• Alpha Spending Function;
  • Family-based studies;
  • Genetic Model;
  • Group Sequential Test;
  • MAX;
  • Robust procedures


In family-based association studies, an optimal test statistic with asymptotic normal distribution is available when the underlying genetic model is known (e.g., recessive, additive, multiplicative, or dominant). In practice, however, genetic models for many complex diseases are usually unknown. Using a single test statistic optimal for one genetic model may lose substantial power when the model is mis-specified. When a family of genetic models is scientifically plausible, the maximum of several tests, each optimal for a specific genetic model, is robust against the model mis-specification. This robust test is preferred over a single optimal test. Recently, cost-effective group sequential approaches have been introduced to genetic studies. The group sequential approach allows interim analyses and has been applied to many test statistics, but not to the maximum statistic. When the group sequential method is applied, type I error should be controlled. We propose and compare several approaches of controlling type I error rates when group sequential analysis is conducted with the maximum test for family-based candidate-gene association studies. For a two-stage group sequential robust procedure with a single interim analysis, two critical values for the maximum tests are provided based on a given alpha spending function to control the desired overall type I error.