Table 3 Estimated Number of Outliers Statistics and Non-replicable SNPs in the GSCAN Dataset.

Phenotype	MAF range	Number of significant SNPs analyzed (P < 1 × 10⁻⁵)	Total expected # of outlier statistics^a	Total expected # of Non-replicable SNPs^b	Average of average # of outliers per study^c	Maximum # outliers at each SNP	Median # of outliers at each SNP
SmkInit	0 < MAF < 0.001	306	62.83	64.85	0.026	2.151	0.007
SmkInit	0.001 < MAF < 0.01	87	22.9	22.73	0.027	1.027	0.015
SmkInit	0.01 < MAF < 0.5	301	6.09	4.63	0.027	2.173	0
SmkCes	0 < MAF < 0.001	424	26.09	22.62	0.046	1.349	0.043
SmkCes	0.001 < MAF < 0.01	100	5.01	3.93	0.043	0.276	0.04
SmkCes	0.01 < MAF < 0.5	201	7.09	4.81	0.045	0.252	0.025
DrnkWk	0 < MAF < 0.001	229	12.72	17.42	0.041	0.874	0.013
DrnkWk	0.001 < MAF < 0.01	74	0.81	0.71	0.042	0.051	0.01
DrnkWk	0.01 < MAF < 0.5	151	0.91	0.73	0.042	0.04	0.003
CigDay	0 < MAF < 0.001	203	16.2	19.86	0.042	0.817	0.025
CigDay	0.001 < MAF < 0.01	61	1.12	0.96	0.038	0.104	0.012
CigDay	0.01 < MAF < 0.5	137	1.27	0.99	0.04	0.1	0.002

Using estimated hyperparameters from MAMBA, we estimated the number of non-replicable SNPs and outlier statistics in each study as a way to quantify the extent of outlier statistics in real data.
^aThe total expected number of outlier statistics is calculated by \(\mathop {\sum}\nolimits_j {[ {\widehat {\Pr }\left( {R_j = 0} \right)\mathop {\sum}\nolimits_k {\widehat {\Pr }\left( {O_{jk} = 1} \right)} } ]} \).
^bThe total expected number of non-replicable SNPs is calculated by \(\mathop {\sum}\nolimits_j {\widehat {\Pr }\left( {R_j = 0} \right)} \).
^cThe average number of outliers per study is calculated by the total number of outliers divided by the number of studies that contributed to the meta-analysis.

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