I’m running a sex-stratified two-sample MR of exposure on outcome using sex-specific GWAS summary stats for both exposure and outcome.

Planned approach.

• Pairwise Wald Z-test comparing male vs female IVW estimates (independent samples).
• Meta-analytic heterogeneity via Cochran’s Q for subgroup differences (or meta-regression with sex as a moderator in metafor).

My understanding is that with two groups Q_between = Z² (same p-value), though the Q-framework is often preferred in reporting.

Questions:

1. Is Z and/or Q_between the recommended way to test sex differences in summary-level MR?

2. Would you report this as “between-sex heterogeneity in MR estimates” rather than “interaction”?

3. For binary outcomes we work on log-odds; does this address concerns about comparing effects when baseline risks differ?

4. Any suggested references or key elements beyond IVW with 95% CIs—e.g., Q_between p-value, instrument strength by sex (F, R²), Steiger, MR-Egger intercept, MR-PRESSO?

Grateful for any guidance, examples, or citations. Thanks in advance!