giabaio
Adding survival models with frailties and flexible baseline hazards to survHE
In many instances in medicine there are is more than one clinical trial for a particular problem, each trial giving slightly different results. This is understandable and expected because each clinical trial has different inclusion/exclusion criteria, slightly different drug or drug dosing schemes, and a different geospatial sample of patients. A proper health economics evaluation would consider all the available information, not just the information from a single trial. Here is an example demonstrating the issue in a project I am working on.
- Assume a well-defined cancer population (e.g. stage 4 bladder cancer that has failed cisplatin chemotherapy)
- Drug A: the current standard of care, one of several chemotherapy drugs, all similar in efficacy
- Drug B: the new drug, an immunotherapy, very expensive
- Biomarker: a test that can be applied to the patient. If positive Drug B more likely to be effective, if negative Drug B and Drug A similar in effectiveness.
- We have trials directly comparing Drug A to Drug B and also single arm trials of Drug A and Drug B
- We have information on the costs of the drugs, their side effects and their costs, and the relevant utilities of health states
- We digitize the overall survival (OS) and progression-free survival (PFS) from all the available trials involving Drug A and Drug B and generate pseudo-individualized patient data
- Assume the baseline hazards vary over time with treatment and a flexible model for the hazard function is required
Our challenge now is to compare two policies:
- Give everyone Drug B because it is, overall, more effective than Drug A
- Test people with the biomarker, if positive give Drug B because it will be more effective, if negative give Drug A because it is cheaper
In order to build an appropriate survival model for the available data we need two things (1) a flexible baseline hazard function and (2) frailties to account for differences between clinical trials (i.e. take into account the multilevel nature of our data). Here are some options in R (I probably missed some):
| Method | Hazard | Frailty |
|---|---|---|
| survival: coxph | Semi-parametric | Yes |
| survival: survreg | Parametric | Yes |
| coxme: coxme | Semi-parametric | Yes |
| frailtypack: frailPenal | Semi-parametric | Yes |
| frailEM : emfrail | Semi-parametric | Yes |
| flexsurv: flexsurvreg | Parametric | No |
| flexsurv: flexsurvspline | Flexible spline | No |
| parfm: parfm | Parametric | Yes |
| INLA: inla_surv | Parametric | Yes |
| rstanarm: stan_surv | Flexible spline | Yes |
For our situation therefore, we probably need rstanarm where we can fit a model of the type
stan_surv(Surv(time, event) ~ drug + biomarker + (1 | trial), basehaz = 'ms')
which fits a model with an M-spline for the baseline hazard and a frailty for each trial in our dataset. We could fit two such models, one for the OS outcome and another for the PFS outcome. Then we could perform a partitioned survival model using the current-progressed-dead states.
I would like to fit these survival models with flexible hazards and frailties using survHE because it has excellent functionality for probability sensitivity analysis and because it can feed into BCEA for subsequent steps. Presently, survHE does not fit models with both flexible baseline hazards and frailties. I would like to request that survHE extend its functionality to use the stan_surv function of rstanarm to fit such models.
Under development - we are working on expanding the range of available models in survHE, particularly under the INLA framework (which could also handle semi-parametric and spline-like models and embedding structured effects in a very natural way). We have already started building models based on running rstan in the background and are looking into expanding the range of models (eg towards "mixture cure" models).
These are ambitious developments and will require some time to complete --- but basically all of your requirements are under our radar! :-)
Perhaps you'd like to be involved in some of these (with testing etc?), @bainman ?
Would love to help.
Brant
On Fri, Feb 19, 2021 at 10:20 AM Gianluca Baio [email protected] wrote:
Under development - we are working on expanding the range of available models in survHE, particularly under the INLA framework (which could also handle semi-parametric and spline-like models and embedding structured effects in a very natural way). We have already started building models based on running rstan in the background and are looking into expanding the range of models (eg towards "mixture cure" models).
These are ambitious developments and will require some time to complete --- but basically all of your requirements are under our radar! :-)
Perhaps you'd like to be involved in some of these (with testing etc?), @bainman https://github.com/bainman ?
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