血球細胞是由不同類型的細胞組成的混和物，每個細胞類型都有各自的基
因表現輪廓，而且不同的細胞類型有一定的關聯性。因此，利用基因表現量將
混和細胞分解成個別細胞類型並得到各自組成比例是一個困難的問題。
過往相關模型都是先對建個別細胞類型的基因表現量建立模型，再據此
拆解全血中混和細胞的組成比例。我們提出一個線性混和模型(Linear Mixed
Model for Deconvolution, LMMD) 分解細胞組成比例，將個別細胞類型和混和
細胞同時建模，共享相同的參數並共同估計混和細胞中各類型基因表現量，同
時可獲得未知的細胞組成比例，我們也特別為LMMD 建立了一套顯著基因的選
取標準。我們將LMMD 的分析流程與其他四個模型進行比較，在處理個別細胞
類型資料和混和細胞資料來自不同實驗的時候，LMMD 具備了更好的表現。

Gene expression of blood cells is a mixture of different cell types. Each cell
type has its own specific profile, and different cell types might be correlated at
the same time. Hence, decomposing the mixed expression profiles into cell typespecific
expression profiles and their respective cellular proportions is a difficult problem.
Previous studies usually build models on reference data that provide cellspecific profiles. We propose a Linear Mixed Model for Deconvolution (LMMD) to estimate the cell-specific expression level by modeling the reference profile and the mixture together in the same construction. We can also obtain the unknown cellular proportions at the same time. We establish the signature gene selection criteria for our LMMD model and compare it with four other models. LMMD has better performance when the reference data and mixture data are from different experiments.

1 Introduction 1
2 Methods 4
2.1 The algorithm of other deconvolution models compared in this study 4
2.1.1 Linear least squares regression (LLSR) . . . . . . . . . . . . 5
2.1.2 Non-negative least squares model (NNLS) . . . . . . . . . . 5
2.1.3 Digital Sorting Algorithm (DSA) . . . . . . . . . . . . . . . 6
2.1.4 CIBERSORT . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Linear Mixed Deconvolution Model . . . . . . . . . . . . . . . . . . 12
2.2.1 Main model . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 Evaluation Criterion . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Signature gene selection strategy . . . . . . . . . . . . . . . . . . . 17
3 Result 18
3.1 Evaluation through simulation . . . . . . . . . . . . . . . . . . . . . 18
3.2 Real data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Data description . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.2 Effect of log transformation . . . . . . . . . . . . . . . . . . 34
3.2.3 Comparison of models with three benchmark data sets . . . 36
3.2.4 Effect of gene selection . . . . . . . . . . . . . . . . . . . . . 40
3.2.5 When the cell-specific profiles are from different experiments 44
4 Conclusion and Discussion 50
References 52

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