Description Usage Arguments Value Note See Also Examples

`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.

1 2 3 4 5 6 |

`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 |

`ap`

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

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*∑^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{∑^c(w*Z)}{∑^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 *∑^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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
# 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")
``` |

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