Hazard Ratio to Relative Risk Conversion

Converts a hazard ratio (HR) from survival analysis into an approximate relative risk (RR) — useful when combining survival studies (HR) with risk studies (RR) in meta-analysis.

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Inputs

• Hazard Ratio (with optional 95% CI)
• Baseline event rate in the control group
• Time point of interest

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Method

conversion_factor = -ln(1 - event_rate) / time
RR = HR ^ conversion_factor

CI bounds converted by applying the same power transformation:

RR_lower = HR_lower ^ conversion_factor
RR_upper = HR_upper ^ conversion_factor

HR and RR are equal only under specific conditions. The approximation is best when the event rate is low (rare-disease assumption).

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