SAFFRON: SAFFRON: Adaptive online FDR control

In dsrobertson/onlineFDR: Online error rate control

SAFFRON: Adaptive online FDR control

Description

Implements the SAFFRON procedure for online FDR control, where SAFFRON stands for Serial estimate of the Alpha Fraction that is Futilely Rationed On true Null hypotheses, as presented by Ramdas et al. (2018). The algorithm is based on an estimate of the proportion of true null hypotheses. More precisely, SAFFRON sets the adjusted test levels based on an estimate of the amount of alpha-wealth that is allocated to testing the true null hypotheses.

Usage

SAFFRON(
  d,
  alpha = 0.05,
  gammai,
  w0,
  lambda = 0.5,
  random = TRUE,
  display_progress = FALSE,
  date.format = "%Y-%m-%d"
)

Arguments

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 in sequence, arriving one at a time.
alpha	Overall significance level of the FDR procedure, the default is 0.05.
gammai	Optional vector of \gamma_i. A default is provided with \gamma_j proportional to 1/j^(1.6).
w0	Initial ‘wealth’ of the procedure, defaults to \alpha/2. Must be between 0 and \alpha.
lambda	Optional threshold for a ‘candidate’ hypothesis, must be between 0 and 1. Defaults to 0.5.
random	Logical. If TRUE (the default), then the order of the p-values in each batch (i.e. those that have exactly the same date) is randomised.
display_progress	Logical. If TRUE prints out a progress bar for the algorithm runtime.
date.format	Optional string giving the format that is used for dates.

Details

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 in sequence, arriving one at a time.

SAFFRON procedure provably controls FDR for independent p-values. Given an overall significance level \alpha, we choose a sequence of non-negative non-increasing numbers \gamma_i that sum to 1.

SAFFRON depends on constants w_0 and \lambda, where w_0 satisfies 0 \le w_0 \le \alpha and represents the initial ‘wealth’ of the procedure, and 0 < \lambda < 1 represents the threshold for a ‘candidate’ hypothesis. A ‘candidate’ refers to p-values smaller than \lambda, since SAFFRON will never reject a p-value larger than \lambda.

Note that FDR control also holds for the SAFFRON procedure if only the p-values corresponding to true nulls are mutually independent, and independent from the non-null p-values.

The SAFFRON procedure can lose power in the presence of conservative nulls, which can be compensated for by adaptively ‘discarding’ these p-values. This option is called by setting discard=TRUE, which is the same algorithm as ADDIS.

Further details of the SAFFRON procedure can be found in Ramdas et al. (2018).

Value

out

A dataframe with the original data d (which will be reordered if there are batches and random = TRUE), the LORD-adjusted significance thresholds \alpha_i and the indicator function of discoveries R. Hypothesis i is rejected if the i-th p-value is less than or equal to \alpha_i, in which case R[i] = 1 (otherwise R[i] = 0).

References

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.

See Also

SAFFRONstar presents versions of SAFFRON for asynchronous testing, i.e. where each hypothesis test can itself be a sequential process and the tests can overlap in time.

Examples

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))

SAFFRON(sample.df, random=FALSE)

set.seed(1); SAFFRON(sample.df)

set.seed(1); SAFFRON(sample.df, alpha=0.1, w0=0.025)

dsrobertson/onlineFDR documentation built on April 21, 2023, 8:17 p.m.