For the region/set-based association analysis of rare variants in family-based studies, we propose a general methodological framework that integrates higher criticism approaches, SKATs, burden, and multivariate tests into the FBAT approach. Using the haplotype algorithm for FBATs to compute the conditional genotype distribution under the null hypothesis of Mendelian transmissions, virtually any association test statistics can be implemented straightforwardly in our approach, requiring no assumptions about the asymptotic distribution or approximations. Given the conditional joint distribution of the rare variants, simulation-based or exact p-values can be computed without the need to estimate the genetic correlation/linkage disequilibrium (LD) structure between variants empirically. Using simulations, we compare the features of the proposed test statistics in our framework with the existing region-based methodology for family-based studies under various scenarios. Under realistic assumptions, the tests of our framework outperform the existing methodology. We provide general guidelines for which scenarios, e.g., the sparseness of the signals or local LD structure, which test statistic will provide distinct power advantages over the others. We illustrate our approach in an application to a whole-genome sequencing dataset with 900 asthmatic trios.