Proportional hazards models have been proposed to analyse time-to-event phenotypes in genome-wide association studies (GWAS). However, little is known about the ability of proportional hazards models to identify genetic associations under different generative models and when ascertainment is present. Here we propose the age-dependent liability threshold (ADuLT) model as an alternative to a Cox regression based GWAS, here represented by SPACox. We compare ADuLT, SPACox, and standard case-control GWAS in simulations under two generative models and with varying degrees of ascertainment as well as in the iPSYCH cohort. We find Cox regression GWAS to be underpowered when cases are strongly ascertained (cases are oversampled by a factor 5), regardless of the generative model used. ADuLT is robust to ascertainment in all simulated scenarios. Then, we analyse four psychiatric disorders in iPSYCH, ADHD, Autism, Depression, and Schizophrenia, with a strong case-ascertainment. Across these psychiatric disorders, ADuLT identifies 20 independent genome-wide significant associations, case-control GWAS finds 17, and SPACox finds 8, which is consistent with simulation results. As more genetic data are being linked to electronic health records, robust GWAS methods that can make use of age-of-onset information will help increase power in analyses for common health outcomes.