Clinical trials are short, but the benefits of many medicines last months or even years beyond the duration of these trials. To quantify the total costs and benefits of a treatment over time (for example, as used for health technology assessment purposes), these clinical benefits must be extrapolated. Typically, this extrapolation is done using a parametric function (as recommended by the NICE Decision Support Unit (DSU) technical support document on survival analysis (Independence Day 14). One challenge is that the parametric functions used to extrapolate survival are often not very flexible. Latimer and Rutherford (2024) Write about these limitations:
In particular, exponential, Weibull, Gompertz, and Gamma models cannot cope with any inflection point in the hazard function over time (i.e., the rate at which the event of interest occurs over time), and log-logistic, log-normal, and generalized Gamma models can only cope with one inflection point.
With new therapies (e.g. CAR T, immuno-oncology) offering durable and long-term survival gains, these standard parametric approaches may not sufficiently capture the likely survival profile. Even in the absence of a completely curative treatment, there may be reasons why cure models are useful. Specifically,
Participants with the worst prognosis are likely to die first, which would change the prognostic mix of those remaining in follow-up. This could lead to a turning point in the risk function, with a reduction in the risk of death in the medium term. In the long term, risks are likely to continue to decrease and may even reach levels expected in the general population, in which case the remaining patients could be considered cured.
On the other hand, payers may be hesitant to use a “cure” model if there is limited data on (i) how long the cure will last and (ii) what proportion of people will be “cured”. However, an updated NICE technical support document (Day 21 of TSD) describes some of these more flexible methods.
The authors describe cure models as partitioning all-cause risk h
There are two types of curing models: mixture curing models (MCM) and non-mix curing models (NMC). The authors explain MCM as follows:
General population survival models assume that there are two groups of individuals: those who have been cured of their disease and those who have not. When fitted to a relative survival framework, general population mortality rates are fed directly into the model and the model uses these, combined with the parametric distribution chosen to represent non-cured patients, to estimate the cure fraction. General population mortality rates are taken from relevant life tables, with the appropriate calendar year rates used, and are further stratified by characteristics such as age and sex, so that each trial participant can be assigned an expected background mortality rate.
MCM combines cured and uncured populations, where the cured have a population-wide mortality. However, it is important to note that the modelers do not “decide” the cure percentage; it is estimated from the data. Specifically, each individual in the dataset is not assigned the probability of cure; rather, they are assigned a probability of cure; only the population-level cure fraction can be estimated by averaging these cure probabilities across the entire population.
To encode MCM, you can use chain mix in Stata or flexosupervision and cure in r.
National Center for MedicineInstead, they directly divide the population into cured and uncured groups. Instead, “curation” is defined as follows:
Risk models do not assume that there is a group of patients who are “cured” at the start of the study. The timing of cure depends on when the modeled risks converge with those observed in the general population. When fitted using standard parametric models, there is no restriction on when this convergence will occur.
Despite these different approaches, the authors note that when MCM and NMC are fit with similar parametric distributions, cure rates are typically similar.
To encode NCM, one could use chain mix either stpm2 in Stata, or flexosupervision, cure and firstpm2 in r.
I recommend you read the Complete documentThe rest of the article contains empirical applications, advice on when to (and not to) use healing models, and much more. A very interesting read.
