TSLS with binary outcome

Ad-hoc method for causal estimation with binary outcomes, where 2nd stage regression is substituted with a logistic regression. 

Genetic variants must satisfy the IV assumptions. Genes each exert a small effect on the exposure in order to approximately identify the same causal effect. Non-collapsibility of odds ratio means that population average rather than individual-level causal effects are estimated. 

References

• Burgess S, Labrecque JA. Mendelian randomization with a binary exposure variable: interpretation and presentation of causal estimates. European journal of epidemiology 2018;33:947-952.
• Bowden J, Vansteelandt S. Mendelian randomization analysis of case-control data using structural mean models. Statistics in Medicine 2011;30:678-694.
• Palmer TM, Thompson JR, Tobin MD, Sheehan NA, Burton PR. Adjusting for bias and unmeasured confounding in Mendelian randomization studies with binary responses. International Journal of Epidemiology 2008;37:1161-1168.

Other terms in 'One-sample MR methods':

• Generalized Method of Moments (GMM) estimator
• MR with a time-to-event outcome
• Non-parametric methods with bounds of causal effect
• Polygenic risk score approach
• Semi-parametric structural mean model (SMMs) for binary outcomes
• Two-stage least squares (TSLS)