Table 6 Results of meta-analyses of SIENA model results for each school modeling the co-evolution of friendship ties and smoking/vaping outcomes (results reported for peer selection homophily and peer influence effects).

From: Selection homophily and peer influence for adolescents’ smoking and vaping norms and outcomes in high and middle-income settings

Outcome^a	Effect^b	All schools (N = 12)^a						Subgroup analysis: Setting (NI: N = 6; Bogotá: N = 6)^a							Subgroup analysis: Intervention (ASSIST: N = 6; DC: N = 6)^a
		Snijders and Baerveldt, (2003)^c		Fisher’s combination tests one-sided^d		Heterogeneity (across schools)^e		Subgroup	Snijders and Baerveldt, (2003)^c		Fisher’s combination tests one-sided^d		Heterogeneity (across subgroups)^f		Subgroup	Snijders and Baerveldt, (2003)^c		Fisher’s combination tests one-sided^d		Heterogeneity (across subgroups)^f
		b	SE	p-value	df	Q-statistic	p-value	Subgroup	b	SE	p-value	df	Q-statistic	p-value	Subgroup	b	SE	p-value	df	Q-statistic	p-value
Experimental injunctive norms	PS	−0.20	0.15	0.2882	24	7.38	0.7672	NI	−0.40	0.23	0.0883	12	1.77	0.1828	ASSIST	−0.25	0.20	0.3214	12	0.11	0.7348
	PS							Bogotá	−0.005	0.19	0.7576	12			DC	−0.13	0.26	0.3221	12
	PI	3.95	1.03	<0.0001^g	24	14.07	0.2292	NI	4.41	2.28	0.0053	12	0.04	0.8380	ASSIST	5.06	1.52	0.0005^g	12	0.70	0.4023
	PI							Bogotá	3.93	1.21	0.0002^g	12			DC	3.38	1.42	0.0019	12
Experimental descriptive norms	PS	0.10	0.22	0.2327	20	11.84	0.2223	NI	0.09	0.37	0.2907	8	<0.01	0.9609	ASSIST	0.17	0.27	0.1360	12	0.24	0.6255
	PS							Bogotá	0.09	0.31	0.2654	12			DC	−0.08	0.43	0.3183	8
	PI	1.57	0.78	0.0056	24	17.88	0.0844	NI	2.43	0.77	0.0371	12	1.24	0.2659	ASSIST	3.25	0.26	0.0012^g	12	42.79	<0.0001^h
	PI							Bogotá	1.60	1.46	0.0267	12			DC	−0.08	1.32	0.4090	12
Experimental donation to ASSIST/Dead Cool	PS	0.18	0.14	0.2494	24	9.33	0.5913	NI	0.22	0.24	0.1670	12	0.18	0.6699	ASSIST	0.37	0.19	0.0589	12	2.60	0.1068
	PS							Bogotá	0.11	0.17	0.4703	12			DC	−0.04	0.18	0.3784	12
	PI	4.13	0.43	<0.0001^g	24	4.69	0.9451	NI	4.41	0.33	<0.0001^g	12	0.93	0.3355	ASSIST	4.03	0.69	<0.0001^g	12	0.07	0.7953
	PI							Bogotá	3.69	0.92	0.0006^g	12			DC	4.26	0.59	0.0001^g	12
Self-report injunctive norms	PS	−0.002	0.13	0.4608	24	7.04	0.7957	NI	0.15	0.21	0.3924	12	2.13	0.1442	ASSIST	0.09	0.18	0.6340	12	0.90	0.3437
	PS							Bogotá	−0.21	0.17	0.2454	12			DC	−0.18	0.22	0.3896	12
	PI	2.30	1.51	0.0757	20	9.21	0.4179	NI	3.16	0.82	0.1306	8	1.14	0.2848	ASSIST	3.62	2.05	0.0345	10	0.87	0.3508
	PI							Bogotá	1.60	2.83	0.1438	12			DC	0.74	2.31	0.4267	10
Self-report descriptive norms 1	PS	0.25	0.21	0.0261	24	16.85	0.1123	NI	0.32	0.10	0.0901	12	0.47	0.4943	ASSIST	0.32	0.23	0.1040	12	0.12	0.7240
	PS							Bogotá	0.19	0.58	0.0626	12			DC	0.31	0.39	0.0537	12
	PI	3.63	3.33	0.0115	12	11.65	0.0399	NI	5.87	6.71	0.0019	6	8.82	0.0030	ASSIST	5.88	6.90	0.0023	6	5.05	0.0247
	PI							Bogotá	0.10	1.20	0.5646	6			DC	0.49	1.41	0.5072	6
Self-report descriptive norms 2	PS	0.38	0.16	0.0176	24	8.50	0.6679	NI	0.42	0.28	0.0314	12	0.02	0.8799	ASSIST	0.57	0.25	0.0363	12	0.91	0.3401
	PS							Bogotá	0.40	0.22	0.1102	12			DC	0.26	0.22	0.0968	12
	PI	3.83	0.74	0.0294	22	2.72	0.9873	NI	4.48	1.25	0.0323	10	0.58	0.4452	ASSIST	3.77	1.34	0.0756	12	0.01	0.9126
	PI							Bogotá	3.27	0.99	0.1720	12			DC	3.91	0.79	0.0848	10
Self-report smoking behavior	PS	0.30	0.13	0.0074	20	8.63	0.4720	NI	0.32	0.17	0.1116	8	0.11	0.7361	ASSIST	0.36	0.14	0.0069	12	0.28	0.5941
	PS							Bogotá	0.37	0.23	0.0121	12			DC	0.20	0.32	0.1859	8
	PI	2.07	0.91	0.3684	12	1.12	0.9527	NI	2.18	2.18	0.3108	4	0.01	0.9401	ASSIST	1.31	1.64	0.5369	8	24.31	<0.0001^h
	PI							Bogotá	2.00	1.24	0.4113	8			DC	2.77	0.14	0.1984	4
Intentions	PS	0.06	0.18	0.3878	14	4.77	0.5739	NI	0.17	0.20	0.3698	6	0.32	0.5689	ASSIST	0.001	0.20	0.5441	8	3.17	0.0748
	PS							Bogotá	−0.02	0.34	0.5418	8			DC	0.74	0.38	0.2434	6
	PI	5.50	3.72	0.0023	12	12.84	0.0249	NI	13.56	4.92	0.0002^g	6	21.75	<0.0001^h	ASSIST	8.64	9.33	0.0066	4	0.21	0.6452
	PI							Bogotá	0.80	1.08	0.5650	6			DC	4.15	4.30	0.0378	8
Knowledge	PS	−0.03	0.12	0.4398	24	6.20	0.8594	NI	−0.01	0.24	0.3261	12	0.09	0.7677	ASSIST	0.14	0.13	0.5077	12	2.72	0.0991
	PS							Bogotá	−0.06	0.09	0.5486	12			DC	−0.21	0.18	0.1751	12
	PI	2.22	0.64	0.0051	24	8.81	0.6395	NI	2.92	0.68	0.0045	12	1.73	0.1887	ASSIST	2.02	1.24	0.0176	12	0.08	0.7786
	PI							Bogotá	1.25	1.19	0.1524	12			DC	2.07	0.65	0.0496	12
Attitudes	PS	0.14	0.26	0.3080	14	6.07	0.4149	NI	0.08	0.44	0.4659	6	0.02	0.8866	ASSIST	0.23	0.46	0.2926	4	0.07	0.7960
	PS							Bogotá	0.17	0.37	0.2343	8			DC	0.08	0.35	0.3467	10
	PI	1.49	0.93	0.0532	24	12.39	0.3354	NI	1.51	1.68	0.0974	12	0.36	0.5482	ASSIST	1.83	1.55	0.0507	12	0.05	0.8233
	PI							Bogotá	2.13	1.07	0.1319	12			DC	1.50	1.34	0.2324	12
Self-efficacy (Emotional)	PS	0.30	0.17	0.0945	22	9.83	0.4554	NI	0.01	0.40	0.5766	10	0.61	0.4338	ASSIST	0.47	0.15	0.0254	12	2.40	0.1210
	PS							Bogotá	0.37	0.22	0.0319	12			DC	−0.09	0.37	0.2938	10
	PI	−2.64	0.89	0.1714	16	2.17	0.9496	NI	2.74	1.63	0.3242	4	14.93	0.0001^h	ASSIST	−2.46	0.99	0.2380	8	0.05	0.8151
	PI							Bogotá	−3.43	0.39	0.0745	12			DC	−2.91	1.84	0.2140	8
Self-efficacy (Friends)	PS	0.22	0.21	0.1493	24	13.25	0.2775	NI	0.15	0.22	0.6242	12	0.16	0.6886	ASSIST	0.49	0.23	0.0530	12	2.28	0.1307
	PS							Bogotá	0.31	0.39	0.0468	12			DC	−0.10	0.33	0.2806	12
	PI	−0.52	1.44	0.3998	18	6.79	0.5599	NI	3.28	4.52	0.2524	6	0.83	0.3611	ASSIST	0.28	2.05	0.5206	8	0.33	0.5667
	PI							Bogotá	−1.05	1.49	0.2292	12			DC	−1.54	2.43	0.3014	10
Self-efficacy (Opportunity)	PS	0.48	0.37	0.0111	16	12.36	0.0893	NI	0.24	0.53	0.1477	4	0.27	0.6043	ASSIST	0.75	0.37	0.0055	8	0.77	0.3802
	PS							Bogotá	0.62	0.53	0.0154	12			DC	0.10	0.77	0.2679	8
	PI	1.96	2.01	0.1275	14	6.76	0.3437	NI	5.57	4.40	0.0302	6	2.01	0.1560	ASSIST	1.33	0.75	0.4310	8	0.72	0.3978
	PI							Bogotá	0.39	1.36	0.6321	8			DC	2.49	5.21	0.0607	6
Perceived physical risks	PS	0.13	0.13	0.2701	24	9.27	0.5969	NI	−0.03	0.12	0.6400	12	2.12	0.1457	ASSIST	−0.14	0.21	0.3412	12	6.84	0.0089
	PS							Bogotá	0.24	0.25	0.0828	12			DC	0.38	0.11	0.1083	12
	PI	1.11	0.54	0.2190	24	6.15	0.8630	NI	1.55	1.00	0.2607	12	0.27	0.6037	ASSIST	1.24	0.71	0.2132	12	0.09	0.7702
	PI							Bogotá	0.92	0.68	0.2776	12			DC	0.89	0.94	0.3345	12
Perceived social risks	PS	−0.11	0.11	0.3890	24	5.36	0.9126	NI	−0.42	0.21	0.2104	12	2.60	0.1069	ASSIST	−0.17	0.21	0.4411	12	0.18	0.6679
	PS							Bogotá	−0.04	0.13	0.6410	12			DC	−0.06	0.14	0.3508	12
	PI	−0.12	0.55	0.3805	24	8.17	0.6980	NI	−1.04	1.32	0.2356	12	0.56	0.4561	ASSIST	−0.25	1.11	0.2415	12	0.01	0.9129
	PI							Bogotá	0.05	0.62	0.5397	12			DC	−0.12	0.80	0.5745	12
Perceived addiction risks	PS	0.08	0.15	0.2726	24	8.96	0.6260	NI	0.34	0.13	0.2040	12	4.13	0.0422	ASSIST	0.17	0.23	0.1319	12	0.34	0.5582
								Bogotá	−0.05	0.26	0.4298	12			DC	−0.002	0.19	0.6427	12
	PI	0.70	0.80	0.5471	24	10.68	0.4707	NI	1.12	0.87	0.3315	12	0.87	0.3502	ASSIST	0.36	0.87	0.6009	12	0.35	0.5569
	PI							Bogotá	−0.80	1.88	0.1642	12			DC	−0.16	1.95	0.2575	12
Perceived benefits	PS	0.46	0.25	0.0356	20	10.33	0.3248	NI	0.34	0.33	0.1850	12	0.23	0.6332	ASSIST	0.12	0.33	0.4457	8	1.33	0.2496
	PS							Bogotá	0.60	0.44	0.0340	8			DC	0.65	0.36	0.0153	12
	PI	−0.78	0.69	0.3437	12	1.60	0.9010	NI	−0.43	1.03	0.3797	8	83.05	<0.0001^h	ASSIST	0.05	1.33	0.7014	6	47.20	<0.0001^h
	PI							Bogotá	−1.57	0.09	0.3102	4			DC	−1.70	0.13	0.2752	6
PBC (easy to quit)	PS	0.23	0.14	0.1722	24	10.11	0.5204	NI	0.35	0.20	0.1210	12	0.95	0.3292	ASSIST	0.24	0.13	0.2072	12	0.16	0.6861
	PS							Bogotá	0.06	0.23	0.4017	12			DC	0.09	0.35	0.2567	12
	PI	0.32	0.40	0.6762	24	5.93	0.8780	NI	0.38	0.69	0.5914	12	0.02	0.8825	ASSIST	0.65	0.56	0.4226	12	0.72	0.3950
	PI							Bogotá	0.26	0.51	0.6090	12			DC	−0.06	0.62	0.4323	12
PBC (to avoid smoking)	PS	0.12	0.29	0.2729	20	9.20	0.4192	NI	−0.20	0.31	0.5539	8	1.20	0.2732	ASSIST	0.19	0.42	0.2516	12	0.14	0.7132
	PS							Bogotá	0.27	0.40	0.1147	12			DC	−0.02	0.43	0.6734	8
	PI	0.68	0.58	0.4756	22	6.17	0.8004	NI	1.71	0.74	0.1760	10	3.24	0.0718	ASSIST	1.01	0.67	0.4064	12	0.48	0.4863
	PI							Bogotá	−0.20	0.77	0.4163	12			DC	0.13	1.12	0.5096	10
Objectively measured smoking behavior	PS	0.39	0.36	0.4672	14	3.63	0.7260	NI	−1.10	0.36	0.2462	4	17.14	<0.0001^h	ASSIST	−0.16	0.23	0.5476	6	5.57	0.0183
	PS							Bogotá	0.59	0.35	0.2521	10			DC	0.51	0.61	0.2537	8
	PI	8.12	1.48	<0.0001^g	20	15.79	0.0713	NI	10.83	2.68	<0.0001^g	10	2.99	0.0839	ASSIST	8.98	2.57	<0.0001^g	12	0.25	0.6175
	PI							Bogotá	6.34	1.27	<0.0001^g	10			DC	7.58	1.46	<0.0001^g	8
Smoking susceptibility	PS	0.17	0.06	0.0017	22	11.35	0.3308	NI	0.19	0.09	0.0101	12	0.05	0.8281	ASSIST	0.11	0.08	0.0388	12	3.58	0.0586
	PS							Bogotá	0.16	0.10	0.0264	10			DC	0.32	0.09	0.0062	10
	PI	0.77	0.49	0.2351	22	5.66	0.8433	NI	0.57	0.61	0.4990	12	0.14	0.7083	ASSIST	0.85	0.74	0.1615	12	0.05	0.8179
	PI							Bogotá	0.94	0.90	0.1305	10			DC	0.62	0.74	0.4671	10

SIENA simulation investigation for empirical network analysis, NI Northern Ireland, ASSIST A Stop Smoking in Schools Trial, DC dead dool, b unstandardized coefficient, SE standard error, df degrees of freedom, PS peer selection, PI peer influence, PBC perceived behavioral control.
^aFor some of the meta-analyses, individual schools are excluded due to non-convergence of the SIENA models. Various parameters are also constrained for some SIENA models due to non-convergence or multi-collinearity issues. Score tests for fixed parameters were all non-significant (p > 0.05) indicating the goodness-of-fit of the models was not decreased. The results of the meta-analyses for each of the smoking/vaping outcomes are reported and discussed in full in Supplementary Tables S11–S31. See the footnotes of Tables S11–S31 for details of excluded schools and constrained parameters for each of the smoking/vaping outcomes.
^bPS: Smoking/vaping outcome similarity (peer selection homophily) effect. PI: Smoking/vaping outcome friends (peer influence) effect. See Table 2 for definitions of effects included in all SIENA models. Table 6 reports the results of peer selection homophily and peer influence effects for the meta-analysis for each outcome. The results of the meta-analyses for each of the smoking/vaping outcomes are reported and discussed in full in Supplementary Tables S11–S31.
^cUnstandardized coefficients according to the meta-analytic method of Snijders and Baerveldt (2003).
^dp-values are calculated using Fisher’s combination of one-sided tests procedure (Fisher, 1925; Hedges and Olkin, 1985). The test statistic follows a chi-squared distribution with (2N) degrees of freedom (N = number of combined estimates for each parameter). Only one-sided p-values in the direction of the sign of the Snijders and Baerveldt coefficients are reported. One-sided p-values in the other direction were all non-significant. Bold values indicate significant results (p ≤ 0.005).
^eHeterogeneity (across schools): Tests the null hypothesis that the effect parameters are constant across schools using the methods of Cochran (1954), adapted for social network analysis by Snijders and Baerveldt (Cochran, 1954; Snijders and Baerveldt, 2003). The Q-statistic follows a chi-squared distribution with (N−1) degrees of freedom (N = number of combined estimates for each parameter). Bold values indicate significant differences across schools (p ≤ 0.01).
^fHeterogeneity (across subgroups): Tests the null hypothesis that the effect parameters are constant across subgroups (NI versus Bogotá for ‘Setting’, ASSIST versus Dead Cool for ‘Intervention’) using methods for testing differences across subgroups from the Cochrane Handbook (Higgins and Thomas, 2022). The Q-statistic follows a chi-squared distribution with (N-1) degrees of freedom (N = number of subgroups, i.e., N = 2). Bold values indicate significant differences across subgroups (p ≤ 0.01).
^gIndicates where the p-value from the Fisher’s combination of one-sided tests procedure retained statistical significance at the 5% level after using the Holm–Bonferroni procedure to correct the p-values for multiple testing (p ≤ 0.025; each p-value is adjusted for 21 tests, i.e., the number of smoking/vaping outcomes).
^hIndicates where the p-value from the heterogeneity test (across schools or across subgroups) retained statistical significance at the 5% level after using the Holm–Bonferroni procedure to correct the p-values for multiple testing (p ≤ 0.05; each p-value is adjusted for 21 tests, i.e., the number of smoking/vaping outcomes).
Bold values show the results meeting the significance level of p ≤ 0.005 for Fisher’s combination tests (one-sided), and p ≤ 0.01 for heterogeneity tests (across schools or subgroups).

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Table 6 Results of meta-analyses of SIENA model results for each school modeling the co-evolution of friendship ties and smoking/vaping outcomes (results reported for peer selection homophily and peer influence effects).

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