Preprints 

# represents corresponding/senior author, * represents mentee  (student  or postdoc) under Dr. Liu's supervision


 "All valid instruments are alike; each invalid instrument is invalid in its own way"






Published

# represents corresponding author, * represents mentee  (student  or postdoc) under Dr. Liu's supervision


Statistical Methodology 

Robust Mendelian Randomization for Causal Inference with Invalid Instruments 


Causal Mediation Analysis with Applications


Statistical Genetics and Genomics


(one of top 10 most-cited papers among work published betweeen 1 Janurary 2022 - 31 December 2023 in Genetic Epidemiology.)

Machine (Deep) Learning and others 



Health Science Research


 aortic valve stenosis: a prospective cohort study of 0.5 million participants. Nutrients, 14(11), 2273; https://doi.org/10.3390/nu14112273