Scientific trials are brief, 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 remedy over time (as an illustration as used for HTA functions), one should extrapolate this medical advantages. Generally, this extrapolation is finished utilizing a parametric perform (as really useful by NICE’s Resolution 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:

specifically, 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 commonplace 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,

Individuals with the worst prognosis are prone to die first, altering the prognostic mixture of these remaining in follow-up. This will lead to a turning level within the hazard perform, with the hazard of loss of life decreasing 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 common inhabitants— during 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 information on (i) how lengthy the treatment will final and (ii) what share of people will probably 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 parts; 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 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 people who usually are not. When fitted in a relative survival framework, common 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 yr used, and these are additional stratified by traits similar 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 common inhabitants mortality. Nonetheless, it is very important notice 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; slightly they’re assigned a chance 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 break up the inhabitants into cured and uncured teams straight. Quite, 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 common inhabitants. When fitted utilizing commonplace parametric fashions, there isn’t a 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 comparable parametric distributions, the treatment charges are sometimes comparable.

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 full paper. The rest of the paper has empirical functions, tips about when one ought to (and shouldn’t) use treatment fashions, and rather more. A really fascinating learn.