UK Biobank (UKB) is a key contributor in mental health genome-wide association studies (GWAS) but only ~31% of participants completed the Mental Health Questionnaire (MHQ responders). We predicted generalized anxiety disorder (GAD), posttraumatic stress disorder (PTSD), and major depression symptoms using elastic net regression in the ~69% of UKB participants lacking MHQ data (MHQ non-responders; NTraining = 50%; NTest = 50%), maximizing the informative sample for these traits. MHQ responders were more likely to be female, from higher socioeconomic positions, and less anxious than non-responders. Genetic correlation of GAD and PTSD between MHQ responders and non-responders ranged from 0.636 to 1.08; both were predicted by polygenic scores generated from independent cohorts. In meta-analyses of GAD (N = 489,579) and PTSD (N = 497,803), we discovered many novel genomic risk loci (13 for GAD and 40 for PTSD). Transcriptomic analyses converged on altered regulation of prenatal dorsolateral prefrontal cortex in these disorders. Our results provide one roadmap by which sample size and statistical power may be improved for gene discovery of incompletely ascertained traits in the UKB and other biobanks with limited mental health assessment.