ProportionalHazardsAnalysis Class

[SerializableAttribute]
public class ProportionalHazardsAnalysis : IRegressionAnalysis, 
	IMultivariateAnalysis, IAnalysis, ISupervisedLearning<ProportionalHazards, Tuple<double[], double>, int>

<SerializableAttribute>
Public Class ProportionalHazardsAnalysis
	Implements IRegressionAnalysis, IMultivariateAnalysis, IAnalysis, ISupervisedLearning(Of ProportionalHazards, Tuple(Of Double(), Double), Integer)

// Consider the following example data, adapted from John C. Pezzullo's
// example for his great Cox's proportional hazards model example in
// JavaScript (http://statpages.org/prophaz2.html). 

// In this data, we have three columns. The first column denotes the
// input variables for the problem. The second column, the survival
// times. And the last one is the output of the experiment (if the
// subject has died [1] or has survived [0]).

double[][] example =
{
    //             input  time censor
    new double[] {   50,    1,    0   },
    new double[] {   70,    2,    1   },
    new double[] {   45,    3,    0   },
    new double[] {   35,    5,    0   },
    new double[] {   62,    7,    1   },
    new double[] {   50,   11,    0   },
    new double[] {   45,    4,    0   },
    new double[] {   57,    6,    0   },
    new double[] {   32,    8,    0   },
    new double[] {   57,    9,    1   },
    new double[] {   60,   10,    1   },
};

// First we will extract the input, times and outputs
double[][] inputs = example.Get(null, 0, 1);
double[] times = example.GetColumn(1);
SurvivalOutcome[] output = example.GetColumn(2).To<SurvivalOutcome[]>();

// Now we can proceed and create the analysis (giving optional variable names)
var cox = new ProportionalHazardsAnalysis(new[] { "input" }, "time", "censor");

// Then compute the analysis, learning a regression in the process:
ProportionalHazards regression = cox.Learn(inputs, times, output);

// Now we can show an analysis summary
// Accord.Controls.DataGridBox.Show(cox.Coefficients);

' Consider the following example data, adapted from John C. Pezzullo's
' example for his great Cox's proportional hazards model example in
' JavaScript (http://statpages.org/prophaz2.html). 

' In this data, we have three columns. The first column denotes the
' input variables for the problem. The second column, the survival
' times. And the last one Is the output of the experiment (if the
' subject has died [1] Or has survived [0]).

Dim example()() As Double =
{
    New Double() {50, 1, 0},
    New Double() {70, 2, 1},
    New Double() {45, 3, 0},
    New Double() {35, 5, 0},
    New Double() {62, 7, 1},
    New Double() {50, 11, 0},
    New Double() {45, 4, 0},
    New Double() {57, 6, 0},
    New Double() {32, 8, 0},
    New Double() {57, 9, 1},
    New Double() {60, 10, 1}
}

' First we will extract the input, times And outputs
Dim inputs()() As Double = example.Get(Nothing, 0, 1)
Dim times() As Double = example.GetColumn(1)
Dim output() As SurvivalOutcome = example.GetColumn(2).To(Of SurvivalOutcome())

' Now we can proceed And create the analysis (giving optional variable names)
Dim cox = New ProportionalHazardsAnalysis(New String() {"input"}, "time", "censor")

' Then compute the analysis, learning a regression in the process
Dim regression As ProportionalHazards = cox.Learn(inputs, times, output)

' Now we can show an analysis summary
' Accord.Controls.DataGridBox.Show(cox.Coefficients);

' We can also investigate all parameters individually. For
' example the coefficients values will be available at

Dim coef As Double() = cox.CoefficientValues    ' should be { 0.37704239281490765 }
Dim stde As Double() = cox.StandardErrors       ' should be { 0.25415746361167235 }

' We can also obtain the hazards ratios         
Dim ratios As Double() = cox.HazardRatios       ' should be { 1.4579661153488215 }

' And other information such as the partial
' likelihood, the deviance And also make 
' hypothesis tests on the parameters

Dim partialL = cox.LogLikelihood                ' should be -2.0252666205735466
Dim deviance = cox.Deviance                     ' should be 4.0505332411470931

' Chi-Square for whole model              
Dim chi As ChiSquareTest = cox.ChiSquare        ' should be 7.3570 (p=0.0067)

' Wald tests for individual parameters    
Dim wald As WaldTest = cox.Coefficients(0).Wald ' should be 1.4834 (p=0.1379)


' Finally, we can also use the model to predict
' scores for New observations (without considering time)

Dim y1 = cox.Regression.Probability(New Double() {63}) ' should be 86.138421225296526
Dim y2 = cox.Regression.Probability(New Double() {32}) ' should be 0.00072281400325299814

' Those scores can be interpreted by comparing then
' to 1. If they are greater than one, the odds are
' the patient will Not survive. If the value Is less
' than one, the patient Is likely to survive.

' The first value, y1, gives approximately 86.138,
' while the second value, y2, gives about 0.00072.


' We can also consider instant estimates for a given time
Dim p1 = cox.Regression.Probability(New Double() {63}, 2)  'should be 0.17989138010770425
Dim p2 = cox.Regression.Probability(New Double() {63}, 10) ' should be 15.950244161356357

' Here, p1 Is the score after 2 time instants, with a 
' value of 0.0656. The second value, p2, Is the time
' after 10 time instants, with a value of 6.2907.

' In addition, if we would Like a higher precision when 
' computing very small probabilities using the methods 
' above, we can use the LogLikelihood methods instead

Dim log_y1 = cox.Regression.LogLikelihood(New Double() {63})     ' should be  4.4559555514489091
Dim log_y2 = cox.Regression.LogLikelihood(New Double() {32})     ' should be -7.2323586258132284
Dim log_p1 = cox.Regression.LogLikelihood(New Double() {63}, 2)  ' should be -1.7154020540835324
Dim log_p2 = cox.Regression.LogLikelihood(New Double() {63}, 10) ' should be  2.7694741370357177

// We can also investigate all parameters individually. For
// example the coefficients values will be available at

double[] coef = cox.CoefficientValues;     // should be { 0.37704239281490765 }
double[] stde = cox.StandardErrors;        // should be { 0.25415746361167235 }

// We can also obtain the hazards ratios
double[] ratios = cox.HazardRatios;        // should be { 1.4579661153488215 }

// And other information such as the partial
// likelihood, the deviance and also make 
// hypothesis tests on the parameters

double partialL = cox.LogLikelihood;       // should be -2.0252666205735466
double deviance = cox.Deviance;            // should be 4.0505332411470931

// Chi-Square for whole model              
ChiSquareTest chi = cox.ChiSquare;         // should be 7.3570 (p=0.0067)

// Wald tests for individual parameters
WaldTest wald = cox.Coefficients[0].Wald;  // should be 1.4834 (p=0.1379)


// Finally, we can also use the model to predict
// scores for new observations (without considering time)

double y1 = cox.Regression.Probability(new double[] { 63 }); // should be 86.138421225296526
double y2 = cox.Regression.Probability(new double[] { 32 }); // should be 0.00072281400325299814

// Those scores can be interpreted by comparing then
// to 1. If they are greater than one, the odds are
// the patient will not survive. If the value is less
// than one, the patient is likely to survive.

// The first value, y1, gives approximately 86.138,
// while the second value, y2, gives about 0.00072.


// We can also consider instant estimates for a given time:
double p1 = cox.Regression.Probability(new double[] { 63 }, 2);   // should be 0.17989138010770425
double p2 = cox.Regression.Probability(new double[] { 63 }, 10);  // should be 15.950244161356357

// Here, p1 is the score after 2 time instants, with a 
// value of 0.0656. The second value, p2, is the time
// after 10 time instants, with a value of 6.2907.

// In addition, if we would like a higher precision when 
// computing very small probabilities using the methods 
// above, we can use the LogLikelihood methods instead:

double log_y1 = cox.Regression.LogLikelihood(new double[] { 63 });      // should be  4.4559555514489091
double log_y2 = cox.Regression.LogLikelihood(new double[] { 32 });      // should be -7.2323586258132284
double log_p1 = cox.Regression.LogLikelihood(new double[] { 63 }, 2);   // should be -1.7154020540835324
double log_p2 = cox.Regression.LogLikelihood(new double[] { 63 }, 10);  // should be  2.7694741370357177