Sequential analysis for microarray data based on sensitivity and meta-analysis

Transcriptomic studies using microarray technology have become a standard tool in life sciences in the last decade. Nevertheless the cost of these experiments remains high and forces scientists to work with small sample sizes at the expense of statistical power. In many cases, little or no prior knowledge on the underlying variability is available, which would allow an accurate estimation of the number of samples (microarrays) required to answer a particular biological question of interest. We investigate sequential methods, also called group sequential or adaptive designs in the context of clinical trials, for microarray analysis. Through interim analyses at different stages of the experiment and application of a stopping rule a decision can be made as to whether more samples should be studied or whether the experiment has yielded enough information already.

The high dimensionality of microarray data facilitates the sequential approach. Since thousands of genes simultaneously contribute to the stopping decision, the marginal distribution of any single gene is nearly independent of the global stopping rule. For this reason, the interim analysis does not seriously bias the final p-values. We propose a meta-analysis approach to combining the results of the interim analyses at different stages. We consider stopping rules that are either based on the estimated number of true positives or on a sensitivity estimate and particularly discuss the difficulty of estimating the latter. We study this sequential method in an extensive simulation study and also apply it to several real data sets. The results show that applying sequential methods can reduce the number of microarrays without substantial loss of power. An R-package SequentialMA implementing the approach is available from the authors.