<p>Genome-wide association studies (GWAS) of disease progression are vulnerable to collider bias caused by selection of participants with disease at study entry. This bias introduces spurious associations between disease progression and genetic variants that are truly only associated with disease incidence. Methods of statistical adjustment to reduce this bias have been published, but rely on assumptions regarding the genetic correlation of disease incidence and disease progression which are likely to be violated in many human diseases. MR-Horse is a recently published Bayesian method to estimate the parameters of a general model of genetic pleiotropy in the setting of Mendelian Randomisation. We adapted this method to provide bias-reduced GWAS estimates of associations with disease progression, robust to the genetic correlation of disease incidence and disease progression and robust to the presence of pleiotropic variants with effects on both incidence and progression. We applied this adapted method to simulated GWAS of disease incidence and progression with pleiotropic variants and varying degrees of genetic correlation. When significant genetic correlation was present, the MR-Horse method produced less biased estimates than unadjusted analyses or analyses adjusted using other existing methods. Type 1 error rates with the MR-Horse method were consistently below the nominal 5% level, at the expense of a modest reduction in power. We then applied this method to summary statistics from the CKDGen consortium GWAS of kidney function decline. MR-Horse attenuated the effects of variants with known likely biased effects in the CKDGen GWAS, whilst preserving effects at loci with likely true effects.</p>