Because of the limitation of single-nucleotide polymorphism (SNP) array-based genotyping technology in detecting rare genetic variants, genome-wide association scans usually focus only on common variants analysis. Advances in DNA sequencing technologies in recent years, however, have allowed the identification and genotyping of rare variants with substantially higher accuracy and rapidly decreasing cost, which makes it practicable to detect rare variants in relatively large populations and thus enables association scans of these variants for human complex diseases. Facilitated by these technologies, investigators have recognized rare variants as one important factor that contributes to human complex-disease-related traits and interest in them is increasing [1–8].
Statistically, because of the extremely low frequency of rare variants in populations, the power of detecting disease-associated individual rare variants usually is poor. To increase the power, investigators have proposed a useful strategy in which multiple rare variants are collapsed into one variant; then, the collective effect of multiple rare variants is tested rather than individual rare variants. Different collapsing methods have been developed [9–14]. Besides the statistical methods, family data provide another additional resource that may add more power in the association analysis of rare variants, because functional rare variants for a specific trait could be more enriched in some families than in populations. However, when family data are used for association analysis, both population structure and familial relatedness between individuals need to be addressed and adjusted to obtain unbiased statistical results. Although linkage-based and transmission-based methods are commonly used for the analysis of family data with no need for adjusting for population structure and familial relatedness, they are not applicable to collapsing tests of the collective effect of multiple rare variants. Therefore most of the previous studies of collective tests of rare variants were focused on binary traits from case and control data, and methods for detecting rare variants collectively associated with quantitative traits using family data have not been well established.
To exploit advantages from both collective tests and family data, we propose to combine a collapsing strategy with the framework of the unified mixed model (UMM)  for the association analysis of rare variants and quantitative traits. The UMM methods were developed primarily for common variant analysis in genome-wide association scans; most of them, however, have not been investigated and validated in the context of rare variants. Here, we borrow the idea from the UMM and present a comparison of several possible methods under the framework of the UMM, with an emphasis on statistical properties of collective association tests of multiple rare variants and quantitative traits using family data.