What must you do if you wish to conduct a cost-effectiveness evaluation primarily based on efficacy estimates from medical trials however the trial has lacking information.  One frequent method—referred to as full case evaluation (CCA)—is to discard the individuals with incomplete observations.  This method is problematic as not solely is there a loss in effectivity of the estimator (because of the smaller pattern measurement), but in addition the estimates could also be biased if the lacking information doesn’t happen at random.  Frequent approaches to deal with this situation 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 submit, we offer an outline of the LMM method largely drawn from a Gabrio et al. (2022) paper.

Contemplate the next regression construction:

On this equation, the time period Yij is the end result of curiosity for particular person i and at completely 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 Combined Mannequin for Repeated Measures. Contemplate the case the place we mannequin affected person estimates of high quality of life information (i.e., utilities), that are collected at 3 times through 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 set 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 remedy and the time the utilities have been collected. Observe that by having the random results time period, we’re capable of account for inside in comparison with between particular person variability in utilities; if there’s vital heterogeneity in utility throughout people, any lacking information would improve the uncertainty of the estimates relative to instances the place there’s little variation in baseline utility ranges throughout people. When information 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 information may be normally addressed by implementing single imputation strategies (e.g., mean-imputation) to acquire full information previous to becoming the mannequin, with out lack of validity or effectivity.”

Gabrio and co-authors additionally submit their code for Stata and R on GitHub (see right here).

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