Causal mediation analysis with mediator values below an assay limit

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).