Medical trials are brief, however the advantages of many medication lasts months and even years past the length of those trials. To quantify the total 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 really helpful by NICE’s Resolution Help Unit (DSU) technical help 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 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 aspects, these commonplace parametric approaches might not sufficiently seize the doubtless survival profile. Even within the absence of totally healing remedy, there could also be the explanation why remedy 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 will even drop to ranges anticipated within the common inhabitants— wherein case, remaining sufferers could also be thought-about to be cured.
Alternatively, payers could also be hesitant to make use of a ‘remedy’ mannequin if there may be restricted knowledge on (i) how lengthy the remedy will final and (ii) what share of people will likely be ‘cured’. Nonetheless, an up to date NICE technical help doc (TSD 21) describes a few of these extra versatile strategies.
The authors describe the remedy 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 commonplace mortality ratios (SMRs) usually 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 remedy fashions: combination remedy fashions (MCM) and non-mixture remedy 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 usually are not. When fitted in a relative survival framework, common inhabitants mortality charges are included 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 remedy 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 resembling age and intercourse, so that every trial participant could be assigned an anticipated background mortality charge.
MCM combine cured and uncured populations the place cured have common inhabitants mortality. Nonetheless, you will need to word that modellers don’t “resolve” the remedy proportion; that is estimated from the information. Particularly, every people within the knowledge set just isn’t assigned to be cured or not; quite they’re assigned a likelihood of being cured; one can solely estimate the remedy fraction on the inhabitants degree by averaging these remedy 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. Moderately, the ‘remedy’ is outlined as follows:
NMCs don’t assume that there’s a group of sufferers who’re ‘cured’ at baseline. The timepoint at which remedy happens will depend on when the modelled hazards converge with these noticed within the common inhabitants. When fitted utilizing commonplace parametric fashions, there isn’t any 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 remedy 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, recommendations on when one ought to (and mustn’t) use remedy fashions, and rather more. A really attention-grabbing learn.