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Abstract
Background: Given its statistical advantages and tendency of homogeneity, the odds ratio (OR) is commonly and possibly will continue to be used in most meta-analyses to summarize the results from individual trials. However, the risk difference (RD) and its derivative number needed to treat are intuitively more comprehensible and clinically more meaningful than the OR for informing decisions.
Objectives: To explore and describe the relation between the OR and RD; provide tools for easy conversion of OR to RD to aid decision making; and identify patients in which the largest RD is obtainable given an OR.
Methods: Mathematical formulas were developed for converting OR to RD and their relation was visually examined by a "Decision Making Graph" which can also be used to covert OR to RD.
Results: A constant OR in a meta-analysis always suggests a varying RD in patients or populations with different risk of event in the absence of treatment unless the OR equals one or the risk does not vary in populations. The largest RD can be obtained in patients with a risk being 1/(1+%OR).
Take antihypertensive drugs for primary prevention of stroke as an example. The combined OR from a meta-analysis is 0.58. The average control risk of the trials varies from 0% to 44% during an average follow-up of 5 years. The corresponding RD is 0% and -13% respectively. The largest obtainable absolute risk reduction is 14% and can be obtained in patients with a risk of 57%, above which the RD will start to decline. Such a high risk is rare in reality in the absence of a stroke history, implying the absolute benefit from antihypertensive drugs will always increase as the control risk rises in real patient populations.
Conclusions: For better interpretation and application of the summary OR of meta-analysis, we suggest to report in meta-analyses, as normal practice, a study-specific graph that describes the OR-RD relation with the 95% confidence intervals and the range of the control risk observed in the trials. Moreover, the need for the OR-RD conversion calls for more studies of disease prognosis to aid decision making.
Objectives: To explore and describe the relation between the OR and RD; provide tools for easy conversion of OR to RD to aid decision making; and identify patients in which the largest RD is obtainable given an OR.
Methods: Mathematical formulas were developed for converting OR to RD and their relation was visually examined by a "Decision Making Graph" which can also be used to covert OR to RD.
Results: A constant OR in a meta-analysis always suggests a varying RD in patients or populations with different risk of event in the absence of treatment unless the OR equals one or the risk does not vary in populations. The largest RD can be obtained in patients with a risk being 1/(1+%OR).
Take antihypertensive drugs for primary prevention of stroke as an example. The combined OR from a meta-analysis is 0.58. The average control risk of the trials varies from 0% to 44% during an average follow-up of 5 years. The corresponding RD is 0% and -13% respectively. The largest obtainable absolute risk reduction is 14% and can be obtained in patients with a risk of 57%, above which the RD will start to decline. Such a high risk is rare in reality in the absence of a stroke history, implying the absolute benefit from antihypertensive drugs will always increase as the control risk rises in real patient populations.
Conclusions: For better interpretation and application of the summary OR of meta-analysis, we suggest to report in meta-analyses, as normal practice, a study-specific graph that describes the OR-RD relation with the 95% confidence intervals and the range of the control risk observed in the trials. Moreover, the need for the OR-RD conversion calls for more studies of disease prognosis to aid decision making.
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