Medical trials are brief, however the advantages of many medicine 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 example as used for HTA functions), one should extrapolate this medical advantages. Generally, this extrapolation is finished utilizing a parametric perform (as advisable by NICE’s Resolution Assist Unit (DSU) technical help doc on survival evaluation (TSD 14). One problem is that the parametric capabilities used to extrapolate survival aren’t sometimes very versatile. As Latimer and Rutherford (2024) write of those limitations:
particularly, exponential, Weibull, Gompertz and Gamma fashions can not deal with 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 deal with one turning level
With new therapies (e.g., CAR T, immuno-oncology) providing long-term, sturdy survival positive aspects, these normal parametric approaches might not sufficiently seize the doubtless survival profile. Even within the absence of absolutely healing remedy, there could also be the explanation why treatment fashions are helpful. Particularly,
Contributors with the worst prognosis are more likely to die first, altering the prognostic mixture of these remaining in follow-up. This will end in a turning level within the hazard perform, 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 normal inhabitants— through which case, remaining sufferers could also be thought of to be cured.
Alternatively, payers could also be hesitant to make use of a ‘treatment’ mannequin if there’s restricted knowledge on (i) how lengthy the treatment will final and (ii) what share of people can 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 parts; the inhabitants hazard perform h*(t) and the illness particular hazard λ(t). The inhabitants normal 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 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 will not be. When fitted in a relative survival framework, normal inhabitants mortality charges are integrated straight into the mannequin and the mannequin makes use of these, mixed with the parametric distribution chosen to signify the uncured sufferers, to estimate the treatment fraction. Common 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 could be assigned an anticipated background mortality price.
MCM combine cured and uncured populations the place cured have normal inhabitants mortality. Nevertheless, it is very important notice that modellers don’t “determine” the treatment proportion; that is estimated from the information. Particularly, every people within the knowledge set just isn’t assigned to be cured or not; reasonably they’re assigned a chance of being cured; one can solely estimate the treatment fraction on the inhabitants stage 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 straight. Moderately, 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 will depend on when the modelled hazards converge with these noticed within the normal inhabitants. When fitted utilizing normal parametric fashions, there isn’t any constraint on when this convergence will happen.
Regardless of these totally different approaches, the authors notice that the when MCM and NMC are match with related parametric distributions, the treatment charges are sometimes related.
To code up NCMs, one may 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 attention-grabbing learn.
