We propose a new family-based association test, FBAT-PC, for repeatedly measured quantitative traits. It is designed for situations where there may be partially or completely unknown confounding factors or covariates which cannot be adequately modelled. Using generalized principal component analysis, FBAT-PC amplifies the genetic effects of each measurement by constructing a new overall phenotype with maximal heritability. Analytically and in simulation studies, we compare FBAT-PC with standard methodology and assess its power. Applications of FBAT-PC to an osteopetrosis study show the practical relevance of FBAT-PC.