Ought to we extrapolate survival utilizing ‘treatment’ fashions? – Healthcare Economist

Scientific trials are brief, however the advantages of many medication 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 scientific advantages. Generally, this extrapolation is finished utilizing a parametric perform (as advisable by NICE’s Resolution Assist 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:

particularly, exponential, Weibull, Gompertz and Gamma fashions can not 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 good points, these customary parametric approaches could not sufficiently seize the seemingly survival profile. Even within the absence of totally healing remedy, there could also be the reason 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 likely lead to a turning level within the hazard perform, with the hazard of dying lowering 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 basic inhabitants— wherein case, remaining sufferers could also be thought-about 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 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 elements; the inhabitants hazard perform 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 kinds 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 will not be. When fitted in a relative survival framework, basic inhabitants mortality charges are included 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 akin to age and intercourse, so that every trial participant may be assigned an anticipated background mortality charge.

MCM combine cured and uncured populations the place cured have basic inhabitants mortality. Nonetheless, IT is vital to notice that modellers don’t “determine” the treatment proportion; that is estimated from the info. Particularly, every people within the information 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 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. 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 basic inhabitants. When fitted utilizing customary parametric fashions, there is no such thing as a constraint on when this convergence will happen.

Regardless of these totally different approaches, the authors be aware that the when MCM and NMC are match with related parametric distributions, the treatment charges are sometimes related.

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 purposes, recommendations on when one ought to (and shouldn’t) use treatment fashions, and far more. A really fascinating learn.