Background: Instrumental variable (IV) methods are widely employed to estimate causal effects when concerns regarding unmeasured confounders. Although comparisons among several IV methods for binary outcomes exist, comprehensive evaluations are insufficient. Therefore, in this study, we aimed to conduct a simulation with some settings for a detailed comparison of these methods, focusing on scenarios where IVs are valid and under effect homogeneity with different instrument strengths.
Methods: We compared six IV methods under 32 simulation scenarios: two-stage least squares (2SLS), two-stage predictor substitutions (2SPS), two-stage residual inclusions (2SRI), limited information maximum likelihood (LIML), inverse-variance weighted methods with a linear outcome model (IVWLI), and inverse-variance weighted methods with a non-linear model (IVWLL). By comparing these methods, we examined three key estimates: the parameter estimates of the exposure variable, the causal risk ratio, and the causal risk differences.
Results: Based on the results, six IV methods could be classified into three groups: 2SLS and IVWLI, 2SRI and 2SPS, and LIML and IVWLL. The first pair showed a clear bias owing to outcome model misspecification. The second pair showed a relatively good performance when strong IVs are available; however, the estimates suffered from a significant bias when only weak IVs are used. The third pair produced relatively conservative results, although they were less affected by weak IV issues.
Conclusions: The findings indicate that no panacea is available for the bias associated with IV methods. We suggest using multiple IV methods: one for primary analysis and another for sensitivity analysis.
Keywords: inverse-variance weighted method; limited information maximum likelihood; two-stage least square; two-stage residual inclusion; weak instrument bias.