survMisc (version 0.4.6)

gof: Goodness of fit test for coxph models

Description

Goodness of fit test for coxph models

Usage

gof(x, ...)
## S3 method for class 'coxph':
gof(x, ..., G = NULL)

Arguments

x

An object of class coxph

...

Additional arguments (not implemented)

G

Number of groups into which to divide risk score. If G=NULL (the default), uses closest integer to $$G = \max(2, \quad \min(10, \quad \frac{ne}{40}))$$ where $ne$ is the number of events overall.

Value

• A list with elements:
• groups
  A data.table with one row per group $G$. The columns are [object Object],[object Object],[object Object],[object Object],[object Object]
• lrTest
  Likelihood-ratio test. Tests the improvement in log-likelihood with addition of an indicator variable with $G-1$ groups. This is done with survival:::anova.coxph. The test is distributed as chi-square with $G-1$ degrees of freedom

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. http://dx.doi.org/10.1023/A:1009612305785{Springer (paywall)}

Details

In order to verify the overall goodness of fit, the risk score $r_i$ for each observation $i$ is given by $$r_i = \hat{\beta} X_i$$ where $\hat{\beta}$ is the vector of fitted coefficients and $X_i$ is the vector of predictor variables for observation $i$. This risk score is then sorted and 'lumped' into a grouping variable with $G$ groups, (containing approximately equal numbers of observations). The number of observed ($e$) and expected ($exp$) events in each group are used to generate a $Z$ statistic for each group, which is assumed to follow a normal distribution with $Z \sim N(0,1)$. 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.

References

Default value for $G$ 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. http://dx.doi.org/10.1023/B:LIDA.0000036393.29224.1d{Springer (paywall)}

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. http://dx.doi.org/10.1002/9781118150672{Wiley (paywall)}

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)