Family data represent a rich resource for detecting association between rare variants (RVs) and human traits. However, most RV association analysis methods developed in recent years are data-driven burden tests which can adaptively learn weights from data but require permutation to evaluate significance, thus are not readily applicable to family data, because random permutation will destroy family structure. Direct application of these methods to family data may result in a significant inflation of false positives. To overcome this issue, we have developed a generalized, weighted sum mixed model (WSMM), and corresponding computational techniques that can incorporate family information into data-driven burden tests, and allow adaptive and efficient permutation test in family data. Using simulated and real datasets, we demonstrate that the WSMM method can be used to appropriately adjust for genetic relatedness among family members and has a good control for the inflation of false positives. We compare WSMM with a nondata-driven, family-based Sequence Kernel Association Test (famSKAT), showing that WSMM has significantly higher power in some cases. WSMM provides a generalized, flexible framework for adapting different data-driven burden tests to analyze data with any family structures, and it can be extended to binary and time-to-onset traits, with or without covariates.