Table 3.

Performance metrics of FedProt and selected meta‑analyses using simulated datasets

Dataset	Method	Mean difference	Maximal difference	FP	FN	Jaccard similarity coefficient
Balanced	FedProt	3.22 × 10−15 ± 3.52 × 10−16	1.85 × 10−13 ± 8.71 × 10−14	0.0 ± 0	0.0 ± 0	1.00 ± 0.00
	Fisher	0.12 ± 0.01	12.50 ± 4.14	2.3 ± 1.5	2.2 ± 1.4	0.95 ± 0.02
	Stouffer	0.14 ± 0.01	8.99 ± 3.39	2.3 ± 1.5	2.6 ± 1.4	0.94 ± 0.02
	REM	0.15 ± 0.01	18.90 ± 4.79	6.2 ± 2.7	7.4 ± 2.5	0.84 ± 0.04
	RankProd	0.78 ± 0.02	27.60 ± 4.00	11.1 ± 3.4	1.0 ± 0.9	0.87 ± 0.03
Mild imbalance	FedProt	6.00 × 10−15 ± 6.22 × 10−16	2.67 × 10−13 ± 7.30 × 10−14	0.0 ± 0	0.0 ± 0	1.00 ± 0.00
	Fisher	0.14 ± 0.01	13.70 ± 4.65	18.2 ± 3.9	17.1 ± 4.6	0.64 ± 0.04
	Stouffer	0.20 ± 0.01	8.70 ± 2.18	17.8 ± 3.9	17.6 ± 4.5	0.64 ± 0.04
	REM	0.19 ± 0.01	23.50 ± 4.06	8.1 ± 2.6	10.3 ± 3.8	0.79 ± 0.04
	RankProd	0.84 ± 0.02	32.10 ± 3.93	38.9 ± 6.7	16.0 ± 4.3	0.54 ± 0.04
Strong imbalance	FedProt	1.33 × 10−14 ± 1.69 × 10−15	6.63 × 10−13 ± 2.74 × 10−13	0.0 ± 0	0.0 ± 0	1.00 ± 0.00
	Fisher	0.15 ± 0.01	13.20 ± 4.67	40.0 ± 5.9	29.4 ± 4.7	0.45 ± 0.04
	Stouffer	0.41 ± 0.06	29.20 ± 8.11	33.4 ± 4.1	36.3 ± 5.6	0.41 ± 0.05
	REM	0.22 ± 0.01	26.20 ± 4.94	7.8 ± 2.8	15.3 ± 3.3	0.75 ± 0.04
	RankProd	0.91 ± 0.02	34.40 ± 5.62	147.0 ± 11.8	28.2 ± 4.8	0.25 ± 0.02

Mean and maximum absolute differences in negative log-transformed BH-adjusted P values, Jaccard similarity coefficients and error rates (FPs and FNs) for the results of FedProt and selected meta-analysis approaches compared with centralized DEqMS results. The values corresponding to the best performance between all methods are highlighted in bold font.

Mean and standard deviation are reported for n = 50 of simulation and the subsequent data analysis runs. Jaccard similarity coefficients and error rates were computed with |log₂FC| > 1 and adjusted P value <0.05 thresholds. Metrics use each method’s own |log₂FC| and BH-adjusted P values.