Using simple microsimulation to estimate risk difference from a meta-analysis

Session Type
Oral presentation
Statistical methods
Murad MH1, Wang Z1, Zhu Y1, Saadi S1, Chu H2, Lin L3
1Mayo Clinic, USA
2University of Minnesota, USA
3University of Arizona, USA

Background: 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 0-100%. 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.

cochrane RD figures.pdf