- A meta-analysis is an approach that combines results from different studies on the same topic. - The random-effects model in a meta-analysis enables the modeling of differences between studies by incorporating the between-study variance.. - The DSLD2 method is compared with 6 other meta-analysis methods based on effect sizes across 8 aspects under three hypothesis settings. - Keywords: Differentially expressed genes, Between-study variance, Random-effects model, Meta-analysis. - The statistical power could be raised through meta-analysis by combining information from individual studies that have small sample sizes [5, 6]. - Meta-analysis is an important method for providing reliable and consistent differentially expressed gene lists by integrating information on the same disease [8]. - As meta-analysis methods use available datasets, they are rel- atively inexpensive [9]. - Meta-analysis methods based on effect sizes, which con- tribute to the early diagnosis and treatment of diseases, can be broadly divided into two classes: the fixed-effects model (FEM) and the random-effects model (REM) [11].. - The fixed-effects model assumes that all studies in a meta-analysis have the same true effect size [12]. - The random-effects model assumes that different studies in a meta-analysis have the different true effect sizes [12].. - meta-analysis methods, including DerSimonian and Laird estimate (DSL) [15], restricted maximum likelihood esti- mate (RML) and Sidik and Jonkman estimate (SJ) [16], were later applied to microarray studies. - The random- effects methods in meta-analysis make possible the mod- eling of differences and the differences between studies often caused by the study design, sample sizes, sex/gender differences in participants and so on. - The random-effects method based on D 2 g and other meta-analysis models were applied to simulation datasets of gene expression levels. - Then, we compared the DSLD2 method with other meta-analysis methods, including the DSL method, the DSLR2 method, the fixed-effects model, the PM method, the RML method and the SJ method across the following metrics: the false discovery rates (FDRs), accuracy, precision, false positive rate (FPR), sensitivity, precision-recall curve and the receiver operating charac- teristic curve (ROC). - DSLD2 performed well among the meta-analysis methods based on effect sizes under the first hypothesis. - k), k is the number of stud- ies in a meta-analysis. - Meta-analysis methods based on effect sizes Fixed-effects model. - The main component of the random-effects meta-analysis model is the between-study variability. - Meta-analysis methods used in simulation datasets Two class simulation datasets were generated to observe the performance of DSLD2 method. - We compared the performances of DSLD2 method and other 6 meta- analysis methods based on effect-sizes in histograms, precision, accuracy, the false discovery rates (FDRs), false positive rate (FPR), Matthews correlation coeffi- cient (MCC), sensitivity, receiver operating characteristic curves (ROC) and precision-recall curves under three hypotheses using simulation datasets of gene expression levels. - A common method was used to produce simulation data for comparing the ability of detecting DE genes among 16 meta-analysis methods under the three hypothesis set- tings [30]. - analysis methods. - However, the FDR 1 value of the DSLD2 method was smaller than that of the other 5 meta-analysis methods.. - The FDR 2 value of the DSLD2 method was 0.0236, which was the smallest among 7 meta-analysis methods based on effect sizes.. - 0.05) among different groups detected by various meta-analysis meth- ods (see Fig. - Line graphs and tables were constructed to compare the precision among 7 meta-analysis methods (see Fig. - Under the first hypothesis, the DSLR2 method had the lowest preci- sion among the meta-analysis methods combining effect sizes. - Under the second and third hypothesis, the FEM method had the highest precision values among 7 meta- analysis methods combining effect sizes (see Additional file 3: Figures S1, S2 and Additional file 4: Tables S2, S3).. - Among the meta-analysis methods based on effect sizes, DSLD2 had the highest accuracy among 7 meta-analysis methods based on effect sizes under the first hypothesis (see Fig. - The accu- racy of FEM method is the lowest among 7 meta-analysis methods based on effect sizes under the first hypoth- esis (see Fig. - Under the second hypothesis, the accuracy of FEM method was highest among 7 meta-analysis methods (Additional file 3:. - Under the third hypothesis, the SJ method had the highest accuracy values among 7 meta-analysis methods when the num- bers of sample sizes per study were between 60 and 220 (Additional file 3: Figure S4 and Additional file 4:. - Under the second and the third hypothesis, the FEM method had the lowest FPR values among 7 meta- analysis methods (see Additional file 3: Figures S5, S6 and Additional file 4: Tables S8, S9).. - Under the first hypothesis, the DSLD2 method had the highest MCC among the 7 meta-analysis methods based on effect sizes (see Fig. - The FEM method had the lowest MCC values among the 7 meta-analysis methods under the first hypothesis (see Fig. - Under the first hypothesis, the SJ method had the lowest MCC values among the 6 random-effects meta-analysis methods (see. - 1 The histograms of DE genes detected by the 7 meta-analysis methods. - Under the second, the FEM method had the highest MCC values among the 7 meta-analysis methods (see Additional file 3: Figure S7 and Additional file 4: Table S11). - Under the third hypoth- esis, the SJ method had the highest MCC values among 7 meta-analysis methods based on effect sizes when the numbers of sample sizes per study were between 60 and 220 (see Additional file 3: Figure S8 and Additional file 4:. - among the 7 meta-analysis methods based on effect sizes (see Fig. - The FEM method had the lowest sensitivity values among the 7 meta-analysis methods under the first hypothesis (see Fig. - Under the sec- ond hypothesis, the 7 meta-analysis methods had close sensitivity curves (see Additional file 3: Figure S9 and Additional file 4: Table S14). - Under the third hypothesis, the random-effect meta-analysis methods had close sensi- tivity curves which are higher than the curve of the FEM method. - 2 Plot of the precision under the first hypothesis. - Under the first hypothesis, the DSLD2 method had the highest roc curve among all 7 meta-analysis methods (see Fig. - Under the first hypothesis, the precision-recall curve of DSLD2 method was the highest among seven meta-analysis meth- ods (see Fig. - Under the second hypothe- sis, the precision-recall curve of DSLD2 method was the highest among the curves of random-effects meta-analysis methods (see Additional file 3: Figure S13). - The random- effects meta-analysis methods had close precision-recall curves which are lower than the curve of FEM under the third hypothesis (see Additional file 3: Figure S14).. - The accuracy of the DSLD2 method is the highest among that of the 7 meta-analysis methods. - The MCC value of the DSLD2 method is the highest among that of the 7 meta-analysis methods. - The sensitivity value of DSLD2 is the highest among that of the 7 meta-analysis methods. - After within- study data preprocessing, filtering out genes with very low gene expression and excluding small variation genes, the meta-analysis of the DSLD2 method was conducted on 3257 target genes in 305 subjects (168 AD and 137 controls).. - The four meta-analysis methods found 299 over- lapping DE genes. - 7 ROC curves of various meta-analysis methods under the first hypothesis. - The ROC curve of DSLD2 is the highest among that of the 7 meta-analysis methods. - 8 Precision-recall plot of various meta-analysis methods under the first hypothesis. - The precision-recall curve of DSLD2 is the highest among that of 7 meta-analysis methods. - 9 Bias plot of 6 meta-analysis methods when τ 2 is set to 0.0 and SMD is chosen as the effect size measure. - 10 RMSE plot of 6 meta-analysis methods when τ 2 is set to 0.0 and SMD is chosen as the effect size measure. - This paper proposed a meta-analysis method (DSLD2) based on new between-study variance estimator D 2 g . - biases and RMSE of D 2 g were lowest among 6 meta analysis methods when τ 2 was set to 0 and SMD was chosen as the effect size measure (see Figs. - We applied 7 meta-analysis methods based on effect sizes to simulation datasets of gene expression levels and compared the performance between the DSLD2 method and the other meta-analysis models. - 11 Bias plot of 6 meta-analysis methods when τ 2 is set to 0.0 and MD is chosen as the effect size measure. - 12 RMSE plot of 6 meta-analysis methods when τ 2 is set to 0.0 and MD is chosen as the effect size measure. - the 7 meta-analysis methods based on effect sizes (see Table 1).. - The accuracy, MCC, sensitivity, ROC and precision- recall curve of the DSLD2 method were the highest among the 7 meta-analysis methods (see Figs. - method was lowest among random-effects meta-analysis methods (see Figs. - The FEM method had the highest values of the precision, accu- racy, FPR and MCC among 7 meta-analysis methods based on effect sizes (see Additional file 3: Figures S1, S3, S5 and S7).. - 13 Mean of I 2 plot of 6 meta-analysis methods when τ 2 is set to 0.0 and SMD is chosen as the effect size measure. - 14 Mean of I 2 plot of 6 meta-analysis methods when τ 2 is set to 0.0 and MD is chosen as the effect size measure. - Figure S15 Bias plot of 6 meta-analysis methods when τ 2 is set to 1.0 and SMD is chosen as the effect size measure. - Figure S16 RMSE plot of 6 meta-analysis methods when τ 2 is set to 1.0 and SMD is chosen as the effect size measure. - Figure S17 Bias plot of 6 meta-analysis methods when τ 2 is set to 1.0 and MD is chosen as the effect size measure. - Figure S18 RMSE plot of 6 meta-analysis methods when τ 2 is set to 1.0 and MD is chosen as the effect size measure. - Figure S19 Mean of I 2 plot of 6 meta-analysis methods when τ 2 is set to 1.0 and SMD is chosen as the effect size measure. - Figure S20 Mean of I 2 plot of 6 meta-analysis methods when τ 2 is set to 1.0 and MD is chosen as the effect size measure.. - Because the data in this meta-analysis are from published articles and the data are publicly available, it was not necessary to obtain ethics approval and consent to participate.. - Meta-analysis of RNA-seq expression data across species, tissues and studies,. - Meta-analysis of prevalence,. - The power of meta-analysis in genome-wide association studies. - Meta-analysis: a tool for clinical and experimental research in psychiatry. - Increasing the power of meta-analysis of genome-wide association studies to detect heterogeneous effects. - 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