parallelStouffer {metapod} | R Documentation

## Combine parallel p-values with Stouffer's Z-score

### Description

Combine p-values from parallel tests with Stouffer's Z-score method. Each group of p-values is defined from the corresponding entries across all vectors.

### Usage

    parallelStouffer(p.values, weights = NULL, log.p = FALSE)

### Arguments

`p.values` | A list of numeric vectors of the same length, containing the p-values to be combined.
`weights` | A numeric vector of positive weights, with one value per vector in `...`. Each weight is applied to all entries of itscorresponding vector, i.e., all p-values in that vector receive the same weight. Alternatively, a list of numeric vectors of weights with the same structure as `p.values`. Each p-value is then assigned the weight in the corresponding entry of `weights`. Alternatively `NULL`, in which case all p-values are assigned equal weight.
`log.p` | Logical scalar indicating whether the p-values in `p.values` are log-transformed.

### Details

The joint null hypothesis for each group is that all of the individual null hypotheses are true. Stouffer's method combines information from all individual nulls to determine if the joint null should be rejected. This serves as a compromise between Fisher's method (sensitive to the smallest p-value) and Pearson's method (sensitive to the largest p-value).

Stouffer's method is only applicable for independent tests. Weights are supported by scaling the contribution of each individual null to the summed Z-score. In this manner, more highly weighted tests will have a greater effect on the final combined p-value.

The representative test for each group is defined as the test with the most negative weighted Z-score, as this has the greatest effect on the combined p-value when the joint null is rejected. All tests for each group are considered to be influential as increasing any of them (e.g., to unity) would result in a larger combined p-value.

When a group contains both zero and unity p-values, we compare the sum of weights for all zero p-values and all unity p-values. If the former is larger, the combined p-value is set to zero; if the latter, to unity. If they are equal, we pretend that the two sets of p-values “cancel out” and contribute nothing to the summed Z-score. This is not entirely rigorous but provides reasonable output in the presence of such boundary values.

### Value

A list containing:

- `p.value`, a numeric vector of length equal to the length of each vector in `p.values`. This contains the combined Stouffer p-value for each group, log-transformed if `log.p=TRUE`.

- `representative`, an integer scalar specifying the representative test in each group. Specifically, this refers to the index of the vector of `p.values` containing the representative test.

- `influential`, a list of logical vectors mirroring the structure of `p.values`. Entries are `TRUE` for any p-value that is deemed “influential” to the final combined p-value.

### Author(s)

Aaron Lun

### References

Stouffer SA et al. (1949). The American Soldier, Vol. 1 - Adjustment during Army Life. Princeton University Press (Princeton).

Whitlock MC (2005). Combining probability from independent tests: the weighted Z-method is superior to Fisher's approach. J. Evol. Biol. 18, 5:1368-73.

### See Also

`groupedStouffer`, for a version that combines p-values based on a grouping factor.

`parallelFisher` and `parallelPearson`, for different approaches to testing a joint null of independent hypotheses.

### Examples

    p1 <- rbeta(100, 0.8, 1)
    p2 <- runif(100)
    p3 <- rbeta(100, 0.5, 1)

    # Standard application:
    out <- parallelStouffer(list(p1, p2, p3))
    str(out)

    # With weights:
    out <- parallelStouffer(list(p1, p2, p3), weights=5:7)
    str(out)

    # With log p-values.
    out <- parallelStouffer(list(log(p1), log(p2), log(p3)), log.p=TRUE)
    str(out)

[Package metapod version 1.0.0 Index]