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Sir,

We would like to thank Dr Pamela J Schwingl for giving us the opportunity to clarify a phrase in our paper which may have been misinterpreted by readers other than Dr Schwingl. When we indicated that the odds ratio (= relative risk for rare diseases) of ischaemic stroke among hypertensive women was independent of combined oral contraceptive (COC) status, this indicated that hypertension implied the same odds ratio among women on OC as among women not using COC. In a multiplicative model this independence means that the exposure of two risk factors implies a risk of stroke corresponding a multiplication of the two risk factors. As low dose COCs (30–40 μg oestrogen) in themselves imply a relative risk of stroke of 1.8 and hypertension a relative risk of about 3.1, the combined relative risk is close to 5.6. All the included risk factors were analyzed for interaction with oral contraceptive use. No evidence of interaction was found.

In general, women with a known increased risk of stroke should be advised against increasing their risk any further by adding other risk factors. There is no contradiction in showing an independence between two risk factors and at the same time advising women with an increased risk of stroke from increasing that risk further by, for example, COC use.

We are well aware that modern epidemiology has demonstrated that two biological exposures acting at the same time may result in a total risk that corresponds to an addition of the two relative risks, rather than a multiplication of the two risks factors. In the example of oral contraceptives and hypertension an additive combined effect would result in a combined relative risk of 4.9, implying an interaction between the two exposures in a multiplicative model. Several different test statistics were used, all resulting in p-values between 0.3 and 0.8. As an analysis of the differences between the observed and fitted values (residuals) showed a good fit, we see no problem in accepting the multiplicative model as a realistic description of the combined effect of the included risk factors. In an additive model this would of course imply an interaction which one might interpret as synergy.