pval_srmsd {simtrait}

Signed RMSD measure of null p-value uniformity

Description

Quantifies null p-value uniformity by computing the RMSD (root mean square deviation) between the sorted observed null (truly non-causal) p-values and their expected quantiles under a uniform distribution. Meant as a more robust alternative to the "inflation factor" common in the GWAS literature, which compares median values only and uses all p-values (not just null p-values). Our signed RMSD, to correspond with the inflation factor, includes a sign that depends on the median null p-value: positive if this median is ⁠<= 0.5⁠ (corresponds with test statistic inflation), negative otherwise (test statistic deflation). Zero corresponds to uniform null p-values, which arises in expectation only if test statistics have their assumed null distribution (there is no misspecification, including inflation).

Usage

pval_srmsd(pvals, causal_indexes, detailed = FALSE)

Arguments

pvals

The vector of association p-values to analyze. This function assumes all p-values are provided (a mix of null and alternative tests). NA values are allowed in input and removed. Non-NA values outside of [0, 1] will trigger an error.

causal_indexes

The vector of causal indexes, whose p-values will be omitted. Values of causal_indexes as returned by sim_trait work. This parameter is required to prevent use of this function except when the true status of every test (null vs alternative) is known. Set to NULL if all loci are truly null (non-causal). Otherwise, causal_indexes must have at least one causal index.

detailed

If FALSE (default) only SRMSD is returned. If TRUE, sorted null p-values without NAs and their expectations are returned (useful for plots).

Value

If detailed is FALSE, returns the signed RMSD between the observed p-value order statistics and their expectation under true uniformity. If detailed is TRUE, returns data useful for plots, a named list containing:

• srmsd: The signed RMSD between the observed p-value order statistics and their expectation under true uniformity.

• pvals_null: Sorted null p-values (observed order statistics). If any input null p-values were NA, these have been removed here (removed by sort()).

• pvals_unif: Expected order statistics assuming uniform distribution, same length as pvals_null.

If the input pvals is NULL (taken for case of singular association test, which is rare but may happen), then the returned value is NA if detailed was FALSE, or otherwise the list contains NA, NULL and NULL for the above three items.

See Also

rmsd() for the generic root-mean-square deviation function.

pval_infl() for the more traditional inflation factor, which focuses on the median of the full distribution (combination of causal and null cases).

pval_type_1_err() for classical type I error rate estimates.

Examples

# simulate truly null p-values, which should be uniform
pvals <- runif(10)
# for toy example, take the first p-value to be truly causal (will be ignored below)
causal_indexes <- 1
# calculate desired measure
pval_srmsd( pvals, causal_indexes )