Classical and Bayesian random-effects meta-analysis models with sample quality weights in gene expression studies

BMC Bioinformatics

Table 4 Performance of weighted random-effects models applied in simulated data

Model	No. DE Genes				MSSE				Precision				Accuracy				AUC
Model	H0	H1	H2	H3	H0	H1	H2	H3	H0	H1	H2	H3	H0	H1	H2	H3	H0	H1	H2	H3
DSLw_P6	62	62	64	65	2.9	3.0	3.0	3.0	0.95	0.96	0.96	0.96	0.97	0.97	0.97	0.97	0.75	0.75	0.75	0.76
DSLR2w_P6	66	72	78	85	1.6	1.6	1.6	1.6	0.96	0.95	0.94	0.92	0.97	0.97	0.97	0.98	0.76	0.78	0.80	0.82
BRE with a uniform(0,1) prior
Model 1: Unweighted data, Gibbs	81	109	140	204	1.7	2.1	2.4	2.6	1.00	0.94	0.81	0.58	0.98	0.99	0.98	0.96	0.84	0.92	0.96	0.97
Model 2: Unweighted data, Gibbs, \( \beta {\overline{w}}_{P6} \)	81	66	51	39	6.0	6.2	6.5	6.9	1.00	1.00	0.97	0.93	0.98	0.97	0.96	0.96	0.84	0.77	0.71	0.65
Model 3: Unweighted data, Gibbs, \( {\tau}^2{\overline{w}}_{P6} \)	161	157	151	142	0.8	1.5	2.1	2.7	0.74	0.76	0.77	0.79	0.98	0.98	0.98	0.98	0.99	0.99	0.97	0.96
Model 4: Weighted data, Gibbs	81	87	92	100	1.8	2.2	2.7	3.1	1.00	0.99	0.97	0.93	0.98	0.98	0.98	0.98	0.84	0.86	0.87	0.89
Model 5: Weighted data, Gibbs, \( \beta {\overline{w}}_{P6} \)	81	65	51	39	6.3	6.5	6. 9	7.3	1.00	1.00	0.97	0.93	0.98	0.97	0.96	0.96	0.84	0.77	0.70	0.65
Model 6: Weighted data, Gibbs, \( {\tau}^2{\overline{w}}_{P6} \)	162	157	151	142	1.6	2.6	3.6	4.5	0.74	0.76	0.77	0.79	0.98	0.98	0.98	0.98	0.99	0.99	0.97	0.96
Model 7: Weighted data, MH	81	87	93	102	2.2	2.7	3.1	3.5	1.00	0.98	0.97	0.92	0.98	0.98	0.98	0.98	0.84	0.86	0.87	0.89

\( {\overline{w}}_{P6} \) is an average of w_P6, \( {w}_{P6}={\left({\sigma}_{ig}^{2\left({w}_{P1}\right)}+{\widehat{\tau}}_g^2\right)}^{-1} \)over the total samples; \( {w}_{P1}\in \left\{{2}^{-{S}_{ij}},0.01{\tilde{P}}_{ij}\right\} \), \( {\tilde{P}}_{ij} \) denoted percent of present calls, S_ij denoted standardized quality indicators of the jth sample in the ith study. DE: differentially expressed, MSSE: minimum sum of squared error, AUC: area-under ROC curve, DSL: DerSimonian-Laird model, DSLR2: two-step estimate of DerSimonian-Laird model, BRE: Bayesian random-effects model, U: uniform, G: gamma, MH: Metropolis–Hastings algorithm. H0, H1, H2, and H3 are the number of {0, 1, 2, and 3} studies containing heterogeneous genes. H0 represents homogenous data. The number of truly DE genes in the simulated data was 120 genes under HSC hypothesis testing.

ISSN: 1471-2105