We propose a family-based association test, FBAT-PC, for studies with quantitative traits that are measured repeatedly. The traits may be influenced by partially or completely unknown factors that may vary for each measurement. Using generalized principal component analysis, FBAT-PC amplifies the genetic effects of each measurement by constructing an overall phenotype with maximal heritability. Analytically, and in the simulation studies, we compare FBAT-PC with standard methodology and assess both the heritability of the overall phenotype and the power of FBAT-PC. Compared to univariate analysis, FBAT-PC achieves power gains of up to 200%. Applications of FBAT-PC to an osteoporosis study and to an asthma study show the practical relevance of FBAT-PC. FBAT-PC has been implemented in the software package PBAT and is freely available at http://www.biostat.harvard.edu/~clange/default.htm.