Alpha_investing {onlineFDR} | R Documentation |
Implements a variant of the Alpha-investing algorithm of Foster and Stine (2008) that guarantees FDR control, as proposed by Ramdas et al. (2018). This procedure uses SAFFRON's update rule with the constant λ replaced by a sequence λ_i = α_i. This is also equivalent to using the ADDIS algorithm with τ = 1 and λ_i = α_i.
Alpha_investing(d, alpha = 0.05, gammai, w0, random = TRUE, date.format = "%Y-%m-%d")
d |
Either a vector of p-values, or a dataframe with three columns: an identifier (‘id’), date (‘date’) and p-value (‘pval’). If no column of dates is provided, then the p-values are treated as being ordered sequentially with no batches. |
alpha |
Overall significance level of the FDR procedure, the default is 0.05. |
gammai |
Optional vector of γ_i. A default is provided with γ_j proportional to 1/j^(1.6). |
w0 |
Initial ‘wealth’ of the procedure, defaults to α/2. Must be between 0 and α. |
random |
Logical. If |
date.format |
Optional string giving the format that is used for dates. |
The function takes as its input either a vector of p-values or a dataframe with three columns: an identifier (‘id’), date (‘date’) and p-value (‘pval’). The case where p-values arrive in batches corresponds to multiple instances of the same date. If no column of dates is provided, then the p-values are treated as being ordered sequentially with no batches.
The Alpha-investing procedure provably controls FDR for independent p-values. Given an overall significance level α, we choose a sequence of non-negative non-increasing numbers γ_i that sum to 1. Alpha-investing depends on a constant w_0, which satisfies 0 ≤ w_0 ≤ α and represents the intial ‘wealth’ of the procedure.
Further details of the Alpha-investing procedure and its modification can be found in Foster and Stine (2008) and Ramdas et al. (2018).
d.out |
A dataframe with the original data |
Foster, D. and Stine R. (2008). α-investing: a procedure for sequential control of expected false discoveries. Journal of the Royal Statistical Society (Series B), 29(4):429-444.
Ramdas, A., Zrnic, T., Wainwright M.J. and Jordan, M.I. (2018). SAFFRON: an adaptive algorithm for online control of the false discovery rate. Proceedings of the 35th International Conference in Machine Learning, 80:4286-4294.
SAFFRON
uses the update rule of Alpha-investing but with
constant λ.
sample.df <- data.frame( id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902', 'C38292', 'A30619', 'D46627', 'E29198', 'A41418', 'D51456', 'C88669', 'E03673', 'A63155', 'B66033'), date = as.Date(c(rep("2014-12-01",3), rep("2015-09-21",5), rep("2016-05-19",2), "2016-11-12", rep("2017-03-27",4))), pval = c(2.90e-08, 0.06743, 0.01514, 0.08174, 0.00171, 3.60e-05, 0.79149, 0.27201, 0.28295, 7.59e-08, 0.69274, 0.30443, 0.00136, 0.72342, 0.54757)) Alpha_investing(sample.df, random=FALSE) set.seed(1); Alpha_investing(sample.df) set.seed(1); Alpha_investing(sample.df, alpha=0.1, w0=0.025)