Causal mediation analysis with mediator values below an assay limit

Chernofsky, Ariel; Bosch, Ronald J.; Lok, Judith J.

Causal indirect and direct effects provide an interpretable method for decomposing the total effect of an exposure on an outcome into the effect through a mediator and the effect through all other pathways. When the mediator is a biomarker, values can be subject to an assay lower limit. The mediator is affected by the treatment and is a putative cause of the outcome, so the assay lower limit presents a compounded problem in mediation analysis. We propose three approaches to estimate indirect and direct effects with a mediator subject to an assay limit: 1. extrapolation 2. numerical optimization and integration of the observed likelihood and 3. the Monte Carlo Expectation Maximization (MCEM) algorithm. Since the described methods solely rely on the so-called Mediation Formula, they apply to most approaches to causal mediation analysis: natural, separable, and organic indirect and direct effects. A simulation study compares the estimation approaches to imputing with half the assay limit. Using HIV interruption study data from the AIDS Clinical Trials Group described in [Li et al. 2016, AIDS; Lok \&Bosch 2021, Epidemiology], we illustrate our methods by estimating the organic/pure indirect effect of a hypothetical HIV curative treatment on viral suppression mediated by two HIV persistence measures: cell-associated HIV-RNA (N = 124) and single copy plasma HIV-RNA (N = 96).