standsurv for flexsurvspline incorporating competing risk?

[XinyuZou97]

thanks for all your work on this amazing package! I'm trying to incorporate competing risk in a flexsurvspline() object. I've read the vignette for multi-state modelling and it mentioned that spline models may also be fitted. Is it possible to calculate the marginal effect of the fitted spline model object using standsurv()?

here is a simple example:

#trans=1 from initial status to event of interest
#trans=2 from initial status to competing event
#trans=3 from event of interest to competing event

dt_trans<-data.frame(
id=c(1,1,2,2,3,3,3),
time=c(8.6,8.6,11,11,0.6,4.7,4.1),
status=c(0,0,0,0,1,0,1),
trans=c(1,2,1,2,1,2,3),
x=c('good','good','good','good','medium','medium','medium'),#covariate of interest
age=c(60,60,65,65,70,70,70))

#fit spline model incorporate competing risk, time-varying effect of x, and covariate age

#the joint likelihood model was fitted because it seems that standsurv() did not support transition-specific models

fit_joint<-flexsurvspline(
Surv(time,status) ~ x +gamma1(x)+trans+age,
scale = "hazard",
k = 2,
data = dt_trans
)

#calculate marginal survival probability for event of interest (i.e, trans=1)

dt_standsurv <- standsurv(fit_joint,
type = 'survival',
at = list(
list(x = "good",trans='1'),
list(x = "medium",trans='1')
),
t = 10,
ci = TRUE
)

is the code above correct? I tried to run these codes in R and it did not return any warnings and error.

huge thanks if you could help solving this question!

[chjackson]

I think that code would calculate the survival probability with respect to the event of interest, but assuming that the competing event cannot occur. It's just considering the transition-specific hazard in isolation from the other transitions.

I don't think standsurv supports multistate model outputs such as transition probabilities and total length of stay. If you want those, you'll probably need to do the maths and averaging over covariates by hand, with the aid of the formulae in the vignette. Combining bootstrap samples would probably be the easiest way to go for uncertainty.

(copying @mikesweeting , the standsurv author, in case he has anything to add)

[XinyuZou97]

@chjackson Thanks for your helpful reply! I'm not quite familiar with the multistate model. To clarify, what I'm interested in is the marginal survival probability or rmst (as detailed in the help page of standsurv) for the event of interest at defined time points and covariate patterns. As you explained, the code I provided actually did not incorporate the competing risk when calculating marginal effects. Am I understanding this correctly? I'd really appreciate a response when you have a moment!

[chjackson]

It sounds to me like your understanding is correct!

[XinyuZou97]

@chjackson again thanks for your timely reply! I have to admit that it's a bit difficult for me to do the math. Is it possible for me to modify the example code to incorporate competing risk in the flexsurvspline() object and calculate the marginal survival probability or rmst for the event of interest in an easier way with functions in the flexsurv package? Thank you once again for your time.

[chjackson]

@dapadapadabupa The "survival probability" that you want sounds like the "transition probability" in a multistate model. That is available in the functions pmatrix.fs or pmatrix.simfs. You could calculate those for particular covariate values, and average the results to give a marginalised/standardised version. bootci.fmsm might be used to get the confidence interval. I'm afraid there is no packaged way to do that, or a worked example that shows how to do it though.

[XinyuZou97]

@chjackson Huge thanks for your comments! I' ll try to calculate the results with pmatrix.fs and bootci.fmsm.