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Background  Cohort-type data are increasingly used to compare health outcomes of immigrants between countries, e.g. to assess the effects of different national integration policies. In such international comparisons, small differences in cardiovascular diseases risk or mortality rates have been interpreted as showing effects of different policies. We conjecture that cohort-type data sets available for such comparisons might not provide unbiased relative risk estimates between countries because of differentials in migration patterns occurring before the cohorts are being observed.    Method  Two simulation studies were performed to assess whether comparisons are biased if there are differences in 1. the way migrants arrived in the host countries, i.e. in a wave or continuously; 2. the effects on health of exposure to the host country; or 3., patterns of return-migration before a cohort is recruited. In the first simulation cardiovascular disease was the outcome and immortality in the second. Bias was evaluated using a Cox regression model adjusted for age and other dependant variables.    Results  Comparing populations from wave vs. continuous migration may lead to bias only if the duration of stay has a dose-response effect (increase in simulated cardiovascular disease risk by 5% every 5 years vs. no risk: hazard-ratio 1.20(0.15); by 10% every 5 years: 1.47(0.14)). Differentials in return-migration patterns lead to bias in mortality rate ratios (MRR). The direction (under- or overestimation) and size of the bias depends on the model (MRR from 0.92(0.01) to 1.09(0.01)).    Conclusion  The order of magnitude of the effects interpreted as due to integration policies in the literature is the same as the bias in our simulations. Future studies need to take into account duration and relevance of exposure and return-migration to make valid inferences about the effects of integration policies on the health of immigrants.    Electronic supplementary material  The online version of this article (10.1186/s12889-019-7267-2) contains supplementary material, which is available to authorized users.

Bias in cohort-based comparisons of immigrants’ health outcomes between countries: a simulation study