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There is a growing interest in cell-type-specific analysis from bulk sampleswith a mixture of different cell types. A critical first step in such analysesis the accurate estimation of cell-type proportions in a bulk sample. Althoughmany methods have been proposed recently, quantifying the uncertaintiesassociated with the estimated cell-type proportions has not been well studied.Lack of consideration of these uncertainties can lead to missed or falsefindings in downstream analyses. In this article, we introduce a flexiblestatistical deconvolution framework that allows a general and subject-specificcovariance of bulk gene expressions. Under this framework, we propose adecorrelated constrained least squares method called DECALS that estimatescell-type proportions as well as the sampling distribution of the estimates.Simulation studies demonstrate that DECALS can accurately quantify theuncertainties in the estimated proportions whereas other methods fail. ApplyingDECALS to analyze bulk gene expression data of post mortem brain samples fromthe ROSMAP and GTEx projects, we show that taking into account theuncertainties in the estimated cell-type proportions can lead to more accurateidentifications of cell-type-specific differentially expressed genes andtranscripts between different subject groups, such as between Alzheimer'sdisease patients and controls and between males and females.

Statistical Inference of Cell-type Proportions Estimated from Bulk Expression Data