cure model

[Grace Antony]

Hi I am working on cure models. using stpm2. I have estimated the cure percentage and median survival of the uncured. How can I estimate the time to cure for each subgroups. for example I am interested in finding time to cure for age >10-15 years.
stpm2 i.agecat ,df(5) scale(hazard) bhazard(rate) eform nolog cure.

[Paul Dickman]

This is non-trivial. Cure exists if the cumulative relative survival curve becomes flat (i.e., excess mortality becomes zero) and - if cure exists - the time to cure (aka cure point) is the time point at which the cumulative relative survival curve becomes flat.

Cure models force cure even if cure is not a reasonable assumption. Parametric cure models force the cure point to be at time infinity whereas the model you are fitting puts the cure point at the time of the last knot (which by default is at the last event time).

I suggest the best way to estimate the cure point is from plots of the empirical relative survival. Then you can simultaneously assess if cure is a reasonable assumption and, if it is, estimate the cure point. One of the difficulties in estimating the cure point is that you are trying to estimate the point the curve reaches an asymptote; this will often have a wide range of plausible values. I suggest always looking at such graphs even if you are using a model for inference. The models will often converge when cure is not a reasonable assumption and model-based inference may be hugely misleading.

Having said that, there are some approaches to estimate the cure point from a model. See, for example,

Modeling excess hazard with time-to-cure as a parameter
https://pubmed.ncbi.nlm.nih.gov/32869288/

A new approach to estimate time-to-cure from cancer registries data
https://pubmed.ncbi.nlm.nih.gov/29414635/

And, to reiterate

We recommend that, regardless of the model used, the underlying assumptions for cure and model fit should always be graphically assessed. [https://pubmed.ncbi.nlm.nih.gov/24042025/]

[Grace Antony]

Many Thanks for the quick response. In fact My relative survival curve without cure option is like this
stpm2 i.agecat ,df(5) scale(hazard) bhazard(rate) eform nolog
predict s1 , meansurv at (agecat 1) ci timevar(_t)

range tt 0 10 200
predict h0, hazard timevar(tt) at(agecat 1) zeros per(1000) ci

I have drawn the relative survival curve for this age group. Also drawn the excess hazard curve,. Please find the attached. From the curve, Approx at years the excess hazard becomes zero. Can I conclude the cure is obtained at 5 years.
I will also try to find the cure point from the paper you have suggested.

[Paul Dickman]

I think your graph illustrates some of my points.

At what time does this become flat? It's flat after time 10, but many would say it is "flat enough" at 8 or even 6 years.

Note that this curve is still model based rather than empirical. This is the curve for the youngest age group from a model assuming proportional hazards for age. This curve may not therefore represent the actually empirical curve for this age group.

It looks like the plot of the excess hazards is for all age groups combined so conclusions based on that are slightly different.

[Grace Antony]

Many Thanks Paul. Do you mean by empirical survival cure ,the KM graph ?

[Paul Dickman]

Many Thanks Paul. Do you mean by empirical survival cure ,the KM graph ?

Yes, except it will be relative survival so not exactly the KM graph but a non-parametric estimate of relative survival. I don't have a problem with a model-based estimate as long as you're certain the model is a very good fit so that it will overlay the empirical estimates.