What is the state of the art for GWAS in terms of the statistical algorithm for either Case/control and Quantitative traits?
I've got the answer to my question at https://www.biostars.org/p/410466/ by chrchang522

&quot;The main regression executed by Plink was introduced by EIGENSTRAT in ~2006; see https://www.nature.com/articles/ng1847 . This is actually straightforward to write in R/Python from scratch; the harder part is optimizing the implementation for large datasets.
The Firth regression added to Plink 2.0 to improve handling of rare variants and imbalanced binary phenotypes was motivated by https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4049324/ .
Mixed linear models provide better statistical power when you have lots of close relatives in your dataset, but are much trickier to solve; actually, this is still a significant research area. Two tools covering parts of the current state-of-the-art are SAIGE (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6119127/ ; handles imbalanced binary phenotypes, but relatively slow) and fastGWA (https://www.nature.com/articles/s41588-019-0530-8 ; great speed, but doesn't support dosage data yet and uses a misspecified model for binary phenotypes).&quot;