ProportionalHazards (JMSL Numerical Library)

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com.imsl.stat
Class ProportionalHazards

java.lang.Object
  com.imsl.stat.ProportionalHazards

All Implemented Interfaces:: Serializable, Cloneable

public class ProportionalHazards
extends Object
implements Serializable, Cloneable
extends Object
implements Serializable, Cloneable

Analyzes survival and reliability data using Cox's proportional hazards model.

Class ProportionalHazards computes parameter estimates and other statistics in Proportional Hazards Generalized Linear Models. These models were first proposed by Cox (1972). Two methods for handling ties are allowed. Time-dependent covariates are not allowed. The user is referred to Cox and Oakes (1984), Kalbfleisch and Prentice (1980), Elandt-Johnson and Johnson (1980), Lee (1980), or Lawless (1982), among other texts, for a thorough discussion of the Cox proportional hazards model.

Let represent the hazard rate at time t for observation number i with covariables contained as elements of row vector . The basic assumption in the proportional hazards model (the proportionality assumption) is that the hazard rate can be written as a product of a time varying function , which depends only on time, and a function , which depends only on the covariable values. The function used in ProportionalHazards is given as $f(z_i) = textup{exp}(w_i + beta z_i)$ where is a fixed constant assigned to the observation, and b is a vector of coefficients to be estimated. With this function one obtains a hazard rate $lambda(t, z_i) = lambda_0(t) textup{exp}(w_i + beta z_i)$ . The form of is not important in proportional hazards models.

The constants may be known theoretically. For example, the hazard rate may be proportional to a known length or area, and the can then be determined from this known length or area. Alternatively, the may be used to fix a subset of the coefficients (say, ) at specified values. When is used in this way, constants $w_i=beta_1z_{1i}$ are used, while the remaining coefficients in are free to vary in the optimization algorithm. Constants are defined as 0.0 by default. If user-specified constants are desired, use the setConstantColumn method to specify which column contains the constant.

With this definition of , the usual partial (or marginal, see Kalbfleisch and Prentice (1980)) likelihood becomes

$L=prod_{i=1}^{n_d}frac{textup{exp}(w_i+beta z_i)} {sum_{jin R(t_i)}^{}textup{exp}(w_j+beta z_j)}$

where denotes the set of indices of observations that have not yet failed at time (the risk set), denotes the time of failure for the i-th observation, is the total number of observations that fail. Right-censored observations (i.e., observations that are known to have survived to time , but for which no time of failure is known) are incorporated into the likelihood through the risk set . Such observations never appear in the numerator of the likelihood. When setTieOptions is set to BRESLOWS_APPROXIMATE (the default), all observations that are censored at time are not included in , while all observations that fail at time are included in .

If it can be assumed that the dependence of the hazard rate upon the covariate values remains the same from stratum to stratum, while the time-dependent term, , may be different in different strata, then ProportionalHazards allows the incorporation of strata into the likelihood as follows. Let k index the m strata (set with setStratumColumn). Then, the likelihood is given by

$L_S=prod_{k=1}^{m}left [ prod_{i=1}^{n_k}frac{textup{exp}(w_{ki}+beta z_{ki})}{sum_{jin R(t_{ki})}^{}textup{exp}(w_{kj}+beta z_{kj})} right ]$

In ProportionalHazards, the log of the likelihood is maximized with respect to the coefficients . A quasi-Newton algorithm approximating the Hessian via the matrix of sums of squares and cross products of the first partial derivatives is used in the initial iterations. When the change in the log-likelihood from one iteration to the next is less than 100 times the convergence tolerance, Newton-Raphson iteration is used. If, during any iteration, the initial step does not lead to an increase in the log-likelihood, then step halving is employed to find a step that will increase the log-likelihood.

Once the maximum likelihood estimates have been computed, the algorithm computes estimates of a probability associated with each failure. Within stratum k, an estimate of the probability that the i-th observation fails at time given the risk set $R(t_{ki})$ is given by

$p_{ki}=frac{textup{exp}(w_{ki}+beta z_{ki})}{sum_{jin R(t_{ki})}^{}textup{exp}(w_{kj}+beta z_{kj})}$

A diagnostic "influence" or "leverage" statistic is computed for each noncensored observation as:

$l_{ki}=-{g}'_{ki}H^{-1}_s{g}'_{ki}$

where

is the matrix of second partial derivatives of the log-likelihood, and

${g}'_{ki}$

is computed as:

${g}'_{ki}=z_{ki}-frac{z_{ki}textup{exp}(w_{ki}+beta z_{ki})}{sum_{jin R(t_{ki})}^{}textup{exp}(w_{kj}+beta z_{kj})}$

Influence statistics are not computed for censored observations.

A "residual" is computed for each of the input observations according to methods given in Cox and Oakes (1984, page 108). Residuals are computed as

$r_{ki}=textup{exp}(w_{ki}+hat{beta} z_{ki})sum_{j in R(t_{ki})}^{}frac{d_{kj}}{sum_{l in R(t_{kj})}^{}textup{exp}(w_{kl}+hat{beta} z_{kl})}$

where $d_{kj}$ is the number of tied failures in group k at time $t_{kj}$ . Assuming that the proportional hazards assumption holds, the residuals should approximate a random sample (with censoring) from the unit exponential distribution. By subtracting the expected values, centered residuals can be obtained. (The j-th expected order statistic from the unit exponential with censoring is given as

$e_j=sum_{l le j}^{}frac{1}{h-l+1}$

where h is the sample size, and censored observations are not included in the summation.)

An estimate of the cumulative baseline hazard within group k is given as

$hat{H}_{k0}(t_{ik})=sum_{t_{kj} le t_{ki}}^{}frac{d_{kj}}{sum_{l in R(t_{kj})}^{}textup{exp}(w_{kl}+hat{beta} z_{kl})}$

The observation proportionality constant is computed as

$textup{exp}(w_{ki}+hat{beta}z_{ki})$

Note that the user can use the JDK JAVA Logging API to generate intermediate output for the solver. Accumulated levels of detail correspond to JAVA's FINE, FINER, and FINEST logging levels with FINE yielding the smallest amount of information and FINEST yielding the most. The levels of output yield the following:

Level	Output
FINE	Logging is enabled, but observational statistics are not printed.
FINER	All output statistics are printed.
FINEST	Tracks progress through internal methods.

See Also:: Example , Serialized Form

Nested Class Summary
`static class`	`ProportionalHazards.ClassificationVariableLimitException` The Classification Variable limit set by the user through `setUpperBound` has been exceeded.

Field Summary
`static int`	`BRESLOWS_APPROXIMATE` Breslows approximate method of handling ties.
`static int`	`SORTED_AS_PER_OBSERVATIONS` Failures are assumed to occur in the same order as the observations input in `x`.

Constructor Summary
`ProportionalHazards(double[][] x, int[] nVarEffects, int[] indEffects)` Constructor for `ProportionalHazards`.

Method Summary
`double[][]`	`getCaseStatistics()` Returns the case statistics for each observation.
`int`	`getCensorColumn()` Returns the column index of `x` containing the optional censoring code for each observation.
`int[]`	`getClassValueCounts()` Returns the number of values taken by each classification variable.
`double[]`	`getClassValues()` Returns the class values taken by each classification variable.
`int`	`getConstantColumn()` Returns the column index of `x` containing the constant to be added to the linear response.
`double`	`getConvergenceTol()` Returns the convergence tolerance used.
`int`	`getFrequencyColumn()` Returns the column index of `x` containing the frequency of response for each observation.
`double[]`	`getGradient()` Returns the inverse of the Hessian times the gradient vector, computed at the initial estimates.
`double[][]`	`getHessian()` Returns the inverse of the Hessian of the negative of the log-likelihood, computed at the initial estimates.
`boolean`	`getHessianOption()` Returns the `boolean` used to indicate whether or not to compute the Hessian and gradient at the initial estimates.
`double[]`	`getInitialEstimates()` Gets the initial parameter estimates.
`double[]`	`getLastUpdates()` Gets the last parameter updates.
`Logger`	`getLogger()` Returns the logger object and enables logging.
`int`	`getMaxClass()` Returns the upper bound used on the sum of the number of distinct values found among the classification variables in `x`.
`double`	`getMaximumLikelihood()` Returns the maximized log-likelihood.
`int`	`getMaxIterations()` Return the maximum number of iterations allowed.
`double[]`	`getMeans()` Returns the means of the design variables.
`int`	`getNumberOfCoefficients()` Returns the number of estimated coefficients in the model.
`int`	`getNumberRowsMissing()` Returns the number of rows of data in `x` that contain missing values in one or more specific columns of `x`.
`double[][]`	`getParameterStatistics()` Returns the parameter estimates and associated statistics.
`int`	`getResponseColumn()` Returns the column index of `x` containing the response time for each observation.
`int`	`getStratumColumn()` Returns the column index of `x` containing the stratum number for each observation.
`int[]`	`getStratumNumbers()` Returns the stratum number used for each observation.
`double`	`getStratumRatio()` Returns the ratio at which a stratum is split into two strata.
`int`	`getTiesOption()` Returns the method used for handling ties.
`double[][]`	`getVarianceCovarianceMatrix()` Returns the estimated asymptotic variance-covariance matrix of the parameters.
`void`	`setCensorColumn(int censorIndex)` Sets the column index of `x` containing the optional censoring code for each observation.
`void`	`setClassVarColumns(int[] classVarIndices)` Sets the column indices of `x` that are the classification variables.
`void`	`setConstantColumn(int fixedIndex)` Sets the column index of `x` containing the constant to be added to the linear response.
`void`	`setConvergenceTol(double convergenceTol)` Set the convergence tolerance.
`void`	`setFrequencyColumn(int frequencyIndex)` Sets the column index of `x` containing the frequency of response for each observation.
`void`	`setHessianOption(boolean wantHessian)` Set the option to have the Hessian and gradient be computed at the initial estimates.
`void`	`setInitialEstimates(double[] initialCoef)` Sets the initial parameter estimates.
`void`	`setMaxClass(int maxClass)` Sets an upper bound on the sum of the number of distinct values found among the classification variables in `x`.
`void`	`setMaxIterations(int maxIterations)` Set the maximum number of iterations allowed.
`void`	`setResponseColumn(int responseIndex)` Sets the column index of `x` containing the response variable.
`void`	`setStratumColumn(int stratumIndex)` Sets the column index of `x` containing the stratification variable.
`void`	`setStratumRatio(double stratumRatio)` Set the ratio at which a stratum is split into two strata.
`void`	`setTiesOption(int iTie)` Sets the method for handling ties.

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Field Detail

BRESLOWS_APPROXIMATE

public static final int BRESLOWS_APPROXIMATE

Breslows approximate method of handling ties. See setTiesOption.

See Also:: Constant Field Values

SORTED_AS_PER_OBSERVATIONS

public static final int SORTED_AS_PER_OBSERVATIONS

Failures are assumed to occur in the same order as the observations input in x. The observations in x must be sorted from largest to smallest failure time within each stratum, and grouped by stratum. All observations are treated as if their failure/censoring times were distinct when computing the log-likelihood. See setTiesOption.

See Also:: Constant Field Values

Constructor Detail

ProportionalHazards

public ProportionalHazards(double[][] x,
                           int[] nVarEffects,
                           int[] indEffects)

Constructor for ProportionalHazards.

Parameters:: x - a double matrix containing the data, including optional data.; nVarEffects - an int array containing the number of variables associated with each effect in the model.; indEffects - an int array containing the column numbers of x associated with each effect. The first nVarEffects[0] elements of indEffects contain the column numbers of x for the variables in the first effect. The next nVarEffects[1] elements of indEffects contain the column numbers of x for the variables in the second effect, etc.

Method Detail

getCaseStatistics

public double[][] getCaseStatistics()
                             throws ProportionalHazards.ClassificationVariableLimitException

Returns the case statistics for each observation.

There is one row for each observation, and the columns of the returned matrix contain the following:

Column	Statistic
`0`	Estimated survival probability at the observation time.
`1`	Estimated observation influence or leverage.
`2`	A residual estimate.
`3`	Estimated cumulative baseline hazard rate.
`4`	Observation proportionality constant.

Returns:: a double matrix containing the case statistics.
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

getCensorColumn

public int getCensorColumn()

Returns the column index of x containing the optional censoring code for each observation.

Returns:: an int specifying the column index of x containing the optional censoring code for each observation.

getClassValueCounts

public int[] getClassValueCounts()
                          throws ProportionalHazards.ClassificationVariableLimitException

Returns the number of values taken by each classification variable. The i-th element of the returned array is the number of distinct values taken by the i-th classification variable.

Returns:: an int array containing the number of values taken by each classification variable.
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

getClassValues

public double[] getClassValues()
                        throws ProportionalHazards.ClassificationVariableLimitException

Returns the class values taken by each classification variable. For description purposes, let
nclval = getClassValueCounts(). Then the first nclval[0] elements contain the values for the first classification variable, the next nclval[1] elements contain the values for the second classification variable, etc.

Returns:: a double array containing the values taken by each classification variable.
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

getConstantColumn

public int getConstantColumn()

Returns the column index of x containing the constant to be added to the linear response.

Returns:: an int specifying the column index of x containing the constant to be added to the linear response.

getConvergenceTol

public double getConvergenceTol()

Returns the convergence tolerance used.

Returns:: a double specifying the convergence tolerance used.

getFrequencyColumn

public int getFrequencyColumn()

Returns the column index of x containing the frequency of response for each observation.

Returns:: an int specifying the column index of x containing the frequency of response for each observation.

getGradient

public double[] getGradient()
                     throws ProportionalHazards.ClassificationVariableLimitException

Returns the inverse of the Hessian times the gradient vector, computed at the initial estimates.

Note that the setHessianOption method must be invoked with wantHessian set to true and the setInitialEstimates method must be invoked prior to invoking this method. Otherwise, the method throws an IllegalStateException exception.

Returns:: a double array containing the inverse of the Hessian times the gradient vector, computed at the initial estimates.
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

getHessian

public double[][] getHessian()
                      throws ProportionalHazards.ClassificationVariableLimitException

Returns the inverse of the Hessian of the negative of the log-likelihood, computed at the initial estimates.

Note that the setHessianOption method must be invoked with wantHessian set to true and the setInitialEstimates method must be invoked prior to invoking this method.

Otherwise, the method throws an IllegalStateException exception.

Returns:: a double matrix containing the inverse of the Hessian of the negative of the log-likelihood, computed at the initial estimates.
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

getHessianOption

public boolean getHessianOption()

Returns the boolean used to indicate whether or not to compute the Hessian and gradient at the initial estimates.

Returns:: a boolean specifying whether or not the Hessian and gradient are to be computed at the initial estimates. A return value equal to true indicates that the Hessian and gradient are to be computed.

getInitialEstimates

public double[] getInitialEstimates()
                             throws ProportionalHazards.ClassificationVariableLimitException

Gets the initial parameter estimates.

Returns:: a double array containing the initial parameter estimates.
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

getLastUpdates

public double[] getLastUpdates()
                        throws ProportionalHazards.ClassificationVariableLimitException

Gets the last parameter updates.

Returns:: a double array containing the last parameter updates (excluding step halvings).
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

getLogger

public Logger getLogger()

Returns the logger object and enables logging.

Returns:: a java.util.logging.Logger object, if present, or null.

getMaxClass

public int getMaxClass()

Returns the upper bound used on the sum of the number of distinct values found among the classification variables in x.

Returns:: an int representing the upper bound used on the sum of the number of distinct values found among the classification variables in x.

getMaximumLikelihood

public double getMaximumLikelihood()
                            throws ProportionalHazards.ClassificationVariableLimitException

Returns the maximized log-likelihood.

The log-likelihood is fully described in the ProportionalHazards class description.

Returns:: a double representing the maximized log-likelihood
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

getMaxIterations

public int getMaxIterations()

Return the maximum number of iterations allowed.

Returns:: an int specifying the maximum number of iterations allowed.

getMeans

public double[] getMeans()
                  throws ProportionalHazards.ClassificationVariableLimitException

Returns the means of the design variables.

Returns:: a double array containing the means of the design variables.
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

getNumberOfCoefficients

public int getNumberOfCoefficients()
                            throws ProportionalHazards.ClassificationVariableLimitException

Returns the number of estimated coefficients in the model.

Returns:: an int scalar representing the number of estimated coefficients in the model.
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

getNumberRowsMissing

public int getNumberRowsMissing()
                         throws ProportionalHazards.ClassificationVariableLimitException

Returns the number of rows of data in x that contain missing values in one or more specific columns of x.

Returns:: an int scalar representing the number of rows of data in x that contain missing values in one or more specific columns of x.
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

getParameterStatistics

public double[][] getParameterStatistics()
                                  throws ProportionalHazards.ClassificationVariableLimitException

Returns the parameter estimates and associated statistics.

There is one row for each coefficient, and the columns of the returned matrix contain the following:

Column	Statistic
`0`	The coefficient estimate,
`1`	Estimated standard deviation of the estimated coefficient
`2`	Asymptotic normal score for testing that the coefficient is zero against the two-sided alternative
`3`	p-value associated with the normal score in column 2

Returns:: a double matrix containing the parameter estimates and associated statistics.
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

getResponseColumn

public int getResponseColumn()

Returns the column index of x containing the response time for each observation.

Returns:: an int specifying the column index of x containing the response time for each observation.

getStratumColumn

public int getStratumColumn()

Returns the column index of x containing the stratum number for each observation.

Returns:: an int specifying the column index of x containing the stratum number for each observation.

getStratumNumbers

public int[] getStratumNumbers()
                        throws ProportionalHazards.ClassificationVariableLimitException

Returns the stratum number used for each observation. If stratumRatio is not -1.0, additional "strata" (other than those specified by column groupIndex of x set via the setStratumColumn method) may be generated. The array also contains a record of the generated strata. See the ProportionalHazards class description for more detail.

Returns:: an int array containing the stratum number used for each observation.
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

getStratumRatio

public double getStratumRatio()

Returns the ratio at which a stratum is split into two strata.

Returns:: a double specifying the ratio at which a stratum is split into two strata.

getTiesOption

public int getTiesOption()

Returns the method used for handling ties.

Returns:

an int specifying the method to be used in handling ties as indicated by the value in the following table:

`Value`	Method
`BRESLOWS_APPROXIMATE`	Breslow's approximate method. This is the default.
`SORTED_AS_PER_OBSERVATIONS`	Failures are assumed to occur in the same order as the observations input in `x`. The observations in `x` must be sorted from largest to smallest failure time within each stratum, and grouped by stratum. All observations are treated as if their failure/censoring times were distinct when computing the log-likelihood.

getVarianceCovarianceMatrix

public double[][] getVarianceCovarianceMatrix()
                                       throws ProportionalHazards.ClassificationVariableLimitException

Returns the estimated asymptotic variance-covariance matrix of the parameters.

Returns:: a double matrix containing the estimated asymptotic variance-covariance matrix of the parameters.
Throws:: ProportionalHazards.ClassificationVariableLimitException - is thrown if the classification variable limit set by the user through setUpperBound has been exceeded.

setCensorColumn

public void setCensorColumn(int censorIndex)

Sets the column index of x containing the optional censoring code for each observation.

If x[i][censorIndex] equals 0, the failure time x[i][responseIndex] is treated as an exact time of failure. Otherwise, it is treated as right-censored time. By default, it is assumed that there is no censor code column in x and all observations are assumed to be exact failure times.

Parameters:: censorIndex - an int specifying the column index of x containing the optional censoring code for each observation.

setClassVarColumns

public void setClassVarColumns(int[] classVarIndices)

Sets the column indices of x that are the classification variables.

Parameters:: classVarIndices - an int array containing the column numbers of x that are the classification variables. By default it is assumed there are no classification variables.

setConstantColumn

public void setConstantColumn(int fixedIndex)

Sets the column index of x containing the constant

to be added to the linear response.

The linear response is taken to be $w_i+z_ihat{beta}$ where is the observation constant, is the observation design row vector, and is the vector of estimated parameters. The "fixed" constant allows one to test hypotheses about parameters via the log-likelihoods. If this method is not called, it is assumed that for all observations.

Parameters:: fixedIndex - an int specifying the column index of x containing the constant to be added to the linear response.

setConvergenceTol

public void setConvergenceTol(double convergenceTol)

Set the convergence tolerance.

Convergence is assumed when the relative change in the maximum likelihood from one iteration to the next is less than convergenceTol. If convergenceTol is zero, convergenceTol = 0.0001 is assumed. The default value is 0.0001.

Parameters:: convergenceTol - a double specifying the convergence tolerance.

setFrequencyColumn

public void setFrequencyColumn(int frequencyIndex)

Sets the column index of x containing the frequency of response for each observation.

By default it is assumed that there is no frequency response column recorded in x. Each observation in the data array is assumed to be for a single failure; that is, the frequency of response for each observation is 1.

Parameters:: frequencyIndex - an int specifying the column index of x containing the frequency of response for each observation.

setHessianOption

public void setHessianOption(boolean wantHessian)

Set the option to have the Hessian and gradient be computed at the initial estimates.

Parameters:: wantHessian - a boolean specifying whether or not the Hessian and gradient are to be computed at the initial estimates. If this option is set to true the user must set the initial estimates via the setInitialEstimates method. By default the Hessian and gradient are not computed at the initial estimates.

setInitialEstimates

public void setInitialEstimates(double[] initialCoef)

Sets the initial parameter estimates.

Care should be taken to ensure that the supplied estimates for the model coefficients correspond to the generated covariate vector $z_{ki}$ .

Parameters:: initialCoef - a double array containing the initial parameter estimates. By default the initial parameter estimates are all 0.0.

setMaxClass

public void setMaxClass(int maxClass)

Sets an upper bound on the sum of the number of distinct values found among the classification variables in x.

For example, if the model consisted of of two class variables, one with the values {1, 2, 3, 4} and a second with the values {0, 1}, then the total number of different classification values is 4 + 2 = 6, and maxClass . The default value is the number of observations in x.

Parameters:: maxClass - an int representing an upper bound on the sum of the number of distinct values found among the classification variables in x.

setMaxIterations

public void setMaxIterations(int maxIterations)

Set the maximum number of iterations allowed.

Parameters:: maxIterations - an int specifying the maximum number of iterations allowed. The default value is 30.

setResponseColumn

public void setResponseColumn(int responseIndex)

Sets the column index of x containing the response variable.

For point observations, x[i][responseIndex] contains the time of the i-th event. For right-censored observations, x[i][responseIndex] contains the right-censoring time. Note that because ProportionalHazards only uses the order of the events, negative "times" are allowed. By default responseIndex = 0.

Parameters:: responseIndex - an int specifying the column index of x containing the response variable.

setStratumColumn

public void setStratumColumn(int stratumIndex)

Sets the column index of x containing the stratification variable.

Column stratumIndex of x contains a unique value for each stratum in the data. The risk set for an observation is determined by its stratum. By default it is assumed that all obvservations are from one statum.

Parameters:: stratumIndex - an int specifying the column index of x containing the stratification variable.

setStratumRatio

public void setStratumRatio(double stratumRatio)

Set the ratio at which a stratum is split into two strata.

Let

$r_k=textup{exp}(z_khat{beta}+w_k)$

be the observation proportionality constant, where

is the design row vector for the k-th observation and

is the optional fixed parameter specified by $x_{k,textup{fixedIndex}}$ . Let $r_{min}$ be the minimum value

in a stratum, where, for failed observations, the minimum is over all times less than or equal to the time of occurrence of the k-th observation. Let $r_{max}$ be the maximum value of

for the remaining observations in the group. Then, if $r_{min}$

stratumRatio $* r_{max}$ , the observations in the group are divided into two groups at k. The default value of stratumRatio = 1000 is usually good.

Set stratumRatio to any negative value if no division into strata is to be made.

Parameters:: stratumRatio - a double specifying the ratio at which a stratum is split into two strata.

setTiesOption

public void setTiesOption(int iTie)

Sets the method for handling ties.

Parameters:

iTie - an int specifying the method to be used in handling ties. It can be either BRESLOWS_APPROXIMATE or SORTED_AS_PER_OBSERVATIONS.

`iTie`	Method
`BRESLOWS_APPROXIMATE`	Breslow's approximate method. This is the default.
`SORTED_AS_PER_OBSERVATIONS`	Failures are assumed to occur in the same order as the observations input in `x`. The observations in `x` must be sorted from largest to smallest failure time within each stratum, and grouped by stratum. All observations are treated as if their failure/censoring times were distinct when computing the log-likelihood.

By default, iTie is BRESLOWS_APPROXIMATE.