## Function to aggregate p values

### Description

dPvalAggregate is supposed to aggregate a input matrix p-values into a vector of aggregated p-values. The aggregate operation is applied to each row of input matrix, each resulting in an aggregated p-value. The method implemented can be based on the order statistics of p-values or according to Fisher's method or Z-transform method.

### Usage

dPvalAggregate(pmatrix, method = c("orderStatistic", "fishers", "Ztransform", "logistic"),
order = ncol(pmatrix), weight = rep(1, ncol(pmatrix)))

### Arguments

pmatrix
a data frame or matrix of p-values
method
the method used. It can be either "orderStatistic" for the method based on the order statistics of p-values, or "fishers" for Fisher's method (summation of logs), or "Ztransform" for Z-transform test (summation of z values, Stouffer's method) and the weighted Z-test, or "logistic" for summation of logits
order
an integeter specifying the order used for the aggregation according to the order statistics of p-values
weight
a vector specifying the weights used for the aggregation according to Z-transform method

### Value

• ap: a vector with the length nrow(pmatrix), containing aggregated p-values

### Note

For each row of input matrix with the c columns, there are c p-values that are uniformly independently distributed over [0,1] under the null hypothesis (uniform distribution). According to the order statisitcs, they follow the Beta distribution with the paramters a=order and b=c-order+1. According to the Fisher's method, after transformation by -2*\sum^clog(pvalue), they follow Chi-Squared distribution. According to the Z-transform method, first converts the one-tailed P-values into standard normal deviates Z, then combines Z via \frac{\sum^c(w*Z)}{\sum^c(w^2)}, where w is the weight (usually square root of the sample size if the weighted Z-test; 1 if Z-transform test), and finally the combined Z follows the standard normal distribution to test the cumulative/aggregated evidence on the common null hypothesis. The logistic method is defined as \sum^clog(\frac{pvalue}{1-pvalue}) * 1/C, where C=sqrt((k pi^2 (5 k + 2)) / (3(5 k + 4))), following Student's t distribution. Generally speaking, Fisher's method places greater emphasis on small p-values, while the Z-transform method on equal footings, the logistic method provides a compromise between these two. In other words, the Z-transform method does well in problems where evidence against the combined null is spread more than a small fraction of the individual tests, or when the total evidence is weak; Fisher's method does best in problems where the evidence is concentrated in a relatively small fraction of the individual tests or when the evidence is at least moderately strong.

### Examples

# 1) generate an iid uniformly-distributed random matrix of 1000x3
pmatrix <- cbind(runif(1000), runif(1000), runif(1000))

# 2) aggregate according to the order statistics
ap <- dPvalAggregate(pmatrix, method="orderStatistic")

# 3) aggregate according to the Fisher's method
ap <- dPvalAggregate(pmatrix, method="fishers")

# 4) aggregate according to the Z-transform method
ap <- dPvalAggregate(pmatrix, method="Ztransform")

# 5) aggregate according to the logistic method
ap <- dPvalAggregate(pmatrix, method="logistic")


## Source code

dPvalAggregate.r

## Source man

dPvalAggregate.Rd dPvalAggregate.pdf

dPvalAggregate