Appendix 1—table 8. Robustness checks based on SNP-specific associations with child’s BMI^* and outcomes: SNPs in adult BMI polygenic score.

	Inverse-variance weighted		MR-Egger: slope		MR-Egger: intercept		MR-Median		MR-Modal
For classic MR models	Beta	p	Beta	p	Beta	p	Beta	p	Beta	p
Depressive symptoms: standardized SMFQ† score	0.12	<0.001	0.09	0.18	0.00	0.56	0.11	<0.001	0.07	0.42
Anxiety symptoms: standardized SCARED‡ score	–0.02	0.13	–0.05	0.45	0.00	0.61	–0.01	0.87	0.01	0.92
ADHD symptoms: standardized RS-DBD§ score	0.10	<0.001	0.02	0.77	0.00	0.19	0.09	0.01	0.07	0.40
ADHD symptoms (inattention): standardized RS-DBD§ score	0.09	<0.001	–0.02	0.73	0.00	0.07	0.09	0.01	–0.02	0.81
ADHD symptoms (hyperactivity): standardized RS-DBD§ score	0.08	<0.001	0.05	0.40	0.00	0.61	0.08	0.02	0.05	0.55
	Inverse-variance weighted		MR-Egger: slope		MR-Egger: intercept		MR-Median		MR-Modal
For within-families MR models	Beta	p	Beta	p	Beta	p	Beta	p	Beta	p
Depressive symptoms: standardized SMFQ† score	0.06	<0.001	0.04	0.67	0.00	0.77	0.07	0.16	0.02	0.83
Anxiety symptoms: standardized SCARED‡ score	0.00	1.00	0.05	0.58	0.00	0.57	0.03	0.57	0.03	0.76
ADHD symptoms: standardized RS-DBD§ score	0.09	<0.001	0.07	0.41	0.00	0.80	0.09	0.07	0.13	0.24
ADHD symptoms (inattention): standardized RS-DBD§ score	0.10	<0.001	0.00	0.97	0.00	0.21	0.10	0.03	0.05	0.63
ADHD symptoms (hyperactivity): standardized RS-DBD§ score	0.07	<0.001	0.13	0.13	0.00	0.44	0.07	0.14	0.06	0.56

^*In the main analyses, all coefficients are expressed in terms of S.D. change in symptoms per 5 kg/m² increase in BMI. In robustness checks, SNP-exposure associations were taken directly from the relevant GWAS. Coefficients above for BMI-outcome associations are therefore on the scale of kg/m².

^†Short Mood and Feelings Questionnaire.

^‡Screen for Child Anxiety Related Disorders.

^§Parent/Teacher Rating Scale for Disruptive Behaviour Disorders.