DNA pooling is a cost-effective strategy for genomewise association studies to identify disease genes. In the context of family-based association studies, Risch & Teng (1998) mainly considered families of identical structures to detect associations between genetic markers and disease, and suggested possible approaches to incorporating different family types without a thorough study of their properties. However, families collected in real genetic studies often have different structures and, more importantly, the informativeness of each family structure depends on the disease model which is generally unknown. So there is a need to develop and investigate statistical methods to combine information from diverse family types. In this article, we propose a general strategy to incorporate different family types by assigning each family an "optimal" weight in association tests. In addition, we consider measurement errors in our analysis. When we evaluate our approach under different disease models and measurement errors, we find that our weighting scheme may lead to a substantial reduction in sample size required over the approach suggested by Risch & Teng (1998), and measurement errors may have significant impact on the required sample size when the error rates are not negligible.