.Probability(inputs);
}
public void PredictTest1()
{
// Data from: http://www.sph.emory.edu/~cdckms/CoxPH/prophaz2.html
double[,] data =
{
{ 50, 1, 0 },
{ 70, 2, 1 },
{ 45, 3, 0 },
{ 35, 5, 0 },
{ 62, 7, 1 },
{ 50, 11, 0 },
{ 45, 4, 0 },
{ 57, 6, 0 },
{ 32, 8, 0 },
{ 57, 9, 1 },
{ 60, 10, 1 },
};
double[] distHazards =
{
0, 0.0351683340828711, 0.0267358118285064, 0,
0.0103643094219679, 0, 0, 0,0, 0.000762266794052363, 0
};
double[] distTimes =
{
11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
};
var regression = new ProportionalHazards(1, new EmpiricalHazardDistribution(distTimes, distHazards));
regression.Coefficients[0] = 0.37704239281494084;
regression.StandardErrors[0] = 0.25415755113043753;
regression.Offsets[0] = 51.181818;
double[][] inputs = data.GetColumn(0).ToJagged();
double[] time = data.GetColumn(1);
double[] expected =
{
0.000000000000, 0.919466527073, 0.000074105451, 0.000001707560,
0.657371730925, 0.046771996036, 0.000074105451, 0.006836271860,
0.000008042445, 0.339562971888, 2.029832541310
};
double[] actual = new double[inputs.Length];
for (int i = 0; i < inputs.Length; i++)
{
actual[i] = regression.Compute(inputs[i], time[i]);
}
for (int i = 0; i < actual.Length; i++)
{
Assert.AreEqual(expected[i], actual[i], 1e-6);
}
regression.Intercept = -regression.Coefficients.Dot(regression.Offsets);
actual = regression.Probability(inputs.Zip(time, Tuple.Create).ToArray());
Assert.IsTrue(actual.IsEqual(expected, 1e-6));
}
public void doc_learn()
{
// Data from: http://www.sph.emory.edu/~cdckms/CoxPH/prophaz2.html / http://statpages.info/prophaz2.html
#region doc_learn
// Let's say we have the following survival problem. Each row in the
// table below represents a patient under care in a hospital. The first
// colum represents their age (a single feature, but there could have
// been many like age, height, weight, etc), the time until an event
// has happened (like, for example, unfortunatey death) and the event
// outcome (i.e. what has exactly happened after this amount of time,
// has the patient died or did he simply leave the hospital and we
// couldn't get more data about him?)
object[,] data =
{
// input time until outcome
// (features) event happened (what happened?)
{ 50, 1, SurvivalOutcome.Censored },
{ 70, 2, SurvivalOutcome.Failed },
{ 45, 3, SurvivalOutcome.Censored },
{ 35, 5, SurvivalOutcome.Censored },
{ 62, 7, SurvivalOutcome.Failed },
{ 50, 11, SurvivalOutcome.Censored },
{ 45, 4, SurvivalOutcome.Censored },
{ 57, 6, SurvivalOutcome.Censored },
{ 32, 8, SurvivalOutcome.Censored },
{ 57, 9, SurvivalOutcome.Failed },
{ 60, 10, SurvivalOutcome.Failed },
}; // Note: Censored means that we stopped recording data for that person,
// so we do not know what actually happened to them, except that things
// were going fine until the point in time appointed by "time to event"
// Parse the data above
double[][] inputs = data.GetColumn(0).ToDouble().ToJagged();
double[] time = data.GetColumn(1).ToDouble();
SurvivalOutcome[] output = data.GetColumn(2).To <SurvivalOutcome[]>();
// Create a new PH Newton-Raphson learning algorithm
var teacher = new ProportionalHazardsNewtonRaphson()
{
ComputeBaselineFunction = true,
ComputeStandardErrors = true,
MaxIterations = 100
};
// Use the learning algorithm to infer a Proportional Hazards model
ProportionalHazards regression = teacher.Learn(inputs, time, output);
// Use the regression to make predictions (problematic)
SurvivalOutcome[] prediction = regression.Decide(inputs);
// Use the regression to make score estimates
double[] score = regression.Score(inputs);
// Use the regression to make probability estimates
double[] probability = regression.Probability(inputs);
#endregion
string str = probability.ToCSharp();
double[] expected = { 0.640442743460877, 1206.22665747906, 0.0972172106179122, 0.00224010744584941, 59.0812230260151, 0.640442743460877, 0.0972172106179122, 8.9683453534747, 0.000722814003252998, 8.9683453534747, 27.7942279934438 };
Assert.IsTrue(expected.IsEqual(probability, rtol: 1e-8));
}
