Using simple microsimulation to estimate risk difference from a meta-analysis
2University of Minnesota, USA
3University of Arizona, USA
Absolute risk reduction or risk difference (RD) is a key effect measure required for decision-making and its confidence interval (CI) is the basis for imprecision judgments. Many methodology groups (e.g., Cochrane and GRADE) recommend obtaining RD from linear transformation of a risk ratio (RR) that is usually derived from a meta-analysis. This transformation uses an assumed baseline risk (BR) and follows the equation RD= RR X (RR-1). The 95% CI of RD is derived from the same equation using the 95% CI of RR.
Objectives: In this proposal, we demonstrate several limitations to this traditional approach using a simulated case study and offer an alternative approach.
Methods: We simulated a case study using a published systematic review [beta blockers vs. placebo on all-cause mortality in symptomatic heart failure with preserved ejection fraction, RR, 0.79 (0.66-0.96)]. The first analysis was based on the traditional linear transformation of RR into RD using BR that we simulated from 0% to 100%. The second analysis is based on the proposed new approach which is a microsimulation in which RR is drawn from a Lognormal distribution with mean and standard error of the identified RR and BR is drawn from a Beta distribution which shape parameters were derived from a population-based study [Olmsted County, Minnesota, Mortality at 1 year= 0.29 (0.27-0.31)]. 10,000 simulations (draws) generated RD histogram with median, 2.5 and 97.5 percentiles (Open-source code in R).
Results: The traditional approach (Figure 1) demonstrates these limitations: 1) RD CI does not incorporate uncertainty in BR and derives all its uncertainty from the treatment effect, 2) CI widens linearly as BR increases, making RD estimates imprecise in higher-risk populations (counterintuitive), and very precise in low-risk populations (potentially misleadingly precise as it ignores uncertainty in BR). The proposed approach (Figure 2), produces a joint distribution of RD that incorporates uncertainty in BR to resolve the limitations of the first approach.
Conclusions: Simple transformation of RR into RD has many limitations and does not incorporate uncertainty in BR. An alternative proposed approach incorporates uncertainty in BR that was derived from a population-based study. Patient/public/consumer involvement: None.