Self-selection into prospective cohort studies and loss to follow-up can cause biased exposure-outcome association estimates. Previous investigations illustrated that such biases can be small in large prospective cohort studies. The structural approach to selection bias shows that general statements about bias are not possible for studies that investigate multiple exposures and outcomes, and that inverse probability of participation weighting (IPPW) but not adjustment for participation predictors generally reduces bias from self-selection and loss to follow-up. We propose to substantiate assumptions in structural models of selection bias through calculation of genetic correlations coefficients between participation predictors, outcome, and exposure, and to estimate a lower bound for bias due to self-selection and loss to follow-up by comparing effect estimates from IPP weighted and unweighted analyses. This study used data from the Norwegian Mother and Child Cohort Study and the Medical Birth Registry of Norway. Using the example of risk factors for ADHD, we find that genetic correlations between participation predictors, exposures, and outcome suggest the presence of bias. The comparison of exposure-outcome associations from regressions with and without IPPW revealed meaningful deviations. Assessment of selection bias for entire multi-exposure multi-outcome cohort studies is not possible. Instead, it has to be assessed and controlled on a case-by-case basis.