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Background  Random-effects (RE) models are commonly applied to account for heterogeneity in effect sizes in gene expression meta-analysis. The degree of heterogeneity may differ due to inconsistencies in sample quality. High heterogeneity can arise in meta-analyses containing poor quality samples. We applied sample-quality weights to adjust the study heterogeneity in the DerSimonian and Laird (DSL) and two-step DSL (DSLR2) RE models and the Bayesian random-effects (BRE) models with unweighted and weighted data, Gibbs and Metropolis-Hasting (MH) sampling algorithms, weighted common effect, and weighted between-study variance. We evaluated the performance of the models through simulations and illustrated application of the methods using Alzheimer’s gene expression datasets.    Results  Sample quality adjusting within study variance ( w   P 6 ) models provided an appropriate reduction of differentially expressed (DE) genes compared to other weighted functions in classical RE models. The BRE model with a uniform(0,1) prior was appropriate for detecting DE genes as compared to the models with other prior distributions. The precision of DE gene detection in the heterogeneous data was increased with the DSLR2 w   P 6  weighted model compared to the DSL w   P 6  weighted model. Among the BRE weighted models, the  w   P 6 weighted- and unweighted-data models and both Gibbs- and MH-based models performed similarly. The  w   P 6  weighted common-effect model performed similarly to the unweighted model in the homogeneous data, but performed worse in the heterogeneous data. The  w   P 6 weighted data were appropriate for detecting DE genes with high precision, while the  w   P 6 weighted between-study variance models were appropriate for detecting DE genes with high overall accuracy. Without the weight, when the number of genes in microarray increased, the DSLR2 performed stably, while the overall accuracy of the BRE model was reduced. When applying the weighted models in the Alzheimer’s gene expression data, the number of DE genes decreased in all metadata sets with the DSLR2 w   P 6 weighted and the  w   P 6 weighted between study variance models. Four hundred and forty-six DE genes identified by the  w   P 6 weighted between study variance model could be potentially down-regulated genes that may contribute to good classification of Alzheimer’s samples.    Conclusions  The application of sample quality weights can increase precision and accuracy of the classical RE and BRE models; however, the performance of the models varied depending on data features, levels of sample quality, and adjustment of parameter estimates.    Electronic supplementary material  The online version of this article (10.1186/s12859-018-2491-9) contains supplementary material, which is available to authorized users.

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