We introduce a multiple testing method that controls the median of the proportion of false discoveries (FDP) in a flexible way. Our method only requires a vector of p-values as input and is comparable to the Benjamini-Hochberg method, which controls the mean of the FDP. Benjamini-Hochberg requires choosing the target FDP alpha before looking at the data, but our method does not. For example, if using alpha=0.05 leads to no discoveries, alpha can be increased to 0.1. We further provide mFDP-adjusted p-values, which consequently also have a post hoc interpretation. The method does not assume independence and was valid in all considered simulation scenarios. The procedure is inspired by the popular estimator of the total number of true hypotheses by Schweder, Spj{\o}tvoll and Storey. We adapt this estimator to provide a median unbiased estimator of the FDP, first assuming that a fixed rejection threshold is used. Taking this as a starting point, we proceed to construct simultaneously median unbiased estimators of the FDP. This simultaneity allows for the claimed flexibility. Our method is powerful and its time complexity is linear in the number of hypotheses, after sorting the p-values.
翻译:我们引入了多种测试方法, 以灵活的方式控制虚假发现比例的中位值。 我们的方法只要求将 p值矢量作为输入值, 并且与控制 FDP 平均值的Benjami-Hochberg 方法相似。 Benjami-Hochberg 要求在查看数据之前选择目标 FDP alpha, 但我们的方法并非如此。 例如, 如果使用 alpha=0.05 导致没有发现, 则alpha 可以增加到 0.1 。 我们进一步提供 mFDP 调整的 p- 值, 从而也有一个后临时解释 。 该方法不具有独立性, 在所有考虑的模拟情景中都有效。 程序受Schweder、 Spj_Ho}tvoll 和 Storey 的全部真实假设的流行估测师的启发。 我们调整了这个估测器, 以提供FDP 的中位不偏向性估测器, 首先假设使用了固定的拒绝阈值。 我们以此作为起点, 我们着手同时构建 FDP 的中位公正估测器, 。 这个模拟模型的精度在要求的精度中, 。 的精度的精度是精度 。