Scientific trials are quick, however the advantages of many medicine lasts months and even years past the period of those trials. To quantify the complete prices and advantages of a therapy over time (as an example as used for HTA functions), one should extrapolate this medical advantages. Generally, this extrapolation is finished utilizing a parametric operate (as beneficial by NICE’s Choice Assist Unit (DSU) technical assist doc on survival evaluation (TSD 14). One problem is that the parametric features used to extrapolate survival aren’t usually very versatile. As Latimer and Rutherford (2024) write of those limitations:
particularly, exponential, Weibull, Gompertz and Gamma fashions can’t address any turning factors within the hazard operate 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 features, these customary parametric approaches might not sufficiently seize the possible survival profile. Even within the absence of absolutely healing therapy, there could also be the reason why treatment fashions are helpful. Particularly,
Members with the worst prognosis are more likely to die first, altering the prognostic mixture of these remaining in follow-up. This will likely end in a turning level within the hazard operate, with the hazard of loss of life lowering within the medium time period. In the long run, hazards are more likely 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 information on (i) how lengthy the treatment will final and (ii) what share of people will likely be ‘cured’. Nonetheless, an up to date NICE technical assist 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 operate h*(t) and the illness particular hazard λ(t). The inhabitants customary mortality ratios (SMRs) usually comes type 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 varieties 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 should not. When fitted in a relative survival framework, basic inhabitants mortality charges are included instantly 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. Basic inhabitants mortality charges are taken from related lifetables, with charges from the suitable calendar 12 months used, and these are additional stratified by traits corresponding to age and intercourse, so that every trial participant will be assigned an anticipated background mortality price.
MCM combine cured and uncured populations the place cured have basic inhabitants mortality. Nonetheless, it is very important be aware that modellers don’t “resolve” the treatment share; that is estimated from the info. Particularly, every people within the information set just isn’t assigned to be cured or not; somewhat they’re assigned a chance of being cured; one can solely estimate the treatment fraction on the inhabitants degree by averaging these treatment chances 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 instantly. Relatively, 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 is determined by when the modelled hazards converge with these noticed within the basic inhabitants. When fitted utilizing customary parametric fashions, there isn’t any constraint on when this convergence will happen.
Regardless of these completely different approaches, the authors be aware 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 complete paper. The rest of the paper has empirical purposes, recommendations on when one ought to (and mustn’t) use treatment fashions, and far more. A really fascinating learn.
