NAG Library Routine Document

g12zaf (coxmodel_risksets)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of data points.

Constraint: $\mathbf{n}\ge 2$.

2:     $\mathbf{m}$ – IntegerInput

On entry: the number of covariates in array z.

Constraint: $\mathbf{m}\ge 1$.

3:     $\mathbf{ns}$ – IntegerInput

On entry: the number of strata. If $\mathbf{ns}>0$ then the stratum for each observation must be supplied in isi.

Constraint: $\mathbf{ns}\ge 0$.

4:     $\mathbf{z}\left(\mathbf{ldz},\mathbf{m}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the $i$th row must contain the covariates which are associated with the $i$th failure time given in t.

5:     $\mathbf{ldz}$ – IntegerInput

On entry: the first dimension of the array z as declared in the (sub)program from which g12zaf is called.

Constraint: $\mathbf{ldz}\ge \mathbf{n}$.

6:     $\mathbf{isz}\left(\mathbf{m}\right)$ – Integer arrayInput

On entry: indicates which subset of covariates are to be included in the model.

$\mathbf{isz}\left(j\right)\ge 1$

The $j$th covariate is included in the model.

$\mathbf{isz}\left(j\right)=0$

The $j$th covariate is excluded from the model and not referenced.

Constraint: $\mathbf{isz}\left(j\right)\ge 0$ and at least one value must be nonzero.

7:     $\mathbf{ip}$ – IntegerInput

On entry: $p$, the number of covariates included in the model as indicated by isz.

Constraint: $\mathbf{ip}=$ the number of nonzero values of isz.

8:     $\mathbf{t}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the vector of $n$ failure censoring times.

9:     $\mathbf{ic}\left(\mathbf{n}\right)$ – Integer arrayInput

On entry: the status of the individual at time $t$ given in t.

$\mathbf{ic}\left(i\right)=0$

Indicates that the $i$th individual has failed at time $\mathbf{t}\left(i\right)$.

$\mathbf{ic}\left(i\right)=1$

Indicates that the $i$th individual has been censored at time $\mathbf{t}\left(i\right)$.

Constraint: $\mathbf{ic}\left(\mathit{i}\right)=0$ or $1$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

10:   $\mathbf{isi}\left(*\right)$ – Integer arrayInput

Note: the dimension of the array isi must be at least $\mathbf{n}$ if $\mathbf{ns}>0$, and at least $1$ otherwise.

On entry: if $\mathbf{ns}>0$, the stratum indicators which also allow data points to be excluded from the analysis.

If $\mathbf{ns}=0$, isi is not referenced.

$\mathbf{isi}\left(i\right)=k$

Indicates that the $i$th data point is in the $k$th stratum, where $k=1,2,\dots ,\mathbf{ns}$.

$\mathbf{isi}\left(i\right)=0$

Indicates that the $i$th data point is omitted from the analysis.

Constraint: if $\mathbf{ns}>0$, $0\le \mathbf{isi}\left(\mathit{i}\right)\le \mathbf{ns}$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

11:   $\mathbf{num}$ – IntegerOutput

On exit: the number of values in the combined risk sets.

12:   $\mathbf{ixs}\left(\mathbf{mxn}\right)$ – Integer arrayOutput

On exit: the factor giving the risk sets/strata for the data in x and id.

If $\mathbf{ns}=0$ or $1$, $\mathbf{ixs}\left(i\right)=l$ for members of the $l$th risk set.

If $\mathbf{ns}>1$, $\mathbf{ixs}\left(i\right)=\left(j-1\right)\times \mathbf{nd}+l$ for the observations in the $l$th risk set for the $j$th strata.

13:   $\mathbf{nxs}$ – IntegerOutput

On exit: the number of levels for the risk sets/strata factor given in ixs.

14:   $\mathbf{x}\left(\mathbf{mxn},\mathbf{ip}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the first num rows contain the values of the covariates for the members of the risk sets.

15:   $\mathbf{mxn}$ – IntegerInput

On entry: the first dimension of the array x and the dimension of the arrays ixs and id as declared in the (sub)program from which g12zaf is called.

Constraint: mxn must be sufficiently large for the arrays to contain the expanded risk sets. The size will depend on the pattern of failures times and censored times. The minimum value will be returned in num unless the routine exits with $\mathbf{ifail}=\mathbf{1}$ or $\mathbf{2}$.

16:   $\mathbf{id}\left(\mathbf{mxn}\right)$ – Integer arrayOutput

On exit: indicates if the member of the risk set given in x failed.

$\mathbf{id}\left(i\right)=1$ if the member of the risk set failed at the time defining the risk set and $\mathbf{id}\left(i\right)=0$ otherwise.

17:   $\mathbf{nd}$ – IntegerOutput

On exit: the number of distinct failure times, i.e., the number of risk sets.

18:   $\mathbf{tp}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: $\mathbf{tp}\left(\mathit{i}\right)$ contains the $\mathit{i}$th distinct failure time, for $\mathit{i}=1,2,\dots ,\mathbf{nd}$.

19:   $\mathbf{irs}\left(\mathbf{n}\right)$ – Integer arrayOutput

On exit: indicates rows in x and elements in ixs and id corresponding to the risk sets. The first risk set corresponding to failure time $\mathbf{tp}\left(1\right)$ is given by rows $1$ to $\mathbf{irs}\left(1\right)$. The $\mathit{l}$th risk set is given by rows $\mathbf{irs}\left(\mathit{l}-1\right)+1$ to $\mathbf{irs}\left(\mathit{l}\right)$, for $\mathit{l}=1,2,\dots ,\mathbf{nd}$.

20:   $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{ldz}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldz}\ge \mathbf{n}$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 1$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 2$.

On entry, $\mathbf{ns}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ns}\ge 0$.

$\mathbf{ifail}=2$

On entry, $i=〈\mathit{\text{value}}〉$, $\mathbf{isi}\left(i\right)=〈\mathit{\text{value}}〉$ and $\mathbf{ns}=〈\mathit{\text{value}}〉$.
Constraint: $0\le \mathbf{isi}\left(i\right)\le \mathbf{ns}$.

On entry, $i=〈\mathit{\text{value}}〉$ and $\mathbf{ic}\left(i\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ic}\left(i\right)=0$ or $1$.

On entry, $i=〈\mathit{\text{value}}〉$ and $\mathbf{isz}\left(i\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{isz}\left(j\right)\ge 0$.

On entry, there are not ip values of $\mathbf{isz}>0$.

$\mathbf{ifail}=3$

On entry, $\mathbf{mxn}=〈\mathit{\text{value}}〉$ and minimum value for $\mathbf{mxn}=〈\mathit{\text{value}}〉$.
Constraint: mxn must be sufficiently large for the arrays to contain the expanded risk set.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g12zafe.f90)

10.2

Program Data

Program Data (g12zafe.d)

10.3

Program Results

Program Results (g12zafe.r)