Here we present an exome-wide rare genetic variant association study for 30 biomarkers in 191,640 individuals in the UK Biobank. We perform gene-based association tests for separate functional variant categories to increase interpretability and identify 201 significant gene-biomarker associations, which include novel associations such as GIGYF1 with diabetes markers. In addition to performing gene-based variant collapsing tests, we design and apply variant-category-specific kernel-based tests that integrate quantitative functional variant effect predictions for missense variants, splicing and the binding of RNA-binding proteins. For these tests we present a powerful and computationally efficient combination of the likelihood-ratio and score tests that found 32% more associations than the score test alone. Kernel-based tests identified 12-31% more associations than their gene-based collapsing counterparts with large overlaps, and had advantages in the presence of gain of function missense variants. We introduce local collapsing by amino acid position for missense variants and use this approach to identify potential novel gain of function variants in PIEZO1, and interpret a position-specific association of ABCA1-variants with inflammation marker CRP. Our results show the benefits of separately investigating different functional mechanisms when performing rare-variant association tests, and highlight the strengths of biomarker panels for large biobanks.