The kernel score statistic is a global covariance component test over a set of genetic markers. It provides a flexible modeling framework and does not collapse marker information. We generalize the kernel score statistic to allow for familial dependencies and to adjust for random confounder effects. With this extension, we adjust our analysis of real and simulated baseline systolic blood pressure for polygenic familial background. We find that the kernel score test gains appreciably in power through the use of sequencing compared to tag-single-nucleotide polymorphisms for very rare single nucleotide polymorphisms with <1% minor allele frequency.