Table 3. Likelihood-based deviance information criterion (DIC) scores for conventional causal (M4) and conventional reverse causal (M5) models, both (i) assume absence of pleiotropic effects of instruments on biomarkers and outcomes, (ii) explicitly exclude unmeasured confounders from modelling and (iii) account for the noise in the measurement; and for the model where the association between the biomarker and outcome is modelled entirely by unmeasured confounders (M6); these models have been compared in Experiment 2.

MODEL	setting 1	setting 2	setting 3
conventional causal(without confounders)	43,347	218,230	21,883
conventional reverse(without confounders)	41,915	211,254	21,189
no causal link but accountingfor unmeasured confounders	81**	−1,549**	689**

Digits after decimal point have been omitted from the table.

Setting 1: precxt = 200, precx = 200, precy = 100; Setting 2: precxt = 1000, precx = 1000, precy = 0.1; Setting 3: precxt = 100, precx = 100, precy = 100. Sparsity parameter gamma is set to 0.025 in all models. In model with confounders (M6) precz = 1.

^**indicates the best model for each setting; preferred modelling hypotheses are characterized by lower DICs.