Fig. 2
Precision of two-step random-effects models (DSLR2) with and without the proper weighted function: \( {w}_{P6}={\left({\sigma}_{ig}^{2\left({w}_{P1}\right)}+{\widehat{\tau}}_g^2\right)}^{-1} \)), \( {w}_{P1}\in \left\{{2}^{-{S}_{ij}},0.01{\tilde{P}}_{ij}\right\} \), \( {\tilde{P}}_{ij} \) denoted percent of present calls, Sij denoted standardized quality indicators of the jth sample in the ith study. 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. DE: differentially expressed