Interval estimate of causal effect in summary data based Mendelian randomization in the presence of winner's curse

This research focuses on the interval estimation of the causal effect of an exposure on an outcome using the summary data-based Mendelian randomization (SMR) method while accounting for the winner's curse caused by the selection of single nucleotide polymorphism instruments. This issue is understudied and is important as the point estimate is biased. Since Fieller's theorem and its variations are not suitable for constructing a confidence interval, we use the box method. This box method is known to be conservative and thus provides a lower bound on the coverage level. To assess the performance of the box method, we use simulation studies and compare it with the support interval we proposed earlier and the Wald interval derived from the SMR method. All three methods are applied to a study of causal genes for Alzheimer's disease. Overall, the box method presents an alternative for constructing interval estimates for a causal effect while addressing the winner's curse issue.