Scientific trials are brief, however the advantages of many medicine lasts months and even years past the length 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 scientific advantages. Generally, this extrapolation is completed utilizing a parametric operate (as really helpful by NICE’s Determination Help Unit (DSU) technical assist 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:
particularly, exponential, Weibull, Gompertz and Gamma fashions can not deal with 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 deal with one turning level
With new therapies (e.g., CAR T, immuno-oncology) providing long-term, sturdy survival positive aspects, these customary parametric approaches might not sufficiently seize the seemingly survival profile. Even within the absence of absolutely healing remedy, there could also be explanation why treatment fashions are helpful. Particularly,
Contributors 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 operate, with the hazard of loss of life lowering 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 normal inhabitants— by 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 may be restricted information on (i) how lengthy the treatment will final and (ii) what share of people can be ‘cured’. Nevertheless, 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) sometimes 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 sorts 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 those that aren’t. When fitted in a relative survival framework, normal inhabitants mortality charges are included straight into the mannequin and the mannequin makes use of these, mixed with the parametric distribution chosen to symbolize 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 similar to age and intercourse, so that every trial participant might be assigned an anticipated background mortality charge.
MCM combine cured and uncured populations the place cured have normal inhabitants mortality. Nevertheless, you will need to observe that modellers don’t “resolve” the treatment share; that is estimated from the info. Particularly, every people within the information set 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 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 break 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 depends upon when the modelled hazards converge with these noticed within the normal 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 observe that the when MCM and NMC are match with comparable parametric distributions, the treatment charges are sometimes comparable.
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 purposes, tips about when one ought to (and shouldn’t) use treatment fashions, and way more. A really attention-grabbing learn.
