Supplemental Methods C – Sensitivity to unmeasured confounding
A number of factors, known or suggested (but not unambiguously) to affect (to some extent) pharmacokinetics of MPA are depicted in Figure S1. However, “pharmacogenetic settings” are complex, and one shoulda priori consider that there are inevitably unmeasured, although reasonably possible (e.g., SLCO1B3 c.334 and UGT1A9 c.98SNPs), but also unknown confounders, i.e., those not indicated in Figure S1.
E-value [1] represents the minimum strength of association, on the risk ratio scale, that unmeasured confounder(s) need(s) to have with the outcome and the treatment to explain away a specific treatment-outcome association, conditional on the measured covariates. A large E-value implies that a considerable unmeasured confounding effect is needed for the purpose. E-value can be determined for different effect measures, i.e., relative risk, odds ratio, hazard ratio, rate ratio, mean difference or a regression coefficient, but is expressed on the risk ratio scale [1]. The effect measure in the present study was geometric means ratio (GMR), i.e., exponentiated difference between two (adjusted) means of ln-transformed values of pharmacokinetic indicators. Calculation of E-value for difference in means is based on standardized difference (d), requires several effect measure conversions, several assumptions, and its interpretation is not very intuitive [1]. However, GMR and RR share some common features: (i) both are exponents of difference in means of ln-transformed quantities (risk or a continuous variable); (ii) both ln(risk) and ln(right-tailed continuous variable) have a normal distribution and their interpretation is similar as they provide information about a relative difference between a treatment and a control. If for a treatment vs. control RR >1.0, e.g., 1.5, it means relatively by 50% higher risk with treatment, just as is the case with GMR: if 1.5, it means relatively by 50% higher value of the measured quantity with treatment. Similar is the relationship between a relative risk (risk ratio) and relative rate (rate ratio), where E-value calculation for a relative rate is identical as for the relative risk [1]. Therefore, in calculation of E-values we “treated” GMRs as relative risks. One can calculate E-value that indicates size of the effect of unmeasured confounding needed to completely explain away the observed effect, i.e., to “push” the estimate of a ratio to 1.0 or a difference to 0.0; but E-value can be determined in respect to any desired level [1]. We determined E-values needed to “push” the GMR point-estimates to 1.20. We considered that GMR 1.20 indicated a cut-off value at which difference (1.20 and higher) becomes practically relevant: in the classical context of equivalent relative exposure, GMR point-estimates of 1.20 are at the upper limit of the conventional acceptance range. E-value may be considered as a total effect of all unmeasured confounding.
Since current literature data [2,3] suggest SLCO1B3 c.334T>G and UGT1A9 c.98T>C SNPs as potentially relevant factors for MPA bioavailability – which remained unmeasured in the present study (Figure S1) – the estimated GMRs (for variant ABCG2 c.421C>A vs. wt genotype) were submitted to a sensitivity analysis in which they were corrected for bias arising from not adjusting for the these two SNPs [4]. For this purpose, using two recent systematic reviews [2,3], we identified studies reporting on associations between SLCO1B3 c.334T>G (as a contrast between TT/TG patients vs. GG patients) and UGT1A9 c.98T>C (as a contrast between variant allele carriers and wt subjects) SNPs, and MPA AUCτ,ss, and we generated meta-analytical pooled estimates (random-effects, REML variance estimator and Hartung-Knapp-Sidik-Jonkman correction using package meta in R [5]) expressed as ratios of means (ROM) [6]. We also identified studies conducted in samples from European populations that provided information about prevalence of SLCO1B3 c.334 TT/TG patients and of UGT1A9 c.98T>C variant carriers to generate prevalence estimates (random-effects, generalized linear mixed model fitted to logit-transformed proportions with ML variance estimator, package meta in R [5]) needed for the sensitivity analysis. We “treated” GMRs and ROMs as relative risks, and calculated bias-adjusted GMRs at different levels of confounder effects using package episensr in R [7].