Medical trials are brief, however the advantages of many medication lasts months and even years past the period of those trials. To quantify the total prices and advantages of a remedy over time (as an illustration as used for HTA functions), one should extrapolate this scientific advantages. Generally, this extrapolation is finished utilizing a parametric perform (as really helpful by NICE’s Choice Help Unit (DSU) technical help doc on survival evaluation (TSD 14). One problem is that the parametric features used to extrapolate survival aren’t sometimes very versatile. As Latimer and Rutherford (2024) write of those limitations:
specifically, exponential, Weibull, Gompertz and Gamma fashions can’t address any turning factors within the hazard perform over time (that’s, the speed at which the occasion of curiosity happens over time), and log-logistic, log regular and Generalised Gamma fashions can solely address one turning level
With new therapies (e.g., CAR T, immuno-oncology) providing long-term, sturdy survival positive factors, these customary parametric approaches might not sufficiently seize the possible survival profile. Even within the absence of totally healing remedy, there could also be the reason why treatment fashions are helpful. Particularly,
Individuals with the worst prognosis are prone to die first, altering the prognostic mixture of these remaining in follow-up. This will likely end in a turning level within the hazard perform, with the hazard of loss of life decreasing within the medium time period. In the long run, hazards are prone to proceed to fall and should even drop to ranges anticipated within the basic inhabitants— wherein case, remaining sufferers could also be thought-about to be cured.
Alternatively, payers could also be hesitant to make use of a ‘treatment’ mannequin if there may be restricted knowledge on (i) how lengthy the treatment will final and (ii) what share of people will probably be ‘cured’. Nevertheless, an up to date NICE technical help doc (TSD 21) describes a few of these extra versatile strategies.
The authors describe the treatment fashions as partitioning all all-cause hazard h(t) into two elements; the inhabitants hazard perform h*(t) and the illness particular hazard λ(t). The inhabitants customary mortality ratios (SMRs) sometimes comes kind age-sex life tables for the nation of curiosity. One can estimate the general survival threat of the illness R(t) because the ratio of all-cause survival S(t) and background inhabitants survival S*(t).
There are two kinds of treatment fashions: combination treatment fashions (MCM) and non-mixture treatment fashions (NMC). The authors clarify MCM as follows:
MCMs assume that there are two teams of people – those that are cured of their illness and people who aren’t. When fitted in a relative survival framework, basic inhabitants mortality charges are integrated straight into the mannequin and the mannequin makes use of these, mixed with the parametric distribution chosen to characterize the uncured sufferers, to estimate the treatment fraction. Normal inhabitants mortality charges are taken from related lifetables, with charges from the suitable calendar 12 months used, and these are additional stratified by traits equivalent to age and intercourse, so that every trial participant may be assigned an anticipated background mortality charge.
MCM combine cured and uncured populations the place cured have basic inhabitants mortality. Nevertheless, you will need to word that modellers don’t “resolve” the treatment proportion; that is estimated from the info. Particularly, every people within the knowledge set will not be assigned to be cured or not; fairly they’re assigned a likelihood of being cured; one can solely estimate the treatment fraction on the inhabitants stage by averaging these treatment possibilities throughout the inhabitants.
To code up MCMs, one can use strsmix in Stata or flexsurv and cuRe in R.
NMC, in distinction, do cut up the inhabitants into cured and uncured teams straight. Fairly, the ‘treatment’ is outlined as follows:
NMCs don’t assume that there’s a group of sufferers who’re ‘cured’ at baseline. The timepoint at which treatment happens depends upon when the modelled hazards converge with these noticed within the basic inhabitants. When fitted utilizing customary parametric fashions, there isn’t a constraint on when this convergence will happen.
Regardless of these totally different approaches, the authors word that the when MCM and NMC are match with related parametric distributions, the treatment charges are sometimes related.
To code up NCMs, one might use strsnmix or stpm2 in Stata, or flexsurv, cuRe and rstpm2 in R.
I like to recommend you learn the full paper. The rest of the paper has empirical functions, tips about when one ought to (and shouldn’t) use treatment fashions, and way more. A really fascinating learn.