Optimal allocation of replicates for measurement evaluation studies

Optimal experimental design is important for the efficient use of modern high-throughput technologies such as microarrays and proteomics. Multiple factors including the reliability of measurement system, which itself must be estimated from prior experimental work, could influence design decisions. In this study, we describe how the optimal number of replicate measures (technical replicates) for each biological sample (biological replicate) can be determined. Different allocations of biological and technical replicates were evaluated by minimizing the variance of the ratio of technical variance (measurement error) to the total variance (sum of sampling error and measurement error). We demonstrate that if the number of biological replicates and the number of technical replicates per biological sample are variable, while the total number of available measures is fixed, then the optimal allocation of replicates for measurement evaluation experiments requires two technical replicates for each biological replicate. Therefore, it is recommended to use two technical replicates for each biological replicate if the goal is to evaluate the reproducibility of measurements.