Consistently estimating risk difference in a jurisdiction of interest: odds solution to relative risk fallacies
Economic analyses in health technology assessment often require estimation of absolute risk difference (ARD) for outcomes such as survival or progression, given base risk in the jurisdiction of interest and trial evidence of treatment effects. We demonstrate that odds ratios (OR) provide distinct advantages over relative risk (RR) in consistently estimating such ARD independent of the framing of effects (e.g. mortality or survival) for direct and indirect comparisons. METHODS: Use of RR is shown to lead to inferential anomalies in estimating ARD, while consistently estimated using OR. These inferential anomalies and odds solution are illustrated for indirect comparison of Natiluzimab versus Interferon beta-1b for multiple sclerosis, as well as direct comparisons. RESULTS: Standard use of relative risk to calculate ARD in indirect comparison suggests Natiluzimab is more effective than Interferon for progression (RR = 0.70, ARD = 21% for a base risk of 70% progression) but less effective than Interferon for no progression (RR = 0.84, ARD = 4.8%). This inferential anomaly is avoided using OR, with odds of progression (0.83) the reciprocal of that for no progression (1.21), and ARD of 4.1% in favor of Nataluzimab with progression or no progression. For direct comparisons ARD is shown to be consistently estimated with OR but change with framing of effects using RR wherever epidemiological risk differs from trial risk in the comparator arm. CONCLUSIONS: Odds ratios allow consistent estimation of absolute risk differences regardless of framing of effects in direct and indirect comparisons. This overcomes inferential anomalies that arise with use of relative risk in such comparisons whenever base risk differs in the jurisdiction of interest from that in trials, or base risk in the common arms differs in indirect comparisons. Consequently, odds ratios avoid selection biases in framing of effects inherent with risk ratios and are suggested as the preferred metric in estimating such risk differences.