/// <summary>
/// The likelihood ratio test of the overall model, also called the model chi-square test.
/// </summary>
///
/// <param name="input">A set of input data.</param>
/// <param name="time">The time-to-event before the output occurs.</param>
/// <param name="output">The corresponding output data.</param>
///
/// <remarks>
/// <para>
/// The Chi-square test, also called the likelihood ratio test or the log-likelihood test
/// is based on the deviance of the model (-2*log-likelihood). The log-likelihood ratio test
/// indicates whether there is evidence of the need to move from a simpler model to a more
/// complicated one (where the simpler model is nested within the complicated one).</para>
/// <para>
/// The difference between the log-likelihood ratios for the researcher's model and a
/// simpler model is often called the "model chi-square".</para>
/// </remarks>
///
public ChiSquareTest ChiSquare(double[][] input, double[] time, SurvivalOutcome[] output)
{
ProportionalHazards regression = new ProportionalHazards(Inputs);
double ratio = GetLogLikelihoodRatio(input, time, output, regression);
return(new ChiSquareTest(ratio, Coefficients.Length));
}
/// <summary>
/// Creates a new Cox's Proportional Hazards that is a copy of the current instance.
/// </summary>
///
public object Clone()
{
var regression = new ProportionalHazards(Coefficients.Length);
regression.Coefficients = (double[])this.Coefficients.Clone();
regression.StandardErrors = (double[])this.StandardErrors.Clone();
regression.Offsets = (double[])this.Offsets.Clone();
return(regression);
}
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 },
};
var regression = new ProportionalHazards(1);
double[][] inputs = data.GetColumn(0).ToArray();
double[] time = data.GetColumn(1);
SurvivalOutcome[] output = data.GetColumn(2).To<SurvivalOutcome[]>();
var target = new ProportionalHazardsNewtonRaphson(regression);
double error = target.Run(inputs, time, output);
double log = -2 * regression.GetPartialLogLikelihood(inputs, time, output);
// Tested against http://www.sph.emory.edu/~cdckms/CoxPH/prophaz2.html
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]));
}
}
/// <summary>
/// Gets the Log-Likelihood Ratio between two models.
/// </summary>
///
/// <remarks>
/// The Log-Likelihood ratio is defined as 2*(LL - LL0).
/// </remarks>
///
/// <param name="input">A set of input data.</param>
/// <param name="time">The time-to-event before the output occurs.</param>
/// <param name="output">The corresponding output data.</param>
/// <param name="hazards">Another Cox Proportional Hazards model.</param>
///
/// <returns>The Log-Likelihood ratio (a measure of performance
/// between two models) calculated over the given data sets.</returns>
///
public double GetLogLikelihoodRatio(double[][] input, double[] time, SurvivalOutcome[] output, ProportionalHazards hazards)
{
return(2.0 * (this.GetPartialLogLikelihood(input, time, output) - hazards.GetPartialLogLikelihood(input, time, output)));
}
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);
regression.Coefficients[0] = 0.37704239281494084;
regression.StandardErrors[0] = 0.25415755113043753;
double[][] inputs = data.GetColumn(0).ToArray();
double[] time = data.GetColumn(1);
int[] output = data.GetColumn(2).ToInt32();
{
double actual = -2 * regression.GetPartialLogLikelihood(inputs, time, output);
double expected = 4.0505;
Assert.AreEqual(expected, actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
{
var test = regression.GetWaldTest(0);
Assert.AreEqual(0.1379, test.PValue, 1e-4);
}
{
var ci = regression.GetConfidenceInterval(0);
Assert.AreEqual(0.8859, ci.Min, 1e-4);
Assert.AreEqual(2.3993, ci.Max, 1e-4);
}
{
double actual = regression.GetHazardRatio(0);
double expected = 1.4580;
Assert.AreEqual(expected, actual, 1e-4);
}
{
var chi = regression.ChiSquare(inputs, time, output);
Assert.AreEqual(7.3570, chi.Statistic, 1e-4);
Assert.AreEqual(1, chi.DegreesOfFreedom);
Assert.AreEqual(0.0067, chi.PValue, 1e-3);
}
}
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);
int[] output = data.GetColumn(2).ToInt32();
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 RunTest2()
{
// Data from: http://www.sph.emory.edu/~cdckms/CoxPH/prophaz2.html
double[,] data =
{
{ 50, 30, 1, 0 },
{ 70, 22, 2, 1 },
{ 45, 12, 3, 0 },
{ 35, 22, 5, 0 },
{ 62, 54, 7, 1 },
{ 50, 12, 11, 0 },
{ 45, 11, 4, 0 },
{ 57, 62, 6, 0 },
{ 32, 16, 8, 0 },
{ 57, 14, 9, 1 },
{ 60, 12, 10, 1 },
};
var regression = new ProportionalHazards(2);
double[][] inputs = data.Submatrix(null, 0, 1).ToArray();
double[] time = data.GetColumn(2);
SurvivalOutcome[] output = data.GetColumn(3).To<SurvivalOutcome[]>();
var target = new ProportionalHazardsNewtonRaphson(regression);
double error = target.Run(inputs, time, output);
double log = -2 * regression.GetPartialLogLikelihood(inputs, time, output);
Assert.AreEqual(3.4261, log, 1e-4);
Assert.IsFalse(Double.IsNaN(log));
double actual = regression.Coefficients[0];
Assert.AreEqual(0.3909, regression.Coefficients[0], 1e-4);
Assert.IsFalse(Double.IsNaN(regression.Coefficients[0]));
Assert.AreEqual(0.0424, regression.Coefficients[1], 1e-4);
Assert.IsFalse(Double.IsNaN(regression.Coefficients[1]));
Assert.AreEqual(0.2536, regression.StandardErrors[0], 1e-4);
Assert.IsFalse(Double.IsNaN(regression.StandardErrors[0]));
Assert.AreEqual(0.0624, regression.StandardErrors[1], 1e-4);
Assert.IsFalse(Double.IsNaN(regression.StandardErrors[1]));
}
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);
}
/// <summary>
/// The likelihood ratio test of the overall model, also called the model chi-square test.
/// </summary>
///
/// <param name="input">A set of input data.</param>
/// <param name="time">The time-to-event before the output occurs.</param>
/// <param name="output">The corresponding output data.</param>
///
/// <remarks>
/// <para>
/// The Chi-square test, also called the likelihood ratio test or the log-likelihood test
/// is based on the deviance of the model (-2*log-likelihood). The log-likelihood ratio test
/// indicates whether there is evidence of the need to move from a simpler model to a more
/// complicated one (where the simpler model is nested within the complicated one).</para>
/// <para>
/// The difference between the log-likelihood ratios for the researcher's model and a
/// simpler model is often called the "model chi-square".</para>
/// </remarks>
///
public ChiSquareTest ChiSquare(double[][] input, double[] time, int[] output)
{
ProportionalHazards regression = new ProportionalHazards(Inputs);
double ratio = GetLogLikelihoodRatio(input, time, output, regression);
return new ChiSquareTest(ratio, Coefficients.Length);
}
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).ToArray();
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(regression.Compute);
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).ToArray();
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(regression.Compute);
/*
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).ToArray();
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);
}
public void RunTest5()
{
double[,] inputs =
{
{ 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 },
{ 0.9, 1.3, 1.5, 1, 2.4, 1.1, 1.3, 1.1, 0.8, 0.7, 1.1, 0.8, 1, 1, 1.4, 1.4, 1.2, 1.1, 1, 1.4, 2.5, 1.6, 1.2, 0.7, 0.8, 0.7, 0.7, 1.3, 1, 1.7, 1, 1.1, 1.3, 0.9, 1, 1.1, 0.7, 0.9, 1.3, 1.3, 0.9, 1.3, 0.9, 0.6, 1.2, 1.1, 1.1, 0.9, 1.1, 1.1, 1.9, 1.1, 0.9, 1.3, 1.1, 1.2, 0.8, 0.9, 1.7, 1.2, 0.7, 1.2, 1.6, 2.9, 1, 0.9, 0.8, 1, 1.5, 0.8, 0.7, 1.1, 1.2, 0.5, 0.9, 0.9, 0.9, 1.2, 1, 0.9, 1.3, 0.6, 1.2, 0.6, 1.7, 0.8, 1.1, 1, 1.1, 1.2, 0.6, 1.3, 1.7, 1.2, 2.7, 0.8, 1, 1, 1, 1.6, 1.2, 1.2, 2.4, 0.7, 0.8, 0.7, 1.3, 0.9, 1.1, 1.2, 1.2, 1.7, 1, 1.1, 2.1, 1.8, 2.2, 0.5, 1, 1.6, 1.2, 1.5, 1.1, 1, 1, 1.4, 1.2, 1.2, 1.1, 1.5, 0.9, 0.9, 1.2, 1.4, 1.2, 1, 0.9, 1.9, 1.7, 1.3, 1.2, 1.4, 1.7, 0.9, 1.6, 0.7, 0.9, 1, 1.1, 1.4, 1, 1.1, 1.4, 1.3, 1.1, 1.8, 1.6, 1.2, 1, 0.8, 1.1, 0.7, 1.4, 1.1, 1.8, 0.7, 1.7, 1, 1.2, 1.5, 1.1, 1.6, 1.7, 1.3, 0.8, 1.7, 1.5, 0.8, 1.4, 0.9, 4.7, 1, 0.7, 0.9, 0.9, 1, 2.6, 1, 1.1, 1.4, 1, 0.9, 1.3, 1.6, 1.8, 0.9, 1.6, 0.9, 1.2, 1, 1.2, 0.7, 1.4, 1.6, 1.2, 1.1, 1.3, 0.9, 1.3, 0.7, 1.2, 1.1, 1, 1, 0.9, 0.8, 1, 1, 1.5, 1.3, 1.2, 1, 1.2, 1.1, 1.6, 1.7, 1.1, 0.9, 1, 0.9, 1.3, 0.8, 0.8, 1, 0.9, 1, 1.2, 1.4, 0.8, 1, 1, 1.2, 1.3, 1.1, 1, 1.6, 1.2, 0.8, 2.1, 1, 1.5, 1, 1.5, 1.2, 1.1, 1.3, 0.8, 1, 1.1, 1.5, 0.8, 1.2, 1.1, 0.8, 0.9, 1.4, 1.5, 1, 1.3, 1.1, 1, 1.2, 2.2, 1.2, 1.3, 1.3, 0.7, 1, 1.1, 1.1, 1.7, 1.3, 1, 1.1, 1, 1.8, 1.2, 1.2, 1.3, 1.1, 1.6, 4.1, 1, 0.9, 1.5, 1.5, 1.4, 1, 0.5, 0.9, 0.8, 0.6, 1.3, 0.7, 0.7, 1.1, 1.4, 0.9, 1, 4.2, 1, 0.9, 1.2, 2.1, 2.4, 1.2, 2.5, 1, 1.2, 1.3, 0.9, 1.1, 1.6, 1, 1.5, 1.1, 1, 2.6, 0.9, 1.3, 1.4, 0.8, 1.4, 2.7, 1.1, 0.8, 1.2, 1.4, 1.2, 1, 1.1, 1.2, 1.2, 1.3, 1.2, 1.2, 1.2, 1.1, 1.3, 0.9, 1, 1.9, 1.4, 1.2, 1.1, 0.7, 0.9, 1.1, 1.1, 1.4, 1, 1.2, 1.4, 1, 2.8, 1.1, 0.7, 0.7, 1.2, 0.7, 1, 1.5, 1.5, 1.7, 0.9, 1.6, 0.9, 1.7, 0.8, 1, 0.8, 1.1, 1.3, 1.2, 0.9, 1.1, 1.1, 0.9, 0.9, 0.7, 1.1, 1.8, 0.8, 0.9, 1.4, 0.9, 1.2, 1.4, 1, 0.8, 1.4, 1.4, 1, 0.7, 0.6, 0.8, 1.4, 1.4, 0.8, 1.9, 1.3, 1, 1.3, 0.9, 0.9, 1.5, 1.5, 0.8, 1.4, 1.1, 0.8, 0.8, 1.4, 1.3, 1.1, 1, 2.2, 1.6, 1.7, 1.2, 0.9, 1.1, 1, 2.6, 1.6, 0.9, 0.9, 0.6, 1.6, 1.1, 1.3, 1.7, 1.2, 1.2, 1.6, 0.9, 0.9, 1.3, 2.2, 1.3, 1, 0.8, 1.5, 1.3, 1, 1.2, 1.4, 1.3, 1.3, 1.4, 1.3, 1.4, 1.2, 1, 1.2, 0.8, 1.1, 1.2, 1.1, 1.2, 1.8, 1.1, 1.6, 1.1, 0.8, 1.2, 1, 1.2, 0.7, 1.9, 1.6, 1.5, 0.9, 1.1, 0.8, 1.3, 1.1, 0.7, 1, 2, 1.2, 1.1, 1.2, 0.9, 0.9, 1, 1.2, 1, 1.2, 1.1, 1.1, 1, 1.4, 0.8, 1.3, 0.8, 1, 1.4, 1.2, 1.1, 1.3, 0.7, 1.2, 0.6, 1.2, 1.4, 1.5, 1.7, 0.9, 1, 0.6, 0.9, 1.4, 1.5, 1.1, 1.3, 0.9, 1.3, 2.1, 1.2, 1.3, 1.1, 1.4, 0.9, 1.4, 1.5, 1, 1.5, 1, 1.3, 0.9, 1.2, 1.1, 0.9, 1.1, 1.4, 1.4, 0.8, 1, 1.2, 1.1, 0.8, 1.2, 4.1, 0.7, 2, 0.8, 1.2, 3.8, 1.2, 1.4, 1, 1, 1.7, 1, 1, 0.9, 1.6, 0.7, 1.2, 1.1, 1, 1, 1, 0.7, 1.5, 1.1, 1, 0.9, 0.8, 0.9, 1.9, 1, 1.4, 1.3, 1.5, 0.9, 1.1, 1.2, 0.8, 1, 1.4, 4.2, 2.5, 1.2, 1.6, 0.9, 1.1, 1, 0.9, 0.6, 1, 1.1, 1.2, 1.2, 1.2, 0.9, 1.2, 1.1, 1.2, 0.8, 1, 1.6, 0.9, 1.2, 1.4, 0.7, 1.6, 1.1, 1.5, 0.8, 1.4, 0.9, 0.9, 1.5, 1.1, 9.1, 1.6, 1.3, 0.8, 4, 0.7, 1.4, 0.8, 3.6, 1.3, 1.3, 1, 1.1, 0.8, 1.2, 0.8, 0.9, 1.5, 1, 0.7, 6.6, 1.2, 1.8, 1, 1.3, 1, 1.3, 1.1, 1.1, 1, 0.9, 0.9, 1.1, 1.1, 0.9, 1.5, 4.5, 1.1, 0.8, 0.7, 0.9, 0.8, 1.6, 0.8, 0.8, 2, 2, 1.5, 1.2, 1.2, 0.9, 1.7, 1.4, 0.8, 1.5, 1, 1.1, 1.1, 0.7, 1.1, 1.2, 0.9, 1.5, 0.7, 1.5, 1.3, 0.8, 0.7, 1.1, 1, 1, 1.2, 0.8, 0.9, 0.8, 1.6, 2.4, 1.1, 2, 0.9, 1.4, 1.2, 1.1, 1.6, 0.9, 0.9, 1.3, 2, 1, 1.4, 1.3, 1.3, 0.7, 0.9, 1.1, 1.7, 1.1, 1.2, 0.9, 0.9, 1.1, 0.9, 5.2, 1.3, 0.7, 1.4, 1.4, 0.8, 1.2, 1.4, 0.9, 1.1, 1.1, 1.3, 1.7, 0.8, 1, 1.2, 1.9, 1.1, 1.3, 1.8, 0.6, 0.8, 1.4, 0.7, 0.9, 0.9, 1.2, 1.5, 0.7, 4.2, 1.1, 1.1, 1, 1.3, 0.8, 1.3, 1.1, 1.1, 0.8, 1.1, 1.5, 1.2, 1.2, 1.1, 1.7, 1, 1, 0.9, 0.9, 0.8, 1.2, 1.1, 0.7, 0.8, 1.1, 0.9, 1.4, 1, 1.1, 1.4, 0.9, 1, 1.7, 0.9, 1.3, 1.3, 0.8, 2.1, 1, 0.9, 1.2, 0.9, 1.1, 1.1, 1.2, 1.2, 0.9, 1.4, 1.2, 0.8, 1.1, 1.3, 1.1, 1.1, 0.8, 0.9, 0.9, 1.2, 1.1, 1.7, 1.3, 1.1, 1.7, 0.8, 0.9, 1.5, 1.1, 1.4, 1.4, 1.5, 1.1, 1.3, 0.9, 1.1, 1.1, 0.7, 1, 1.1, 0.6, 1, 1.2, 1.4, 1.1, 0.8, 1, 1.3, 0.9, 1, 1, 0.9, 1.5, 1.1, 1.5, 6.3, 1.4, 1.1, 5.2, 1.6, 1, 1.2, 1.3, 0.6, 1.1, 1.2, 1.1, 1.2, 1, 1.1, 1.9, 1.1, 1.2, 1.1, 0.7, 1.4, 2.2, 1.1, 1.5, 0.9, 1.2, 1.1, 0.8, 1.3, 1.1, 1.3, 1.8, 1.1, 1.1, 1.1, 1, 0.8, 1.7, 1.2, 1.4, 1.1, 1.4, 1.1, 0.8, 1, 1.1, 1.2, 1.4, 1, 1.3, 1.1, 2.3, 0.7, 1.3, 0.7, 0.9, 0.9, 1.2, 2, 0.7, 1.2, 1.6, 1.3, 1.4, 2.7, 1.5, 1, 1, 1.5, 1 }
};
double[,] outputs =
{
{ 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 9, 30, 30, 30, 30, 30, 2, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 2, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 13, 30, 30, 30, 30, 30, 30, 0, 30, 13, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 1, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 16, 30, 30, 30, 30, 30, 30, 0, 30, 30, 30, 30, 30, 30, 30, 30, 5, 30, 30, 30, 30, 30, 30, 30, 30, 1, 30, 21, 30, 30, 30, 30, 30, 30, 30, 30, 1, 30, 30, 30, 16, 30, 30, 30, 30, 30, 30, 30, 30, 2, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 16, 30, 30, 30, 30, 30, 3, 30, 18, 30, 30, 30, 30, 30, 28, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 0, 30, 30, 30, 30, 30, 1, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 17, 30, 1, 30, 30, 1, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 9, 30, 30, 30, 30, 1, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 9, 30, 30, 30, 27, 30, 30, 30, 30, 30, 30, 30, 30, 30, 0, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 16, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 20, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 1, 30, 30, 4, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 26, 30, 30, 30, 30, 12, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 21, 30, 1, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 9, 30, 30, 30, 30, 30, 30, 30, 1, 30, 1, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 0, 30, 25, 30, 30, 12, 30, 30, 30, 30, 30, 30, 10, 30, 30, 30, 30, 3, 30, 11, 30, 30, 30, 30, 30, 11, 30, 30, 30, 30, 30, 30, 4, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 1, 30, 30, 30, 30, 30, 1, 0, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 11, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 2, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 1, 30, 10, 30, 30, 30, 0, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 3, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 19, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 29, 30, 30, 30, 30, 30, 30, 2, 30, 30, 30, 30, 15, 30, 30, 30, 30, 30, 30, 30, 30, 3, 30, 30, 0, 30, 30, 30, 2, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 9, 30, 30, 30, 2, 30, 30, 30, 2, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 8, 30, 30, 30, 30, 30, 30, 0, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 14, 30, 30, 30, 9, 30, 30, 30, 30, 30, 13, 30, 30, 30, 4, 30, 30, 30, 30, 1, 30, 30, 30, 30, 30, 30, 10, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 1, 30, 30, 2, 30, 30, 30, 30, 30 },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0 }
};
double[][] covariates = inputs.Transpose().ToArray();
double[] time = outputs.GetRow(0);
int[] censor = outputs.GetRow(1).ToInt32();
// string inputStr = inputs.Transpose().ToString(Accord.Math.DefaultMatrixFormatProvider.InvariantCulture);
// string outputStr = outputs.Transpose().ToString(Accord.Math.DefaultMatrixFormatProvider.InvariantCulture);
var regression = new ProportionalHazards(2);
var target = new ProportionalHazardsNewtonRaphson(regression);
double error = target.Run(covariates, time, censor);
double log = -2 * regression.GetPartialLogLikelihood(covariates, time, censor);
Assert.AreEqual(-0.270, regression.Coefficients[0], 1e-4);
Assert.AreEqual(0.463, regression.Coefficients[1], 1e-2);
Assert.IsFalse(Double.IsNaN(regression.Coefficients[0]));
Assert.IsFalse(Double.IsNaN(regression.Coefficients[1]));
Assert.AreEqual(0.2454, regression.StandardErrors[0], 1e-4);
Assert.AreEqual(0.0671, regression.StandardErrors[1], 1e-4);
Assert.IsFalse(Double.IsNaN(regression.StandardErrors[0]));
Assert.IsFalse(Double.IsNaN(regression.StandardErrors[1]));
}
public void RunTest4()
{
// Data from: http://www.sph.emory.edu/~cdckms/CoxPH/prophaz2.html
// with added tied times
double[,] data =
{
{ 50, 1, 1 },
{ 60, 1, 1 },
{ 40, 1, 1 },
{ 51, 1, 1 },
{ 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).ToArray();
double[] time = data.GetColumn(1);
int[] output = data.GetColumn(2).ToInt32();
var target = new ProportionalHazardsNewtonRaphson(regression);
double error = target.Run(inputs, time, output);
double log = -2 * regression.GetPartialLogLikelihood(inputs, time, output);
Assert.AreEqual(0.04863, regression.Coefficients[0], 1e-4);
Assert.IsFalse(Double.IsNaN(regression.Coefficients[0]));
Assert.AreEqual(0.04186, regression.StandardErrors[0], 1e-4);
Assert.IsFalse(Double.IsNaN(regression.StandardErrors[0]));
}
public void KaplanMeierTest2()
{
int[][] data = Groups.Expand(
new[] { 1, 2, 3, 4, 5, 6 }, // years
new[] { 3, 3, 3, 3, 3, 0 }, // died
new[] { 5, 10, 15, 20, 25, 10 } // censored
);
double[] time = data.GetColumn(0).ToDouble();
int[] censor = data.GetColumn(1);
ProportionalHazards kp;
ProportionalHazards km;
double errkm, errp;
{
km = new ProportionalHazards(inputs: 0);
var target = new ProportionalHazardsNewtonRaphson(km)
{
Estimator = HazardEstimator.KaplanMeier
};
errkm = target.Run(time, censor);
Assert.AreEqual(-63.734599918211551, errkm);
}
{
kp = new ProportionalHazards(inputs: 0);
var target = new ProportionalHazardsNewtonRaphson(kp)
{
Estimator = HazardEstimator.BreslowNelsonAalen
};
errp = target.Run(time, censor);
Assert.AreEqual(errkm, errp);
}
}
/// <summary>
/// Gets the Log-Likelihood Ratio between two models.
/// </summary>
///
/// <remarks>
/// The Log-Likelihood ratio is defined as 2*(LL - LL0).
/// </remarks>
///
/// <param name="input">A set of input data.</param>
/// <param name="time">The time-to-event before the output occurs.</param>
/// <param name="output">The corresponding output data.</param>
/// <param name="hazards">Another Cox Proportional Hazards model.</param>
///
/// <returns>The Log-Likelihood ratio (a measure of performance
/// between two models) calculated over the given data sets.</returns>
///
public double GetLogLikelihoodRatio(double[][] input, double[] time, int[] output, ProportionalHazards hazards)
{
return 2.0 * (this.GetPartialLogLikelihood(input, time, output) - hazards.GetPartialLogLikelihood(input, time, output));
}
public void KaplanMeierTest()
{
double[,] data =
{
// time censor
{ 1, 0 }, // died at time 1
{ 2, 1 }, // lost at time 2
{ 3, 0 }, // died at time 3
{ 5, 0 }, // died at time 5
{ 7, 1 }, // lost at time 7
{ 11, 0 }, // ...
{ 4, 0 },
{ 6, 0 },
{ 8, 0 },
{ 9, 1 },
{ 10, 1 },
};
double[] time = data.GetColumn(0);
int[] censor = data.GetColumn(1).ToInt32();
var regression = new ProportionalHazards(inputs: 0);
var target = new ProportionalHazardsNewtonRaphson(regression)
{
Estimator = HazardEstimator.KaplanMeier
};
double error = target.Run(time, censor);
Assert.AreEqual(-5.7037824746562009, error);
}
/// <summary>
/// Creates a new Cox's Proportional Hazards that is a copy of the current instance.
/// </summary>
///
public object Clone()
{
var regression = new ProportionalHazards(Coefficients.Length);
regression.Coefficients = (double[])this.Coefficients.Clone();
regression.StandardErrors = (double[])this.StandardErrors.Clone();
regression.Offsets = (double[])this.Offsets.Clone();
return regression;
}
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]));
}
}
