gof {survMisc} | R Documentation |
goodness of fit test for a coxph
object
Description
goodness of fit test for a coxph
object
Usage
gof(x, ...)
## S3 method for class 'coxph'
gof(x, ..., G = NULL)
Arguments
x |
An object of class |
... |
Additional arguments (not implemented) |
G |
Number of groups into which to divide risk score.
If
where |
Details
In order to verify the overall goodness of fit,
the risk score for each observation
is given by
where is the vector of fitted coefficients
and
is the vector of predictor variables for
observation
.
This risk score is then sorted and 'lumped' into
a grouping variable with groups,
(containing approximately equal numbers of observations).
The number of observed () and expected (
) events in
each group are used to generate a
statistic for each group,
which is assumed to follow a normal distribution with
.
The indicator variable indicG
is added to the
original model and the two models are compared to determine the
improvement in fit via the likelihood ratio test.
Value
A list
with elements:
groups |
A
|
lrTest |
Likelihood-ratio test.
Tests the improvement in log-likelihood with addition
of an indicator variable with |
Note
The choice of is somewhat arbitrary but rarely should
be
.
As illustrated in the example, a larger value for
makes the
test for each group more likely to be significant.
This does not affect the significance of adding the
indicator variable
indicG
to the original model.
The score is chosen for simplicity, as for large sample sizes
the Poisson distribution approaches the normal. Strictly speaking,
the Poisson would be more appropriate for
and
as
per Counting Theory.
The score may be somewhat conservative as the expected events
are calculated using the martingale residuals from the overall model,
rather than by group. This is likely to bring the expected events
closer to the observed events.
This test is similar to the Hosmer-Lemeshow test for logistic regression.
Source
Method and example are from:
May S, Hosmer DW 1998.
A simplified method of calculating an overall goodness-of-fit test
for the Cox proportional hazards model.
Lifetime Data Analysis 4(2):109–20.
doi:10.1023/A:1009612305785
References
Default value for as per:
May S, Hosmer DW 2004.
A cautionary note on the use of the Gronnesby and Borgan
goodness-of-fit test for the Cox proportional hazards model.
Lifetime Data Analysis 10(3):283–91.
doi:10.1023/B:LIDA.0000036393.29224.1d
Changes to the pbc
dataset in the example are as detailed in:
Fleming T, Harrington D 2005.
Counting Processes and Survival Analysis.
New Jersey: Wiley and Sons. Chapter 4, section 4.6, pp 188.
doi:10.1002/9781118150672
Examples
data("pbc", package="survival")
pbc <- pbc[!is.na(pbc$trt), ]
## make corrections as per Fleming
pbc[pbc$id==253, "age"] <- 54.4
pbc[pbc$id==107, "protime"] <- 10.7
### misspecified; should be log(bili) and log(protime) instead
c1 <- coxph(Surv(time, status==2) ~
age + log(albumin) + bili + edema + protime,
data=pbc)
gof(c1, G=10)
gof(c1)