Stain imputation in multiplex immunofluorescence (mIF) imaging addresses the challenge of missing or damaged biomarker channels by reconstructing target biomarker images from a limited set of available stains. This approach offers a faster and more efficient alternative to full-panel staining, enabling detailed analysis of the tumour microenvironment. Existing One-Step Inference Models (OSIMs), primarily based on generative adversarial networks (GAN) or autoencoders, often generate suboptimal images with significant artifacts or reduced signal intensity. These limitations impair visual interpretability and reliability of the downstream immunotherapy response assessment. The challenge is further amplified when imputing cytoplasmic biomarkers such as CD8 from commonly used stains such as DAPI, due to the limited spatial correlation and the inherently complex structure of cytoplasmic signals. To address these limitations, we propose a self-refining diffusion model, OS2CR-Diff, which utilises the results from OSIMs as additional conditional representations. Unlike prior studies that rely on a single or limited conditional inputs, OS2CR-Diff incorporates three conditional inputs: the OSIM-imputed target biomarker image, OSIM-imputed complementary biomarker images, and non-antibody-stained images. Furthermore, we propose a feature fusion module that employs a cross-gated attention mechanism to effectively integrate these inputs, enabling context-aware feature refinement and improving the quality and reliability of imputed biomarker images. We evaluated OS2CR-Diff for CD8 biomarker imputation on mIF images of melanoma tissues. Our method outperformed state-of-the-art methods, achieving a$\mathbf{7 3. 4 \%}$increase in the Structural Similarity Index Measure (SSIM), a 28.9 % gain in the Peak Signal-to-Noise Ratio (PSNR), a$\mathbf{6 1. 2 \%}$improvement in Mean Absolute Error (MAE), and significantly lower false positive rates compared to OSIM.

MOTIVATION: Gene annotation and pathway databases such as Gene Ontology and Kyoto Encyclopaedia of Genes and Genomes are important tools in Gene-Set Test (GST) that describe gene biological functions and associated pathways. GST aims to establish an association relationship between a gene-set of interest and an annotation. Importantly, GST tests for over-representation of genes in an annotation term. One implicit assumption of GST is that the gene expression platform captures the complete or a very large proportion of the genome. However, this assumption is neither satisfied for the increasingly popular boutique array nor the custom designed gene expression profiling platform. Specifically, conventional GST is no longer appropriate due to the gene-set selection bias induced during the construction of these platforms. RESULTS: We propose bcGST, a bias-corrected GST by introducing bias-correction terms in the contingency table needed for calculating the Fisher's Exact Test. The adjustment method works by estimating the proportion of genes captured on the array with respect to the genome in order to assist filtration of annotation terms that would otherwise be falsely included or excluded. We illustrate the practicality of bcGST and its stability through multiple differential gene expression analyses in melanoma and the Cancer Genome Atlas cancer studies. AVAILABILITY AND IMPLEMENTATION: The bcGST method is made available as a Shiny web application at http://shiny.maths.usyd.edu.au/bcGST/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.