In cases where the tests are not independent, the null distribution of X2 is more complicated. A common strategy is to approximate the null distribution with a scaled χ2-distribution random variable. Different approaches may be used depending on whether or not the covariance between the different p-values is known.
Brown's method [3] can be used to combine dependent p-values whose underlying test statistics have a multivariate normal distribution with a known covariance matrix. Kost's method [4] extends Brown's to allow one to combine p-values when the covariance matrix is known only up to a scalar multiplicative factor.