Biological research often involves testing a growing number of null hypotheses as new data are accumulated over time. We study the problem of online control of the familywise error rate, that is testing an a priori unbounded sequence of hypotheses ( p-values) one by one over time without knowing the future, such that with high probability there are no false discoveries in the entire sequence. This paper unifies algorithmic concepts developed for offline (single batch) familywise error rate control and online false discovery rate control to develop novel online familywise error rate control methods. Though many offline familywise error rate methods (e.g., Bonferroni, fallback procedures and Sidak’s method) can trivially be extended to the online setting, our main contribution is the design of new, powerful, adaptive online algorithms that control the familywise error rate when the p-values are independent or locally dependent in time. Our numerical experiments demonstrate substantial gains in power, that are also formally proved in an idealized Gaussian sequence model. A promising application to the International Mouse Phenotyping Consortium is described.

Motivation Gene-gene co-expression networks (GCN) are of biological interest for the useful information they provide for understanding gene-gene interactions. The advent of single cell RNA-sequencing allows us to examine more subtle gene co-expression occurring within a cell type. Many imputation and denoising methods have been developed to deal with the technical challenges observed in single cell data; meanwhile, several simulators have been developed for benchmarking and assessing these methods. Most of these simulators, however, either do not incorporate gene co-expression or generate co-expression in an inconvenient manner. Results Therefore, with the focus on gene co-expression, we propose a new simulator, ESCO, which adopts the idea of the copula to impose gene co-expression, while preserving the highlights of available simulators, which perform well for simulation of gene expression marginally. Using ESCO, we assess the performance of imputation methods on GCN recovery and find that imputation generally helps GCN recovery when the data are not too sparse, and the ensemble imputation method works best among leading methods. In contrast, imputation fails to help in the presence of an excessive fraction of zero counts, where simple data aggregating methods are a better choice. These findings are further verified with mouse and human brain cell data. Availability The ESCO implementation is available as R package ESCO. Users can either download the development version via github (https://github.com/JINJINT/ESCO) or the archived version via Zenodo (https://zenodo.org/record/4455890). Supplementary information Supplementary data are available at Bioinformatics online.

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