NAG Library Function Document

nag_prod_limit_surviv_fn (g12aac)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{n}$ – IntegerInput

On entry: the number of failure and censored times given in t.

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

2:    $\mathbf{t}\left[\mathbf{n}\right]$ – const doubleInput

On entry: the failure and censored times; these need not be ordered.

3:    $\mathbf{ic}\left[\mathbf{n}\right]$ – const IntegerInput

On entry: $\mathbf{ic}\left[\mathit{i}-1\right]$ contains the censoring code of the $\mathit{i}$th observation, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

$\mathbf{ic}\left[i-1\right]=0$

The $i$th observation is a failure time.

$\mathbf{ic}\left[i-1\right]=1$

The $i$th observation is right-censored.

Constraint: $\mathbf{ic}\left[i-1\right]=0$ or $1$, for $i=1,2,\dots ,\mathbf{n}$.

4:    $\mathbf{freq}\left[\mathbf{n}\right]$ – const IntegerInput

On entry: indicates whether frequencies are provided for each failure and censored time point. If frequencies are provided then freq must be dimensioned at least n. If the failure and censored times are to be considered as single observations, i.e., a frequency of 1 is to be assumed then freq must be set to NULL.

Constraint: either $\mathbf{freq}=\left(\mathrm{Integer}*\right)0$ or $\mathbf{freq}\left[\mathit{i}-1\right]\ge 0$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

5:    $\mathbf{nd}$ – Integer *Output

On exit: the number of distinct failure times, $n_d$.

6:    $\mathbf{tp}\left[\mathbf{n}\right]$ – doubleOutput

On exit: $\mathbf{tp}\left[\mathit{i}-1\right]$ contains the $\mathit{i}$th ordered distinct failure time, $t_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n_d$.

7:    $\mathbf{p}\left[\mathbf{n}\right]$ – doubleOutput

On exit: $\mathbf{p}\left[i-1\right]$ contains the Kaplan–Meier estimate of the survival probability, $\hat{S}\left(t\right)$, for time $\mathbf{tp}\left[\mathit{i}-1\right]$, for $\mathit{i}=1,2,\dots ,n_d$.

8:    $\mathbf{psig}\left[\mathbf{n}\right]$ – doubleOutput

On exit: $\mathbf{psig}\left[\mathit{i}-1\right]$ contains an estimate of the standard deviation of $\mathbf{p}\left[\mathit{i}-1\right]$, for $\mathit{i}=1,2,\dots ,n_d$.

9:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_INT_ARG_LT

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

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

NE_INVALID_CENSOR_CODE

On entry, $\mathbf{ic}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$. The censor code for an observation must be either 0 or 1.

NE_INVALID_FREQ

On entry, $\mathbf{freq}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$. The value of frequency for an observation must be $\ge 0$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g12aace.c)

10.2

Program Data

Program Data (g12aace.d)

10.3

Program Results

Program Results (g12aace.r)