# Interpretation of risk ratios for competing risk from AFT

I want to analyse the time to disease with a competing event with an accelerated failure time model (AFT) with Weibull distribution. I wonder how exactly we can interpret the resulting coefficients for the main event considering we have a competing event. As an example using the dataset in library(mstate), I have patients that either develop AIDS or SI. I am interested in the time to AIDS, for the covariate ccr5WM, with the 'time ratio' from the AFT model = 1.366 for AIDS.

If it was not a competing risk model, I would say that the time to AIDS is 37% longer for patients with ccr5WM. Is this also correct for the competing risk model, keeping in mind that the model also estimates a coefficient for SI?

If anyone has a thought on this or a paper to share, I would very much appreciate it.

Note: I followed the tutorial for mstate to create a long data format and define the model. And the paper Survival Analysis Part II by Bradburn, Clark, Love and Altman (2003) to understand the AFT model and am therefore asking whether the interpretation applies to competing risk as well.

Code to obtain the above result if someone wants to reproduce it:

library(mstate)
library(survival)
data("aidssi", package= "mstate")
dta = aidssi


For the multistate model, we need to transform the wide data into long data:

evt_label= c("No evt", "AIDS", "SI")
tmat = trans.comprisk(2,names=evt_label)
dta$stat1 = as.numeric(dta$status == 1)
dta$stat2 = as.numeric(dta$status == 2)
mycovar = "ccr5"
dta_long = msprep(time=c(NA,'time','time'),
status = c(NA,'stat1','stat2'),data=dta,keep=mycovar,trans=tmat)
dta_long = expand.covs(dta_long, mycovar)
dta_long = transform(dta_long, endpt= evt_label[to])


The model fit for the AFT model with Weibull distribution and only for the transition to AIDS, but with competing risk SI, is done with the subset function:

fit = survreg(Surv(time, status) ~ ccr5WM.1,
subset(dta_long, trans==1), dist = "weibull")


With the results:

summary(fit)

Call:
survreg(formula = Surv(time, status) ~ ccr5WM.1, data = subset(dta_long,
trans == 1), dist = "weibull")
Value Std. Error     z        p
(Intercept)  2.514     0.0566 44.40 0.00e+00
ccr5WM.1     0.312     0.1178  2.65 8.05e-03
Log(scale)  -0.692     0.0754 -9.18 4.38e-20

Scale= 0.501

Weibull distribution
Loglik(model)= -417.3   Loglik(intercept only)= -421.3
Chisq= 7.91 on 1 degrees of freedom, p= 0.0049
Number of Newton-Raphson Iterations: 7
n=323 (6 observations deleted due to missingness)

• When the question is predominantly about R rather than statistics it is off topic for this site. It may be possible to get an answer by migrating to the Stack Overflow site. – Michael Chernick Mar 28 '17 at 19:11
• I was asked to moved it here from Stack Overflow because it is a statistical question, unrelated to what language it is coded in. – Brigitte Mar 28 '17 at 20:45