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
};
ProportionalHazards 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).ToArray();
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);
Assert.IsFalse(Double.IsNaN(actual[i]));
}
}
public void RunTest()
{
// 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 },
};
ProportionalHazards regression = new ProportionalHazards(1);
double[][] inputs = data.GetColumn(0).ToArray();
double[] time = data.GetColumn(1);
int[] output = data.GetColumn(2).ToInt32();
ProportionalHazardsNewtonRaphson target = new ProportionalHazardsNewtonRaphson(regression);
double error = target.Run(inputs, time, output);
double log = -2 * regression.GetPartialLogLikelihood(inputs, time, output);
Assert.AreEqual(0.3770, regression.Coefficients[0], 1e-4);
Assert.IsFalse(Double.IsNaN(regression.Coefficients[0]));
Assert.AreEqual(0.2542, regression.StandardErrors[0], 1e-4);
Assert.IsFalse(Double.IsNaN(regression.StandardErrors[0]));
double[] actual = new double[inputs.Length];
for (int i = 0; i < actual.Length; i++)
{
actual[i] = regression.Compute(inputs[i]);
}
double[] expected =
{
// Computed using R's predict(fit,type="risk")
0.640442743, 1206.226657448, 0.097217211, 0.002240107,
59.081223025, 0.640442743, 0.097217211, 8.968345353,
0.000722814, 8.968345353, 27.794227993
};
for (int i = 0; i < actual.Length; i++)
{
Assert.AreEqual(expected[i], actual[i], 1e-3);
Assert.IsFalse(Double.IsNaN(actual[i]));
}
}
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 },
};
ProportionalHazards regression = new ProportionalHazards(1);
double[][] inputs = data.GetColumn(0).ToArray();
double[] time = data.GetColumn(1);
int[] output = data.GetColumn(2).ToInt32();
ProportionalHazardsNewtonRaphson target = new ProportionalHazardsNewtonRaphson(regression);
double error = target.Run(inputs, time, output);
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);
Assert.IsFalse(Double.IsNaN(actual[i]));
}
}
private void computeInformation()
{
// Store model information
this.result = regression.Compute(inputData, timeData);
this.deviance = regression.GetDeviance(inputData, timeData, censorData);
this.logLikelihood = regression.GetPartialLogLikelihood(inputData, timeData, censorData);
this.chiSquare = regression.ChiSquare(inputData, timeData, censorData);
// Store coefficient information
for (int i = 0; i < regression.Coefficients.Length; i++)
{
this.standardErrors[i] = regression.StandardErrors[i];
this.waldTests[i] = regression.GetWaldTest(i);
this.coefficients[i] = regression.Coefficients[i];
this.confidences[i] = regression.GetConfidenceInterval(i);
this.hazardRatios[i] = regression.GetHazardRatio(i);
}
}
/// <summary>
/// Runs one iteration of the Newton-Raphson update for Cox's hazards learning.
/// </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, int[] 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.");
}
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 = Accord.Statistics.Tools.StandardDeviation(inputs);
inputs = inputs.Subtract(means, 0).ElementwiseDivide(sdev, 0, inPlace: true);
}
// Sort data by time to accelerate performance
if (!time.IsSorted(ComparerDirection.Descending))
{
sort(ref inputs, ref time, ref censor);
}
// Compute actual outputs
double[] output = new double[inputs.Length];
for (int i = 0; i < output.Length; i++)
{
output[i] = regression.Compute(inputs[i]);
}
// 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)
{
return(createBaseline(time, censor, output));
}
CurrentIteration = 0;
double smooth = 0.1;
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] == 0)
{
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
//
// Moreover, the computation of the inverse is optional, as it will
// be used only to compute the standard errors of the regression.
// Hessian Matrix is singular, try pseudo-inverse solution
decomposition = new SingularValueDecomposition(hessian);
double[] deltas = decomposition.Solve(gradient);
// Update coefficients using the calculated deltas
for (int i = 0; i < regression.Coefficients.Length; i++)
{
regression.Coefficients[i] -= smooth * deltas[i];
}
smooth += 0.1;
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(convergence.Delta);
}
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);
}
public void BaselineHazardTestR()
{
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);
SurvivalOutcome[] censor = data.GetColumn(1).To <SurvivalOutcome[]>();
double[][] inputs = data.GetColumn(2).ToJagged();
var regression = new ProportionalHazards(1);
var target = new ProportionalHazardsNewtonRaphson(regression);
double error = target.Run(inputs, time, censor);
// Assert.AreEqual(-10.257417973830666, error, 1e-8);
/*
* library('survival')
* options(digits=17)
* time <- c(8, 4, 12, 6, 10, 8, 5, 5, 3, 14, 8, 11, 7, 7, 12, 8, 7)
* x <- c(13, 56, 25, 64, 38, 80, 0, 81, 81, 38, 23, 99, 12, 36, 63, 92, 38)
* c <- c(0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0)
*
* fit <- coxph(Surv(time, c) ~ x, ties="breslow")
*
* predict(fit,type="risk")
*
* fit$loglik
*
* coef exp(coef) se(coef) z p
* x 0.01633097532122 1.016465054586 0.01711960930183 0.9539338797573 0.340117112635
*
* Likelihood ratio test=0.94 on 1 df, p=0.332836850925 n= 17, number of events= 5
*/
// Tested against GNU R
Assert.AreEqual(49.352941176470587, regression.Offsets[0]);
Assert.AreEqual(0.01633097532122, regression.Coefficients[0], 1e-10);
Assert.AreEqual(0.01711960930183, regression.StandardErrors[0], 1e-10);
Assert.AreEqual(0.340117112635, regression.GetWaldTest(0).PValue, 1e-5);
Assert.AreEqual(-10.2879332934202168, regression.GetPartialLogLikelihood(time, censor));
Assert.AreEqual(-9.8190189050165948, regression.GetPartialLogLikelihood(inputs, time, censor));
double[] actual = inputs.Apply(x => regression.Compute(x));
/*
* predict(r,type="risk")
* [1] 0.55229166964915244 1.11466393245000361 0.67185866444081555 1.27023351821156782 0.83076808526813917 1.64953983529334769 0.44664925161695829 1.67669959872327912
* [9] 1.67669959872327912 0.83076808526813917 0.65026895029003673 2.24967304521214029 0.54334545703992021 0.80407192663266613 1.24965783376477391 2.00665280971219540
* [17] 0.83076808526813917
*/
double[] expected =
{
0.55229166964915244, 1.11466393245000361, 0.67185866444081555, 1.27023351821156782,
0.83076808526813917, 1.64953983529334769, 0.44664925161695829, 1.67669959872327912,
1.67669959872327912, 0.83076808526813917, 0.65026895029003673, 2.24967304521214029,
0.54334545703992021, 0.80407192663266613, 1.24965783376477391, 2.00665280971219540,
0.83076808526813917
};
for (int i = 0; i < actual.Length; i++)
{
Assert.AreEqual(expected[i], actual[i], 0.025);
}
}
public void PredictTest1()
{
// Data from: http://statpages.org/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 },
};
var regression = new ProportionalHazards(1);
double[][] inputs = data.GetColumn(0).ToJagged();
double[] time = data.GetColumn(1);
int[] censor = data.GetColumn(2).ToInt32();
var target = new ProportionalHazardsNewtonRaphson(regression);
double error = target.Run(inputs, time, censor);
// Tested against http://statpages.org/prophaz2.html
Assert.AreEqual(0.3770, regression.Coefficients[0], 1e-4);
Assert.AreEqual(0.2542, regression.StandardErrors[0], 1e-4);
Assert.AreEqual(51.18181818181818, regression.Offsets[0]);
double mean = regression.Offsets[0];
// Baseline survivor function at predictor means
double[] baseline =
{
regression.Survival(2),
regression.Survival(7),
regression.Survival(9),
regression.Survival(10),
};
// Tested against http://statpages.org/prophaz2.html
Assert.AreEqual(0.9979, baseline[0], 1e-4);
Assert.AreEqual(0.9820, baseline[1], 1e-4);
Assert.AreEqual(0.9525, baseline[2], 1e-4);
Assert.AreEqual(0.8310, baseline[3], 1e-4);
double[] expected =
{
0, 2.51908236823927, 0.000203028311170645, 4.67823782106946E-06, 1.07100164957025,
0.118590728553659, 0.000203028311170645, 0.0187294821517496, 1.31028937819308E-05,
0.436716853556834, 5.14665484304978
};
double[] actual = new double[inputs.Length];
for (int i = 0; i < inputs.Length; i++)
{
double a = actual[i] = regression.Compute(inputs[i], time[i]);
double e = expected[i];
Assert.AreEqual(e, a, 1e-3);
}
// string exStr = actual.ToString(CSharpArrayFormatProvider.InvariantCulture);
}