Transformation to estimate the causal effect in Mendelian randomization study with binary risk factor and outcome

The findings indicated that increasing the strength of the instrumental variable led to a reduction in bias, with the best performance observed at instrumental strengths of 0.5 and 0.7. The LPM and transformation approaches produced relatively lower bias in the TSPS framework when the confounder effect was below 0.1 and the prevalence of the outcome or the exposure is within 0.5 to 0.62. When the prevalence of the exposure and outcome ranged from 0.67 to 0.84 and the instrumental strength was high (0.7), the bias of the LPM and transformation methods were slightly higher but comparable to that observed when the prevalence ranged from 0.5 to 0.62. Furthermore, low prevalence of exposure or outcome (ranged from 0.12 to 0.23) produced larger bias than those observed at higher prevalence values (ranged from 0.67 to 0.84). In the real data analysis, the bias of the Wald ratio using LPM and transformation methods were lower under TSPS and TSRI and higher under the SEM method, while the bias of the Wald ratio using logistic regression was lower under SEM compared to the other methods.