Sample size determination for high dimensional parameter estimation with application to biomarker identification

We consider sample size calculation to obtain sufficient estimation precision and control the length of confidence intervals under high dimensional assumptions. In particular, we intend to provide more general results for sample size determination when a large number of parameter values need to be computed for a fixed sample. We consider three design approaches: normal approximation, inequality method and regression method. These approaches are applied to sample size calculation in estimating the Net Reclassification Improvement (NRI) and the Integrated Discrimination Improvement (IDI) for a diagnostic or screening study. Two medical examples are also provided as illustration. Our results suggest the regression method in general can yield a much smaller sample size than other methods.