Scientific trials are brief, however the advantages of many medicine lasts months and even years past the length of those trials. To quantify the complete prices and advantages of a remedy over time (for 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 Help Unit (DSU) technical assist 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:
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 features, these commonplace parametric approaches might not sufficiently seize the probably survival profile. Even within the absence of absolutely healing remedy, there could also be the reason why treatment fashions are helpful. Particularly,
Members with the worst prognosis are prone 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 dying decreasing within the medium time period. In the long run, hazards are prone to proceed to fall and will 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 may be restricted information on (i) how lengthy the treatment will final and (ii) what share of people shall 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 perform h*(t) and the illness particular hazard λ(t). The inhabitants commonplace mortality ratios (SMRs) sometimes comes kind age-sex life tables for the nation of curiosity. One can estimate the general survival danger 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, normal inhabitants mortality charges are integrated instantly 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. 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 comparable 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. Nonetheless, it is very important notice that modellers don’t “determine” the treatment share; that is estimated from the info. Particularly, every people within the information set shouldn’t be assigned to be cured or not; quite 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 instantly. 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 normal inhabitants. When fitted utilizing commonplace parametric fashions, there isn’t any constraint on when this convergence will happen.
Regardless of these completely 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 purposes, recommendations on when one ought to (and mustn’t) use treatment fashions, and far more. A really attention-grabbing learn.
