public void EmpiricalHazardConstructorTest3()
{
double[] times = { 11, 10, 9, 8, 6, 5, 4, 2 };
double[] values = { 0.22, 0.67, 1.00, 0.18, 1.00, 1.00, 1.00, 0.55 };
EmpiricalHazardDistribution distribution = new EmpiricalHazardDistribution(times, values);
double mean = distribution.Mean; // 0.93696461879063664
double median = distribution.Median; // 3.9999999151458066
double var = distribution.Variance; // 2.0441627748096289
double chf = distribution.CumulativeHazardFunction(x: 4.2); // 1.55
double cdf = distribution.DistributionFunction(x: 4.2); // 0.7877520261732569
double pdf = distribution.ProbabilityDensityFunction(x: 4.2); // 0.046694554241883471
double lpdf = distribution.LogProbabilityDensityFunction(x: 4.2); // -3.0641277326297756
double hf = distribution.HazardFunction(x: 4.2); // 0.22
double ccdf = distribution.ComplementaryDistributionFunction(x: 4.2); // 0.21224797382674304
double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.3483975243778978
string str = distribution.ToString(); // H(x; v, t)
Assert.AreEqual(0.93696461879063664, mean);
Assert.AreEqual(3.9999999151458066, median, 1e-6);
Assert.AreEqual(2.0441627748096289, var);
Assert.AreEqual(1.55, chf);
Assert.AreEqual(0.7877520261732569, cdf);
Assert.AreEqual(0.046694554241883471, pdf);
Assert.AreEqual(-3.0641277326297756, lpdf);
Assert.AreEqual(0.22, hf);
Assert.AreEqual(0.21224797382674304, ccdf);
Assert.AreEqual(4.3483975243778978, icdf, 1e-8);
Assert.AreEqual("H(x; v, t)", str);
}
public void LeukemiaExampleCensoring_FlemingHarrington_NelsonAalen()
{
// http://www-personal.umich.edu/~yili/lect2notes.pdf
// The following are times of remission (weeks) for 21 leukemia
// patients receiving control treatment (Table 1.1 of Cox & Oakes):
double[] t = { 6, 6, 6, 6, 7, 9, 10, 10, 11, 13, 16, 17, 19, 20, 22, 23, 25, 32, 32, 34, 35 };
int[] c = { 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 };
var distribution = EmpiricalHazardDistribution.Estimate(t, c,
SurvivalEstimator.FlemingHarrington, HazardEstimator.BreslowNelsonAalen);
int[] intervals = { 6, 7, 9, 10, 11, 13, 16, 17, 19, 20, 22, 23, 25, 32, 34, 35 };
double[] expected =
{
0.8571, 0.8067, 0.8067, 0.7529, 0.7529, 0.6902,
0.6275, 0.6275, 0.6275, 0.6275, 0.5378, 0.4482,
0.4482, 0.4482, 0.4482, 0.4482
};
for (int i = 0; i < intervals.Length; i++)
{
double x = intervals[i];
double actual = distribution.ComplementaryDistributionFunction(x);
double e = expected[i];
Assert.AreEqual(e, actual, 0.1);
}
}
public void LeukemiaExampleCensoring_KaplanMeier_FlemingHarrington()
{
// The following are times of remission (weeks) for 21 leukemia
// patients receiving control treatment (Table 1.1 of Cox & Oakes):
double[] t = { 6, 6, 6, 6, 7, 9, 10, 10, 11, 13, 16, 17, 19, 20, 22, 23, 25, 32, 32, 34, 35 };
int[] c = { 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 };
var distribution = new EmpiricalHazardDistribution(SurvivalEstimator.FlemingHarrington);
distribution.Fit(t, new SurvivalOptions {
Outcome = c.To <SurvivalOutcome[]>()
});
int[] intervals = { 6, 7, 9, 10, 11, 13, 16, 17, 19, 20, 22, 23, 25, 32, 34, 35 };
double[] expected =
{
0.8571, 0.8067, 0.8067, 0.7529, 0.7529, 0.6902,
0.6275, 0.6275, 0.6275, 0.6275, 0.5378, 0.4482,
0.4482, 0.4482, 0.4482, 0.4482
};
for (int i = 0; i < intervals.Length; i++)
{
double x = intervals[i];
double actual = distribution.ComplementaryDistributionFunction(x);
double e = expected[i];
Assert.AreEqual(e, actual, 0.1);
}
}
public void KaplanMeierTest1()
{
// Example from
// http://sas-and-r.blogspot.fr/2010/05/example-738-kaplan-meier-survival.html
double[] times;
SurvivalOutcome[] censor;
CreateExample1(out times, out censor);
var distribution = new EmpiricalHazardDistribution(SurvivalEstimator.KaplanMeier);
Assert.AreEqual(SurvivalEstimator.KaplanMeier, distribution.Estimator);
distribution.Fit(times, new EmpiricalHazardOptions(HazardEstimator.KaplanMeier, censor));
int[] t = { 1, 2, 3, 4, 6, 8, 9, 12, 14, 20 };
double[] e = { 0.889, 0.833, 0.774, 0.714, 0.649, 0.577, 0.505, 0.421, 0.337, 0.168 };
double[] actual = t.ToDouble().Apply(distribution.ComplementaryDistributionFunction);
for (int i = 0; i < e.Length; i++)
{
Assert.AreEqual(e[i], actual[i], 1e-3);
}
// Assert.AreEqual(11.177, distribution.Mean);
Assert.AreEqual(12, distribution.Median, 1e-5);
}
public void EmpiricalHazardConstructorTest3()
{
double[] times = { 11, 10, 9, 8, 6, 5, 4, 2 };
double[] values = { 0.22, 0.67, 1.00, 0.18, 1.00, 1.00, 1.00, 0.55 };
EmpiricalHazardDistribution distribution = new EmpiricalHazardDistribution(times, values);
double mean = distribution.Mean; // 0.93696461879063664
double median = distribution.Median; // 3.9999999151458066
double var = distribution.Variance; // 2.0441627748096289
double chf = distribution.CumulativeHazardFunction(x: 4.2); // 1.55
double cdf = distribution.DistributionFunction(x: 4.2); // 0.7877520261732569
double pdf = distribution.ProbabilityDensityFunction(x: 4.2); // 0.046694554241883471
double lpdf = distribution.LogProbabilityDensityFunction(x: 4.2); // -3.0641277326297756
double hf = distribution.HazardFunction(x: 4.2); // 0.22
double ccdf = distribution.ComplementaryDistributionFunction(x: 4.2); // 0.21224797382674304
double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.3483975243778978
string str = distribution.ToString(); // H(x; v, t)
Assert.AreEqual(0.93696461879063664, mean);
Assert.AreEqual(3.9999999151458066, median, 1e-6);
Assert.AreEqual(2.0441627748096289, var);
Assert.AreEqual(1.55, chf);
Assert.AreEqual(0.7877520261732569, cdf);
Assert.AreEqual(0.046694554241883471, pdf);
Assert.AreEqual(-3.0641277326297756, lpdf);
Assert.AreEqual(0.22, hf);
Assert.AreEqual(0.21224797382674304, ccdf);
Assert.AreEqual(4.3483975243778978, icdf, 1e-8);
Assert.AreEqual("H(x; v, t)", str);
}
public void NelsonAalenTest1()
{
// Example from
// http://sas-and-r.blogspot.fr/2010/05/example-738-kaplan-meier-survival.html
// http://sas-and-r.blogspot.fr/2010/05/example-739-nelson-aalen-estimate-of.html
double[] times;
SurvivalOutcome[] censor;
CreateExample1(out times, out censor);
// Test with Breslow method
{
var distribution = EmpiricalHazardDistribution.Estimate(times, censor, HazardTiesMethod.Breslow);
double[] expectedCHF =
{
0.0000000, 0.1111111, 0.1111111, 0.1736111, 0.1736111, 0.2450397, 0.3219628,
0.3219628, 0.4128719, 0.4128719, 0.5239830, 0.6489830, 0.6489830, 0.8156496,
1.0156496, 1.0156496, 1.0156496, 1.5156496, 1.5156496
};
double[] actualCHF = times.Apply(distribution.CumulativeHazardFunction);
for (int i = 0; i < actualCHF.Length; i++)
{
Assert.AreEqual(expectedCHF[i], actualCHF[i], 1e-6);
}
//Assert.AreEqual(11.177, distribution.Mean);
Assert.AreEqual(12, distribution.Median, 1e-5);
}
// Test with Effron method
{
var distribution = EmpiricalHazardDistribution.Estimate(times, censor);
double[] expectedCHF =
{
0.0000000, 0.1111111, 0.1111111, 0.1756496, 0.1756496, 0.2497576, 0.3298003,
0.3298003, 0.4251104, 0.4251104, 0.5428935, 0.6764249, 0.6764249, 0.8587464,
1.0818900, 1.0818900, 1.0818900, 1.7750372, 1.7750372
};
double[] actualCHF = times.Apply(distribution.CumulativeHazardFunction);
for (int i = 0; i < actualCHF.Length; i++)
{
Assert.AreEqual(expectedCHF[i], actualCHF[i], 1e-6);
}
//Assert.AreEqual(11.177, distribution.Mean);
Assert.AreEqual(12, distribution.Median, 1e-5);
}
}
public void DistributionFunctionTest()
{
double[] values =
{
1.0000000000000000, 0.8724284533876597, 0.9698946958777951,
1.0000000000000000, 0.9840887140861863, 1.0000000000000000,
1.0000000000000000, 1.0000000000000000, 1.0000000000000000,
0.9979137773216293, 1.0000000000000000
};
double[] times =
{
11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
};
EmpiricalHazardDistribution target = EmpiricalHazardDistribution
.FromSurvivalValues(times, values);
// Data from: http://www.sph.emory.edu/~cdckms/CoxPH/prophaz2.html
double[] expectedBaselineSurvivalFunction =
{
1.0000, 0.9979, 0.9979, 0.9979,
0.9979, 0.9979, 0.9820,
0.9820, 0.9525, 0.8310, 0.8310,
};
double[] hazardFunction = new double[expectedBaselineSurvivalFunction.Length];
double[] survivalFunction = new double[expectedBaselineSurvivalFunction.Length];
for (int i = 0; i < 11; i++)
{
hazardFunction[i] = target.CumulativeHazardFunction(i + 1);
}
for (int i = 0; i < 11; i++)
{
survivalFunction[i] = target.ComplementaryDistributionFunction(i + 1);
}
for (int i = 0; i < expectedBaselineSurvivalFunction.Length; i++)
{
Assert.AreEqual(expectedBaselineSurvivalFunction[i], survivalFunction[i], 0.01);
// Ho = -log(So)
Assert.AreEqual(hazardFunction[i], -Math.Log(survivalFunction[i]), 0.01);
// So = exp(-Ho)
Assert.AreEqual(survivalFunction[i], Math.Exp(-hazardFunction[i]), 0.01);
}
}
/// <summary>
/// Runs the Newton-Raphson update for Cox's hazards learning until convergence.
/// </summary>
///
/// <param name="censor">The output (event) associated with each input vector.</param>
/// <param name="time">The time-to-event for the non-censored training samples.</param>
///
/// <returns>The maximum relative change in the parameters after the iteration.</returns>
///
public double Run(double[] time, SurvivalOutcome[] censor)
{
if (time.Length != censor.Length)
{
throw new DimensionMismatchException("time",
"The time and output vector must have the same length.");
}
// Sort data by time to accelerate performance
EmpiricalHazardDistribution.Sort(ref time, ref censor);
createBaseline(time, censor);
return(regression.GetPartialLogLikelihood(time, censor));
}
public void inverse_cdf()
{
// Consider the following hazard rates, occurring at the given time steps
double[] times = { 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 20, 21 };
double[] hazards =
{
0, 0.111111111111111, 0.0625, 0.0714285714285714, 0.0769230769230769,
0, 0.0909090909090909, 0, 0.111111111111111, 0.125,0,
0.166666666666667, 0.2, 0, 0.5, 0
};
var distribution = new EmpiricalHazardDistribution(times, hazards);
Assert.AreEqual(0, distribution.Support.Min);
Assert.AreEqual(22, distribution.Support.Max);
Assert.AreEqual(0, distribution.InverseDistributionFunction(0));
Assert.AreEqual(22, distribution.InverseDistributionFunction(1));
Assert.AreEqual(22, distribution.InverseDistributionFunction(0.999));
Assert.AreEqual(0, distribution.DistributionFunction(0));
Assert.AreEqual(0.1051606831856301d, distribution.DistributionFunction(1));
Assert.AreEqual(0.1593762566654946d, distribution.DistributionFunction(2));
Assert.AreEqual(0.78033456236530996d, distribution.DistributionFunction(20));
Assert.AreEqual(0.78033456236530996d, distribution.DistributionFunction(21));
Assert.AreEqual(0.78033456236530996d, distribution.InnerDistributionFunction(21));
Assert.AreEqual(1.0, distribution.DistributionFunction(22));
Assert.AreEqual(1.0, distribution.InnerDistributionFunction(22));
Assert.AreEqual(1.0, distribution.InnerDistributionFunction(23));
Assert.AreEqual(1.0, distribution.InnerDistributionFunction(24));
Assert.AreEqual(1.0, distribution.DistributionFunction(22));
double[] percentiles = Vector.Interval(0.0, 1.0, stepSize: 0.1);
for (int i = 0; i < percentiles.Length; i++)
{
double p = percentiles[i];
double icdf = distribution.InverseDistributionFunction(p);
double cdf = distribution.DistributionFunction(icdf);
Assert.AreEqual(cdf, p, 0.1);
}
}
public void LeukemiaExample_KaplanMeier()
{
// The following are times of remission (weeks) for 21 leukemia
// patients receiving control treatment (Table 1.1 of Cox & Oakes):
// http://www-personal.umich.edu/~yili/lect2notes.pdf
double[] t = { 1, 1, 2, 2, 3, 4, 4, 5, 5, 8, 8, 8, 8, 11, 11, 12, 12, 15, 17, 22, 23 };
var distribution = new EmpiricalHazardDistribution(SurvivalEstimator.KaplanMeier);
distribution.Fit(t, new EmpiricalHazardOptions {
Estimator = HazardEstimator.KaplanMeier
});
Assert.AreEqual(1, distribution.Survivals[0]);
Assert.AreEqual(0.905, distribution.Survivals[1], 1e-3);
Assert.AreEqual(0.809, distribution.Survivals[2], 1e-3);
Assert.AreEqual(0.762, distribution.Survivals[3], 1e-3);
/*
* http://statpages.org/prophaz2.html
* 1, 1
* 1, 1
* 2, 1
* 2, 1
* 3, 1
* 4, 1
* 4, 1
* 5, 1
* 5, 1
* 8, 1
* 8, 1
* 8, 1
* 8, 1
* 11, 1
* 11, 1
* 12, 1
* 12, 1
* 15, 1
* 17, 1
* 22, 1
* 23, 1
*/
}
public void MedianTest()
{
double[] values =
{
0.0000000000000000, 0.0351683340828711, 0.0267358118285064,
0.0000000000000000, 0.0103643094219679, 0.0000000000000000,
0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
0.000762266794052363, 0.000000000000000
};
double[] times =
{
11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
};
EmpiricalHazardDistribution target =
new EmpiricalHazardDistribution(times, values);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
public void ConstructorTest1()
{
double[] times;
SurvivalOutcome[] censor;
CreateExample1(out times, out censor);
var distribution = EmpiricalHazardDistribution.Estimate(times, censor,
SurvivalEstimator.FlemingHarrington, HazardEstimator.BreslowNelsonAalen);
double[] t = distribution.Times;
double[] s = distribution.Survivals;
double[] h = distribution.Hazards;
double[] nt = distribution.Times.Distinct();
double[] nh = nt.Apply(distribution.HazardFunction);
var target = new EmpiricalHazardDistribution(nt, nh, SurvivalEstimator.FlemingHarrington);
for (int i = 0; i < times.Length; i++)
{
double expected = distribution.HazardFunction(times[i]);
double actual = target.HazardFunction(times[i]);
Assert.AreEqual(expected, actual);
}
for (int i = 0; i < times.Length; i++)
{
double expected = distribution.CumulativeHazardFunction(times[i]);
double actual = target.CumulativeHazardFunction(times[i]);
Assert.AreEqual(expected, actual, 1e-5);
}
for (int i = 0; i < times.Length; i++)
{
double expected = distribution.ProbabilityDensityFunction(times[i]);
double actual = target.ProbabilityDensityFunction(times[i]);
Assert.AreEqual(expected, actual, 1e-5);
}
}
public void MeasuresTest_KaplanMeier()
{
double[] values =
{
0.0000000000000000, 0.0351683340828711, 0.0267358118285064,
0.0000000000000000, 0.0103643094219679, 0.9000000000000000,
0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
0.000762266794052363, 0.000000000000000
};
double[] times =
{
11, 1, 9, 8, 7, 3, 6, 5, 4, 2, 10
};
var target = new EmpiricalHazardDistribution(times, values, SurvivalEstimator.KaplanMeier);
var general = new GeneralContinuousDistribution(target);
//Assert.AreEqual(general.Mean, target.Mean);
//Assert.AreEqual(general.Variance, target.Variance);
Assert.AreEqual(general.Median, target.Median);
for (int i = -10; i < 10; i++)
{
double x = i;
double expected = general.CumulativeHazardFunction(x);
double actual = target.CumulativeHazardFunction(x);
Assert.AreEqual(expected, actual, 1e-4);
}
for (int i = -10; i < 10; i++)
{
double x = i;
double expected = general.HazardFunction(x);
double actual = target.HazardFunction(x);
Assert.AreEqual(expected, actual, 1e-5);
}
}
public void MedianTest_KaplanMeier()
{
double[] values =
{
0.0000000000000000, 0.0351683340828711, 0.0267358118285064,
0.0000000000000000, 0.0103643094219679, 0.0000000000000000,
0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
0.000762266794052363, 0.000000000000000
};
double[] times =
{
11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
};
var target = new EmpiricalHazardDistribution(times, values, SurvivalEstimator.KaplanMeier);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
Assert.AreEqual(1, target.ComplementaryDistributionFunction(0));
Assert.AreEqual(0, target.ComplementaryDistributionFunction(Double.PositiveInfinity));
}
/// <summary>
/// Runs the Newton-Raphson update for Cox's hazards learning until convergence.
/// </summary>
///
/// <param name="inputs">The input data.</param>
/// <param name="censor">The output (event) associated with each input vector.</param>
/// <param name="time">The time-to-event for the non-censored training samples.</param>
///
/// <returns>The maximum relative change in the parameters after the iteration.</returns>
///
public double Run(double[][] inputs, double[] time, SurvivalOutcome[] censor)
{
if (inputs.Length != time.Length || time.Length != censor.Length)
{
throw new DimensionMismatchException("time",
"The inputs, time and output vector must have the same length.");
}
// Sort data by time to accelerate performance
EmpiricalHazardDistribution.Sort(ref time, ref censor, ref inputs);
double[] means = new double[parameterCount];
double[] sdev = new double[parameterCount];
for (int i = 0; i < sdev.Length; i++)
{
sdev[i] = 1;
}
if (normalize)
{
// Store means as regression centers
means = inputs.Mean();
for (int i = 0; i < means.Length; i++)
{
regression.Offsets[i] = means[i];
}
// Convert to unit scores for increased accuracy
sdev = BestCS.Statistics.Tools.StandardDeviation(inputs);
inputs = inputs.Subtract(means, 0).ElementwiseDivide(sdev, 0, inPlace: true);
for (int i = 0; i < regression.Coefficients.Length; i++)
{
regression.Coefficients[i] *= sdev[i];
}
}
// Compute actual outputs
double[] output = new double[inputs.Length];
for (int i = 0; i < output.Length; i++)
{
double sum = 0;
for (int j = 0; j < regression.Coefficients.Length; j++)
{
sum += regression.Coefficients[j] * inputs[i][j];
}
output[i] = Math.Exp(sum);
}
// Compute ties
int[] ties = new int[inputs.Length];
for (int i = 0; i < inputs.Length; i++)
{
for (int j = 0; j < time.Length; j++)
{
if (time[j] == time[i])
{
ties[i]++;
}
}
}
if (parameterCount == 0)
{
createBaseline(time, censor, output);
return(regression.GetPartialLogLikelihood(inputs, time, censor));
}
CurrentIteration = 0;
double smooth = Lambda;
do
{
// learning iterations until convergence
// or maximum number of iterations reached
CurrentIteration++;
// Reset Hessian matrix and gradient
Array.Clear(gradient, 0, gradient.Length);
Array.Clear(hessian, 0, hessian.Length);
// For each observation instance
for (int i = 0; i < inputs.Length; i++)
{
// Check if we should censor
if (censor[i] == SurvivalOutcome.Censored)
{
continue;
}
// Compute partials
double den = 0;
Array.Clear(partialGradient, 0, partialGradient.Length);
Array.Clear(partialHessian, 0, partialHessian.Length);
for (int j = 0; j < inputs.Length; j++)
{
if (time[j] >= time[i])
{
den += output[j];
}
}
for (int j = 0; j < inputs.Length; j++)
{
if (time[j] >= time[i])
{
// Compute partial gradient
for (int k = 0; k < partialGradient.Length; k++)
{
partialGradient[k] += inputs[j][k] * output[j] / den;
}
// Compute partial Hessian
for (int ii = 0; ii < inputs[j].Length; ii++)
{
for (int jj = 0; jj < inputs[j].Length; jj++)
{
partialHessian[ii, jj] += inputs[j][ii] * inputs[j][jj] * output[j] / den;
}
}
}
}
// Compute gradient vector
for (int j = 0; j < gradient.Length; j++)
{
gradient[j] += inputs[i][j] - partialGradient[j];
}
// Compute Hessian matrix
for (int j = 0; j < partialGradient.Length; j++)
{
for (int k = 0; k < partialGradient.Length; k++)
{
hessian[j, k] -= partialHessian[j, k] - partialGradient[j] * partialGradient[k];
}
}
}
// Decompose to solve the linear system. Usually the Hessian will
// be invertible and LU will succeed. However, sometimes the Hessian
// may be singular and a Singular Value Decomposition may be needed.
// The SVD is very stable, but is quite expensive, being on average
// about 10-15 times more expensive than LU decomposition. There are
// other ways to avoid a singular Hessian. For a very interesting
// reading on the subject, please see:
//
// - Jeff Gill & Gary King, "What to Do When Your Hessian Is Not Invertible",
// Sociological Methods & Research, Vol 33, No. 1, August 2004, 54-87.
// Available in: http://gking.harvard.edu/files/help.pdf
//
decomposition = new SingularValueDecomposition(hessian);
double[] deltas = decomposition.Solve(gradient);
if (convergence.Iterations > 0 || convergence.Tolerance > 0)
{
// Update coefficients using the calculated deltas
for (int i = 0; i < regression.Coefficients.Length; i++)
{
regression.Coefficients[i] -= smooth * deltas[i];
}
}
smooth += Lambda;
if (smooth > 1)
{
smooth = 1;
}
// Check relative maximum parameter change
convergence.NewValues = regression.Coefficients;
if (convergence.HasDiverged)
{
// Restore previous coefficients
for (int i = 0; i < regression.Coefficients.Length; i++)
{
regression.Coefficients[i] = convergence.OldValues[i];
}
}
// Recompute current outputs
for (int i = 0; i < output.Length; i++)
{
double sum = 0;
for (int j = 0; j < regression.Coefficients.Length; j++)
{
sum += regression.Coefficients[j] * inputs[i][j];
}
output[i] = Math.Exp(sum);
}
} while (!convergence.HasConverged);
for (int i = 0; i < regression.Coefficients.Length; i++)
{
regression.Coefficients[i] /= sdev[i];
}
if (computeStandardErrors)
{
// Grab the regression information matrix
double[,] inverse = decomposition.Inverse();
// Calculate coefficients' standard errors
double[] standardErrors = regression.StandardErrors;
for (int i = 0; i < standardErrors.Length; i++)
{
standardErrors[i] = Math.Sqrt(Math.Abs(inverse[i, i])) / sdev[i];
}
}
if (computeBaselineFunction)
{
createBaseline(time, censor, output);
}
return(regression.GetPartialLogLikelihood(inputs, time, censor));
}
public void DocumentationExample_KaplanMeier()
{
// Consider the following hazard rates, occurring at the given time steps
double[] times = { 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 20, 21 };
double[] hazards =
{
0, 0.111111111111111, 0.0625, 0.0714285714285714, 0.0769230769230769,
0, 0.0909090909090909, 0, 0.111111111111111, 0.125, 0,
0.166666666666667, 0.2, 0, 0.5, 0
};
// Create a new distribution given the observations and event times
var distribution = new EmpiricalHazardDistribution(times, hazards, SurvivalEstimator.KaplanMeier);
// Common measures
double mean = distribution.Mean; // 5.49198237428757
double median = distribution.Median; // 11.999999704601453
double var = distribution.Variance; // 39.83481657555663
// Cumulative distribution functions
double cdf = distribution.DistributionFunction(x: 4); // 0.275274821017619
double ccdf = distribution.ComplementaryDistributionFunction(x: 4); // 0.018754904264376961
double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.4588994137113307
// Probability density functions
double pdf = distribution.ProbabilityDensityFunction(x: 4); // 0.055748090690952365
double lpdf = distribution.LogProbabilityDensityFunction(x: 4); // -2.8869121169242962
// Hazard (failure rate) functions
double hf = distribution.HazardFunction(x: 4); // 0.0769230769230769
double chf = distribution.CumulativeHazardFunction(x: 4); // 0.32196275946275932
string str = distribution.ToString(); // H(x; v, t)
try { double mode = distribution.Mode; Assert.Fail(); }
catch { }
Assert.AreEqual(SurvivalEstimator.KaplanMeier, distribution.Estimator);
Assert.AreEqual(1, distribution.ComplementaryDistributionFunction(0));
Assert.AreEqual(0, distribution.ComplementaryDistributionFunction(Double.PositiveInfinity));
Assert.AreEqual(5.49198237428757, mean);
Assert.AreEqual(11.999999704601453, median, 1e-6);
Assert.AreEqual(39.83481657555663, var);
Assert.AreEqual(0.33647223662121273, chf);
Assert.AreEqual(0.28571428571428559, cdf);
Assert.AreEqual(0.054945054945054937, pdf);
Assert.AreEqual(-2.9014215940827497, lpdf);
Assert.AreEqual(0.0769230769230769, hf);
Assert.AreEqual(0.71428571428571441, ccdf);
Assert.AreEqual(5.8785425101214548, icdf, 1e-8);
Assert.AreEqual("H(x; v, t)", str);
var range1 = distribution.GetRange(0.95);
var range2 = distribution.GetRange(0.99);
var range3 = distribution.GetRange(0.01);
Assert.AreEqual(1, range1.Min, 1e-3);
Assert.AreEqual(20.562, range1.Max, 1e-3);
Assert.AreEqual(1, range2.Min, 1e-3);
Assert.AreEqual(20.562, range2.Max, 1e-3);
Assert.AreEqual(1, range3.Min, 1e-3);
Assert.AreEqual(20.562, range3.Max, 1e-3);
for (int i = 0; i < hazards.Length; i++)
Assert.AreEqual(hazards[i], distribution.HazardFunction(times[i]));
}
public void LeukemiaExample_KaplanMeier()
{
// The following are times of remission (weeks) for 21 leukemia
// patients receiving control treatment (Table 1.1 of Cox & Oakes):
// http://www-personal.umich.edu/~yili/lect2notes.pdf
double[] t = { 1, 1, 2, 2, 3, 4, 4, 5, 5, 8, 8, 8, 8, 11, 11, 12, 12, 15, 17, 22, 23 };
var distribution = new EmpiricalHazardDistribution(SurvivalEstimator.KaplanMeier);
distribution.Fit(t, new EmpiricalHazardOptions { Estimator = HazardEstimator.KaplanMeier });
Assert.AreEqual(1, distribution.Survivals[0]);
Assert.AreEqual(0.905, distribution.Survivals[1], 1e-3);
Assert.AreEqual(0.809, distribution.Survivals[2], 1e-3);
Assert.AreEqual(0.762, distribution.Survivals[3], 1e-3);
/*
http://statpages.org/prophaz2.html
1, 1
1, 1
2, 1
2, 1
3, 1
4, 1
4, 1
5, 1
5, 1
8, 1
8, 1
8, 1
8, 1
11, 1
11, 1
12, 1
12, 1
15, 1
17, 1
22, 1
23, 1
*/
}
public void DocumentationExample_Aalen()
{
// Consider the following hazard rates, occurring at the given time steps
double[] times = { 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 20, 21 };
double[] hazards =
{
0, 0.111111111111111, 0.0625, 0.0714285714285714, 0.0769230769230769,
0, 0.0909090909090909, 0, 0.111111111111111, 0.125, 0,
0.166666666666667, 0.2, 0, 0.5, 0
};
// Create a new distribution given the observations and event times
var distribution = new EmpiricalHazardDistribution(times, hazards);
// Common measures
double mean = distribution.Mean; // 6.1658527179584119
double median = distribution.Median; // 11.999999704601453
double var = distribution.Variance; // 44.101147497430993
// Cumulative distribution functions
double cdf = distribution.DistributionFunction(x: 4); // 0.275274821017619
double ccdf = distribution.ComplementaryDistributionFunction(x: 4); // 0.724725178982381
double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.4588994137113307
// Probability density functions
double pdf = distribution.ProbabilityDensityFunction(x: 4); // 0.055748090690952365
double lpdf = distribution.LogProbabilityDensityFunction(x: 4); // -2.8869121169242962
// Hazard (failure rate) functions
double hf = distribution.HazardFunction(x: 4); // 0.0769230769230769
double chf = distribution.CumulativeHazardFunction(x: 4); // 0.32196275946275932
string str = distribution.ToString(); // H(x; v, t)
try { double mode = distribution.Mode; Assert.Fail(); }
catch { }
Assert.AreEqual(SurvivalEstimator.FlemingHarrington, distribution.Estimator);
Assert.AreEqual(1, distribution.ComplementaryDistributionFunction(0));
Assert.AreEqual(0, distribution.ComplementaryDistributionFunction(Double.PositiveInfinity));
Assert.AreEqual(6.1658527179584119, mean);
Assert.AreEqual(11.999999704601453, median, 1e-6);
Assert.AreEqual(44.101147497430993, var);
Assert.AreEqual(0.32196275946275932, chf);
Assert.AreEqual(0.275274821017619, cdf);
Assert.AreEqual(0.055748090690952365, pdf);
Assert.AreEqual(-2.8869121169242962, lpdf);
Assert.AreEqual(0.0769230769230769, hf);
Assert.AreEqual(0.724725178982381, ccdf);
Assert.AreEqual(4.4588994137113307, icdf, 1e-8);
Assert.AreEqual("H(x; v, t)", str);
var range1 = distribution.GetRange(0.95);
var range2 = distribution.GetRange(0.99);
var range3 = distribution.GetRange(0.01);
Assert.AreEqual(1, range1.Min, 1e-3);
Assert.AreEqual(20.562, range1.Max, 1e-3);
Assert.AreEqual(1, range2.Min, 1e-3);
Assert.AreEqual(20.562, range2.Max, 1e-3);
Assert.AreEqual(1, range3.Min, 1e-3);
Assert.AreEqual(20.562, range3.Max, 1e-3);
for (int i = 0; i < hazards.Length; i++)
Assert.AreEqual(hazards[i], distribution.HazardFunction(times[i]));
}
public void LeukemiaExampleCensoring_KaplanMeier_FlemingHarrington()
{
// The following are times of remission (weeks) for 21 leukemia
// patients receiving control treatment (Table 1.1 of Cox & Oakes):
double[] t = { 6, 6, 6, 6, 7, 9, 10, 10, 11, 13, 16, 17, 19, 20, 22, 23, 25, 32, 32, 34, 35 };
int[] c = { 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 };
var distribution = new EmpiricalHazardDistribution(SurvivalEstimator.FlemingHarrington);
distribution.Fit(t, new SurvivalOptions { Outcome = c.To<SurvivalOutcome[]>() });
int[] intervals = { 6, 7, 9, 10, 11, 13, 16, 17, 19, 20, 22, 23, 25, 32, 34, 35 };
double[] expected =
{
0.8571 , 0.8067, 0.8067, 0.7529, 0.7529, 0.6902,
0.6275, 0.6275, 0.6275, 0.6275, 0.5378, 0.4482,
0.4482, 0.4482, 0.4482, 0.4482
};
for (int i = 0; i < intervals.Length; i++)
{
double x = intervals[i];
double actual = distribution.ComplementaryDistributionFunction(x);
double e = expected[i];
Assert.AreEqual(e, actual, 0.1);
}
}
public void KaplanMeierTest1()
{
// Example from
// http://sas-and-r.blogspot.fr/2010/05/example-738-kaplan-meier-survival.html
double[] times;
SurvivalOutcome[] censor;
CreateExample1(out times, out censor);
var distribution = new EmpiricalHazardDistribution(SurvivalEstimator.KaplanMeier);
Assert.AreEqual(SurvivalEstimator.KaplanMeier, distribution.Estimator);
distribution.Fit(times, new EmpiricalHazardOptions(HazardEstimator.KaplanMeier, censor));
int[] t = { 1, 2, 3, 4, 6, 8, 9, 12, 14, 20 };
double[] e = { 0.889, 0.833, 0.774, 0.714, 0.649, 0.577, 0.505, 0.421, 0.337, 0.168 };
double[] actual = t.ToDouble().Apply(distribution.ComplementaryDistributionFunction);
for (int i = 0; i < e.Length; i++)
Assert.AreEqual(e[i], actual[i], 1e-3);
// Assert.AreEqual(11.177, distribution.Mean);
Assert.AreEqual(12, distribution.Median, 1e-5);
}
public void DocumentationExample_Aalen()
{
// Consider the following hazard rates, occurring at the given time steps
double[] times = { 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 20, 21 };
double[] hazards =
{
0, 0.111111111111111, 0.0625, 0.0714285714285714, 0.0769230769230769,
0, 0.0909090909090909, 0, 0.111111111111111, 0.125,0,
0.166666666666667, 0.2, 0, 0.5, 0
};
// Create a new distribution given the observations and event times
var distribution = new EmpiricalHazardDistribution(times, hazards);
// Common measures
double mean = distribution.Mean; // 6.1658527179584119
double median = distribution.Median; // 11.999999704601453
double var = distribution.Variance; // 44.101147497430993
// Cumulative distribution functions
double cdf = distribution.DistributionFunction(x: 4); // 0.275274821017619
double ccdf = distribution.ComplementaryDistributionFunction(x: 4); // 0.724725178982381
double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.4588994137113307
// Probability density functions
double pdf = distribution.ProbabilityDensityFunction(x: 4); // 0.055748090690952365
double lpdf = distribution.LogProbabilityDensityFunction(x: 4); // -2.8869121169242962
// Hazard (failure rate) functions
double hf = distribution.HazardFunction(x: 4); // 0.0769230769230769
double chf = distribution.CumulativeHazardFunction(x: 4); // 0.32196275946275932
string str = distribution.ToString(); // H(x; v, t)
try { double mode = distribution.Mode; Assert.Fail(); }
catch { }
Assert.AreEqual(SurvivalEstimator.FlemingHarrington, distribution.Estimator);
Assert.AreEqual(1, distribution.ComplementaryDistributionFunction(0));
Assert.AreEqual(0, distribution.ComplementaryDistributionFunction(Double.PositiveInfinity));
Assert.AreEqual(6.1658527179584119, mean);
Assert.AreEqual(11.999999704601453, median, 1e-6);
Assert.AreEqual(44.101147497430993, var);
Assert.AreEqual(0.32196275946275932, chf);
Assert.AreEqual(0.275274821017619, cdf);
Assert.AreEqual(0.055748090690952365, pdf);
Assert.AreEqual(-2.8869121169242962, lpdf);
Assert.AreEqual(0.0769230769230769, hf);
Assert.AreEqual(0.724725178982381, ccdf);
Assert.AreEqual(4.4588994137113307, icdf, 1e-8);
Assert.AreEqual("H(x; v, t)", str);
var range1 = distribution.GetRange(0.95);
var range2 = distribution.GetRange(0.99);
var range3 = distribution.GetRange(0.01);
Assert.AreEqual(1, range1.Min, 1e-3);
Assert.AreEqual(20.562, range1.Max, 1e-3);
Assert.AreEqual(1, range2.Min, 1e-3);
Assert.AreEqual(20.562, range2.Max, 1e-3);
Assert.AreEqual(1, range3.Min, 1e-3);
Assert.AreEqual(20.562, range3.Max, 1e-3);
for (int i = 0; i < hazards.Length; i++)
{
Assert.AreEqual(hazards[i], distribution.HazardFunction(times[i]));
}
}
public void ConstructorTest1()
{
double[] times;
SurvivalOutcome[] censor;
CreateExample1(out times, out censor);
var distribution = EmpiricalHazardDistribution.Estimate(times, censor,
SurvivalEstimator.FlemingHarrington, HazardEstimator.BreslowNelsonAalen);
double[] t = distribution.Times;
double[] s = distribution.Survivals;
double[] h = distribution.Hazards;
double[] nt = distribution.Times.Distinct();
double[] nh = nt.Apply(distribution.HazardFunction);
var target = new EmpiricalHazardDistribution(nt, nh, SurvivalEstimator.FlemingHarrington);
for (int i = 0; i < times.Length; i++)
{
double expected = distribution.HazardFunction(times[i]);
double actual = target.HazardFunction(times[i]);
Assert.AreEqual(expected, actual);
}
for (int i = 0; i < times.Length; i++)
{
double expected = distribution.CumulativeHazardFunction(times[i]);
double actual = target.CumulativeHazardFunction(times[i]);
Assert.AreEqual(expected, actual, 1e-5);
}
for (int i = 0; i < times.Length; i++)
{
double expected = distribution.ProbabilityDensityFunction(times[i]);
double actual = target.ProbabilityDensityFunction(times[i]);
Assert.AreEqual(expected, actual, 1e-5);
}
}
public void DocumentationExample_KaplanMeier()
{
// Consider the following hazard rates, occurring at the given time steps
double[] times = { 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 20, 21 };
double[] hazards =
{
0, 0.111111111111111, 0.0625, 0.0714285714285714, 0.0769230769230769,
0, 0.0909090909090909, 0, 0.111111111111111, 0.125,0,
0.166666666666667, 0.2, 0, 0.5, 0
};
// Create a new distribution given the observations and event times
var distribution = new EmpiricalHazardDistribution(times, hazards, SurvivalEstimator.KaplanMeier);
// Common measures
double mean = distribution.Mean; // 5.49198237428757
double median = distribution.Median; // 11.999999704601453
double var = distribution.Variance; // 39.83481657555663
// Cumulative distribution functions
double cdf = distribution.DistributionFunction(x: 4); // 0.275274821017619
double ccdf = distribution.ComplementaryDistributionFunction(x: 4); // 0.018754904264376961
double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.4588994137113307
// Probability density functions
double pdf = distribution.ProbabilityDensityFunction(x: 4); // 0.055748090690952365
double lpdf = distribution.LogProbabilityDensityFunction(x: 4); // -2.8869121169242962
// Hazard (failure rate) functions
double hf = distribution.HazardFunction(x: 4); // 0.0769230769230769
double chf = distribution.CumulativeHazardFunction(x: 4); // 0.32196275946275932
string str = distribution.ToString(); // H(x; v, t)
try { double mode = distribution.Mode; Assert.Fail(); }
catch { }
Assert.AreEqual(SurvivalEstimator.KaplanMeier, distribution.Estimator);
Assert.AreEqual(1, distribution.ComplementaryDistributionFunction(0));
Assert.AreEqual(0, distribution.ComplementaryDistributionFunction(Double.PositiveInfinity));
Assert.AreEqual(5.49198237428757, mean);
Assert.AreEqual(11.999999704601453, median, 1e-6);
Assert.AreEqual(39.83481657555663, var);
Assert.AreEqual(0.33647223662121273, chf);
Assert.AreEqual(0.28571428571428559, cdf);
Assert.AreEqual(0.054945054945054937, pdf);
Assert.AreEqual(-2.9014215940827497, lpdf);
Assert.AreEqual(0.0769230769230769, hf);
Assert.AreEqual(0.71428571428571441, ccdf);
Assert.AreEqual(5.8785425101214548, icdf, 1e-8);
Assert.AreEqual("H(x; v, t)", str);
var range1 = distribution.GetRange(0.95);
var range2 = distribution.GetRange(0.99);
var range3 = distribution.GetRange(0.01);
Assert.AreEqual(1, range1.Min, 1e-3);
Assert.AreEqual(20.562, range1.Max, 1e-3);
Assert.AreEqual(1, range2.Min, 1e-3);
Assert.AreEqual(20.562, range2.Max, 1e-3);
Assert.AreEqual(1, range3.Min, 1e-3);
Assert.AreEqual(20.562, range3.Max, 1e-3);
for (int i = 0; i < hazards.Length; i++)
{
Assert.AreEqual(hazards[i], distribution.HazardFunction(times[i]));
}
}
public void MeasuresTest_KaplanMeier()
{
double[] values =
{
0.0000000000000000, 0.0351683340828711, 0.0267358118285064,
0.0000000000000000, 0.0103643094219679, 0.9000000000000000,
0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
0.000762266794052363, 0.000000000000000
};
double[] times =
{
11, 1, 9, 8, 7, 3, 6, 5, 4, 2, 10
};
var target = new EmpiricalHazardDistribution(times, values, SurvivalEstimator.KaplanMeier);
var general = new GeneralContinuousDistribution(target);
//Assert.AreEqual(general.Mean, target.Mean);
//Assert.AreEqual(general.Variance, target.Variance);
Assert.AreEqual(general.Median, target.Median);
for (int i = -10; i < 10; i++)
{
double x = i;
double expected = general.CumulativeHazardFunction(x);
double actual = target.CumulativeHazardFunction(x);
Assert.AreEqual(expected, actual, 1e-4);
}
for (int i = -10; i < 10; i++)
{
double x = i;
double expected = general.HazardFunction(x);
double actual = target.HazardFunction(x);
Assert.AreEqual(expected, actual, 1e-5);
}
}
public void MedianTest_KaplanMeier()
{
double[] values =
{
0.0000000000000000, 0.0351683340828711, 0.0267358118285064,
0.0000000000000000, 0.0103643094219679, 0.0000000000000000,
0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
0.000762266794052363, 0.000000000000000
};
double[] times =
{
11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
};
var target = new EmpiricalHazardDistribution(times, values, SurvivalEstimator.KaplanMeier);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
Assert.AreEqual(1, target.ComplementaryDistributionFunction(0));
Assert.AreEqual(0, target.ComplementaryDistributionFunction(Double.PositiveInfinity));
}
/// <summary>
/// Creates a new Cox Proportional-Hazards Model.
/// </summary>
///
public ProportionalHazards()
{
BaselineHazard = new EmpiricalHazardDistribution();
}
public void BaselineHazardTest()
{
double[,] data =
{
// t c in
{ 8, 0, 13 },
{ 4, 1, 56 },
{ 12, 0, 25 },
{ 6, 0, 64 },
{ 10, 0, 38 },
{ 8, 1, 80 },
{ 5, 0, 0 },
{ 5, 0, 81 },
{ 3, 1, 81 },
{ 14, 1, 38 },
{ 8, 0, 23 },
{ 11, 0, 99 },
{ 7, 0, 12 },
{ 7, 1, 36 },
{ 12, 0, 63 },
{ 8, 0, 92 },
{ 7, 0, 38 },
};
double[] time = data.GetColumn(0);
int[] censor = data.GetColumn(1).ToInt32();
double[][] inputs = data.GetColumn(2).ToArray();
ProportionalHazards regression = new ProportionalHazards(1);
ProportionalHazardsNewtonRaphson target = new ProportionalHazardsNewtonRaphson(regression);
target.Normalize = false;
double error = target.Run(inputs, time, censor);
double log = -2 * regression.GetPartialLogLikelihood(inputs, time, censor);
EmpiricalHazardDistribution baseline = regression.BaselineHazard as EmpiricalHazardDistribution;
double[] actual = new double[(int)baseline.Support.Max];
for (int i = (int)baseline.Support.Min; i < baseline.Support.Max; i++)
{
actual[i] = baseline.CumulativeHazardFunction(i);
}
Assert.AreEqual(14, actual.Length);
double[] expected =
{
0, 0, 0,
0.025000345517572315, 0.052363663484639708, 0.052363663484639708, 0.052363663484639708,
0.16317880290786446,
0.34217461190678861, 0.34217461190678861, 0.34217461190678861,
0.34217461190678861, 0.34217461190678861, 0.34217461190678861
};
for (int i = 0; i < actual.Length; i++)
{
Assert.AreEqual(expected[i], actual[i], 0.025);
}
}
public void MedianTest()
{
double[] values =
{
0.0000000000000000, 0.0351683340828711, 0.0267358118285064,
0.0000000000000000, 0.0103643094219679, 0.0000000000000000,
0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
0.000762266794052363, 0.000000000000000
};
double[] times =
{
11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
};
EmpiricalHazardDistribution target =
new EmpiricalHazardDistribution(times, values);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
public void DistributionFunctionTest2()
{
double[] values =
{
0.0000000000000000, 0.0351683340828711, 0.0267358118285064,
0.0000000000000000, 0.0103643094219679, 0.0000000000000000,
0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
0.000762266794052363, 0.000000000000000
};
double[] times =
{
11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
};
EmpiricalHazardDistribution target =
new EmpiricalHazardDistribution(times, values);
double[] expected =
{
1.000000000000000,
0.999238023657475,
0.999238023657475,
0.999238023657475,
0.999238023657475,
0.999238023657475,
0.98893509519066469,
0.98893509519066469,
0.96284543081744489,
0.92957227114936058,
0.92957227114936058,
};
double[] hazardFunction = new double[expected.Length];
double[] survivalFunction = new double[expected.Length];
double[] complementaryDistribution = new double[expected.Length];
for (int i = 0; i < 11; i++)
hazardFunction[i] = target.CumulativeHazardFunction(i + 1);
for (int i = 0; i < 11; i++)
survivalFunction[i] = target.ComplementaryDistributionFunction(i + 1);
for (int i = 0; i < expected.Length; i++)
{
Assert.AreEqual(expected[i], survivalFunction[i], 1e-5);
// Ho = -log(So)
Assert.AreEqual(hazardFunction[i], -Math.Log(survivalFunction[i]), 1e-5);
// So = exp(-Ho)
Assert.AreEqual(survivalFunction[i], Math.Exp(-hazardFunction[i]), 1e-5);
}
}
public void DistributionFunctionTest2_KaplanMeier()
{
double[] values =
{
0.0000000000000000, 0.0351683340828711, 0.0267358118285064,
0.0000000000000000, 0.0103643094219679, 0.0000000000000000,
0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
0.000762266794052363, 0.000000000000000
};
double[] times =
{
11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
};
var target = new EmpiricalHazardDistribution(times, values, SurvivalEstimator.KaplanMeier);
double[] expected =
{
1.000000000000000,
0.999238023657475,
0.999238023657475,
0.999238023657475,
0.999238023657475,
0.999238023657475,
0.98893509519066469,
0.98893509519066469,
0.96284543081744489,
0.92957227114936058,
0.92957227114936058,
};
double[] hazardFunction = new double[expected.Length];
double[] survivalFunction = new double[expected.Length];
for (int i = 0; i < 11; i++)
{
hazardFunction[i] = target.CumulativeHazardFunction(i + 1);
}
for (int i = 0; i < 11; i++)
{
survivalFunction[i] = target.ComplementaryDistributionFunction(i + 1);
}
for (int i = 0; i < expected.Length; i++)
{
Assert.AreEqual(expected[i], survivalFunction[i], 1e-3);
// Ho = -log(So)
Assert.AreEqual(hazardFunction[i], -Math.Log(survivalFunction[i]), 1e-5);
// So = exp(-Ho)
Assert.AreEqual(survivalFunction[i], Math.Exp(-hazardFunction[i]), 1e-5);
}
Assert.AreEqual(1, target.ComplementaryDistributionFunction(0));
Assert.AreEqual(0, target.ComplementaryDistributionFunction(Double.PositiveInfinity));
}
public void BaselineHazardTest()
{
double[,] data =
{
// t c in
{ 8, 0, -1.2372626521865966 },
{ 4, 1, 0.22623087329625477 },
{ 12, 0, -0.8288458543774289 },
{ 6, 0, 0.49850873850236665 },
{ 10, 0, -0.38639432341749696 },
{ 8, 1, 1.0430644689145904 },
{ 5, 0, -1.6797141831465285 },
{ 5, 0, 1.0770992020653544 },
{ 3, 1, 1.0770992020653544 },
{ 14, 1, -0.38639432341749696 },
{ 8, 0, -0.8969153206789568 },
{ 11, 0, 1.6897243987791061 },
{ 7, 0, -1.2712973853373605 },
{ 7, 0, -0.38639432341749696 },
{ 7, 1, -0.45446378971902495 },
{ 12, 0, 0.4644740053516027 },
{ 8, 0, 1.4514812667237584 },
};
double[] time = data.GetColumn(0);
SurvivalOutcome[] censor = data.GetColumn(1).To <SurvivalOutcome[]>();
double[][] inputs = data.GetColumn(2).ToJagged();
var regression = new ProportionalHazards(1);
var target = new ProportionalHazardsNewtonRaphson(regression);
target.Normalize = false;
target.Lambda = 0;
regression.Coefficients[0] = 0.47983261821350764;
double error = target.Run(inputs, time, censor);
/* Tested against http://statpages.org/prophaz2.html
* 13, 8, 0
* 56, 4, 1
* 25, 12, 0
* 64, 6, 0
* 38, 10, 0
* 80, 8, 1
* 0 , 5, 0
* 81, 5, 0
* 81, 3, 1
* 38, 14, 1
* 23, 8, 0
* 99, 11, 0
* 12, 7, 0
* 38, 7, 0
* 36, 7, 1
* 63, 12, 0
* 92, 8, 0
*/
double[] baseline =
{
regression.Survival(3), // 0.9465
regression.Survival(4), // 0.8919
regression.Survival(7), // 0.8231
regression.Survival(8), // 0.7436
regression.Survival(12), // 0.7436
regression.Survival(14), // 0.0000
};
Assert.AreEqual(0.9465, baseline[0], 1e-4);
Assert.AreEqual(0.8919, baseline[1], 1e-4);
Assert.AreEqual(0.8231, baseline[2], 1e-4);
Assert.AreEqual(0.7436, baseline[3], 1e-4);
Assert.AreEqual(0.7436, baseline[4], 1e-4);
Assert.AreEqual(0.0000, baseline[5], 1e-4);
// The value of the baseline must be exact the same if it was computed
// after the Newton-Raphson or in a standalone EmpiricalHazard computation
double[] outputs = inputs.Apply(x => regression.Compute(x));
var empirical = EmpiricalHazardDistribution.Estimate(time, censor, outputs);
baseline = new[]
{
empirical.ComplementaryDistributionFunction(3), // 0.9465
empirical.ComplementaryDistributionFunction(4), // 0.8919
empirical.ComplementaryDistributionFunction(7), // 0.8231
empirical.ComplementaryDistributionFunction(8), // 0.7436
empirical.ComplementaryDistributionFunction(12), // 0.7436
empirical.ComplementaryDistributionFunction(14), // 0.0000
};
Assert.AreEqual(0.9465, baseline[0], 1e-4);
Assert.AreEqual(0.8919, baseline[1], 1e-4);
Assert.AreEqual(0.8231, baseline[2], 1e-4);
Assert.AreEqual(0.7436, baseline[3], 1e-4);
Assert.AreEqual(0.7436, baseline[4], 1e-4);
Assert.AreEqual(0.0000, baseline[5], 1e-4);
}