What do you have to do once you need to conduct a cost-effectiveness evaluation primarily based on efficacy estimates from scientific trials however the trial has lacking knowledge. One widespread strategy—often known as full case evaluation (CCA)—is to discard the individuals with incomplete observations. This strategy is problematic as not solely is there a loss in effectivity of the estimator (as a result of smaller pattern dimension), but in addition the estimates could also be biased if the lacking knowledge doesn’t happen at random. Frequent approaches to deal with this challenge embody a number of imputation (MI) (see Leurent et al. 2018) or Bayesian strategies (see Gabrio et al. 2019), and the linear blended fashions (LMM). On this publish, we offer an outline of the LMM strategy largely drawn from a Gabrio et al. (2022) paper.
Contemplate the next regression construction:
On this equation, the time period Yij is the result of curiosity for individual i and at totally different time factors j. There are a sequence of P predictors Xi1,…,XiP with corresponding coefficients β1,…,βP+1. The common error phrases is εij and the time period ωi is random intercept. The equation treats the information as having a 2-level construction, the place σ2ω and σ2ε seize the variance of the responses inside (degree 1) and between (degree 2) people, respectively.
The paper additionally describes one kind of LMM which is a Blended Mannequin for Repeated Measures. Contemplate the case the place we mannequin affected person estimates of high quality of life knowledge (i.e., utilities), that are collected at thrice in the course of the trial (i.e., baseline and a pair of follow-ups). We will write this mannequin mathematically as:
On this equation, we see that utilities have a hard and fast indicator for whether or not the utilities have been collected at baseline, the primary follow-up or the second follow-up. After the baseline estimate, the follow-up equations additionally embody an interplay time period between therapy and the time the utilities have been collected. Notice that by having the random results time period, we’re in a position to account for inside in comparison with between individual variability in utilities; if there’s important heterogeneity in utility throughout people, any lacking knowledge would improve the uncertainty of the estimates relative to circumstances the place there’s little variation in baseline utility ranges throughout people. When knowledge are lacking, one can nonetheless estimate utility or QALY impacts primarily based on weighted linear mixtures of the coefficient estimates of this utility mannequin.
The authors be aware that one key limitation of LMM is that it requires all covariates to be noticed at baseline. Whereas that will generally be the case, the authors argue that “in randomized managed trials, lacking baseline knowledge will be normally addressed by implementing single imputation strategies (e.g., mean-imputation) to acquire full knowledge previous to becoming the mannequin, with out lack of validity or effectivity.”
Gabrio and co-authors additionally publish their code for Stata and R on GitHub (see right here).