Appendix 1—table 9. Robustness checks based on SNP-specific associations with child’s BMI^* and outcomes: SNPs in childhood body size 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	0.06	0.03	0.10	0.30	0.00	0.57	0.05	0.52	0.04	0.67
Anxiety symptoms: standardized SCARED‡ score	–0.02	0.40	0.01	0.90	0.00	0.66	–0.02	0.74	–0.01	0.95
ADHD symptoms: standardized RS-DBD§ score	–0.04	0.14	–0.02	0.85	0.00	0.75	–0.06	0.36	–0.05	0.65
ADHD symptoms (inattention): standardized RS-DBD§ score	–0.02	0.47	–0.04	0.64	0.00	0.81	–0.08	0.28	–0.08	0.42
ADHD symptoms (hyperactivity): standardized RS-DBD§ score	–0.05	0.05	0.01	0.90	0.00	0.42	–0.05	0.48	–0.04	0.68
	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	0.02	0.59	0.05	0.70	0.00	0.75	0.03	0.76	0.04	0.79
Anxiety symptoms: standardized SCARED‡ score	0.02	0.60	0.07	0.64	0.00	0.69	0.04	0.66	0.05	0.74
ADHD symptoms: standardized RS-DBD§§ score	–0.02	0.53	0.09	0.49	0.00	0.35	–0.01	0.94	0.03	0.85
ADHD symptoms (inattention): standardized RS-DBD§ score	–0.04	0.28	0.06	0.65	0.00	0.41	–0.04	0.68	0.01	0.95
ADHD symptoms (hyperactivity): standardized RS-DBD§ score	0.00	0.98	0.11	0.43	0.00	0.39	0.02	0.80	0.06	0.67

^*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.