PoolBal

Help for package PoolBal const macros = { "\\R": "\\textsf{R}", "\\mbox": "\\text", "\\code": "\\texttt"}; function processMathHTML() { var l = document.getElementsByClassName('reqn'); for (let e of l) { katex.render(e.textContent, e, { throwOnError: false, macros }); } return; } Package {PoolBal} Contents altFrequencyMat betaDiv chiKappa chiPc chiPool chiPr chiQ convertGeneticSigma estimatePc estimatePrb estimateQ findA hrPc hrPool hrPr hrQ hrStat klDiv marHistHeatMap rBetaH4 satterApproxP satterChiPool Version: 0.1-0 Encoding: UTF-8 Title: Balancing Central and Marginal Rejection of Pooled p-Values Description: When using pooled p-values to adjust for multiple testing, there is an inherent balance that must be struck between rejection based on weak evidence spread among many tests and strong evidence in a few, explored in Salahub and Olford (2023) < doi:10.48550/arXiv.2310.16600 >. This package provides functionality to compute marginal and central rejection levels and the centrality quotient for p-value pooling functions and provides implementations of the chi-squared quantile pooled p-value (described in Salahub and Oldford (2023)) and a proposal from Heard and Rubin-Delanchy (2018) < doi:10.1093/biomet/asx076 > to control the quotient's value. Author: Chris Salahub [aut, cre] Maintainer: Chris Salahub <chris.salahub@uwaterloo.ca> Depends: R (≥ 4.3.0) Imports: methods License: GPL (≥ 3) NeedsCompilation: no Repository: CRAN RoxygenNote: 7.2.3 Packaged: 2023-11-21 22:30:01 UTC; Chris Date/Publication: 2023-11-22 10:10:02 UTC Identify a region of plausible alternative hypotheses in the proportion, strength of non-null evidence space Description This function provides a convenient way to interact with simulations performed over a grid of possible alternatives spanning the proportion (eta) and strength (KL divergence) of evidence against the null hypothesis under beta alternatives. Usage altFrequencyMat(logKappaRange, logW = FALSE) Arguments logKappaRange pair of numeric values logW logical, should the log scale simulation be used? Details The simulation this function summarized used a range of eta, w, and KL divergence values to generate thousands of potential alternative distributions. The power of each chi-squared pooled p-value for 161 kappa values ranging from exp(-8) to exp(8) selected uniformly on the log scale was then computed for each alternative using 10,000 simulated examples. Every choice of kappa was compared to the maximum power across all kappas for each setting using a binomial test of differences. This same simulation was repeated twice: once for w values selected uniformly from 0 to 1 and another where selection was uniform on the log scale. The internal data summarizes the results by reporting the count of instances in w (or logw) where a given kappa value was most powerful for a given eta and KL divergence. Though the simulation data is not exported to users and so cannot be accessed directly, this function allows a user to query the data with a range of kappa values (corresponding to those where a given sample seems most powerful) and returns the count of cases in w where a kappa in the corresponding kappa range was most powerful given the eta, KL-divergence combination with beta alternatives. The simulations only spanned kappa values from exp(-8) to exp(8), so providing values outside this range will give very inaccurate results. Value An 81 by 81 matrix giving summarized counts of cases. Author(s) Chris Salahub Examples altFrequencyMat(c(-1, 1), logW = FALSE) altFrequencyMat(c(-1, 1), logW = TRUE) Compute the Kullback-Leibler divergence between the beta and uniform distributions Description Computes the Kullback-Leibler divergence for the special case of the uniform density against the beta density. Usage betaDiv(a, w = (1 - a)/(b - a), b = 1/w + a * (1 - 1/w)) Arguments a first shape parameter between 0 and infinity w UMP parameter between 0 and 1 b second shape parameter between 0 and infinity Details This function accepts either the a/b parameterization (equivalent to shape1/shape2 in R), or the a/w parameterization which links the divergence to the UMP test. Value A real value. Author(s) Chris Salahub Examples betaDiv(a = 0.5, w = 0.5) betaDiv(a = 0.1, b = 1) Chi-squared kappa for a given centrality quotient Description Computes the kappa (degrees of freedom) required to obtain a given centrality quotient using the chi-square pooled p-value. Usage chiKappa( cq, M, alpha = 0.05, interval = c(0, 100), tol = .Machine$double.eps^0.5 ) Arguments cq numeric between 0 and 1 M integer sample size greater than 0 alpha numeric between 0 and 1 interval numeric of length 2, where should roots be sought? tol numeric, how close do values need to be for equality? Details This function is essentially a wrapper for uniroot which finds where chiCentQuot gives an output equal to the given centrality quotient to provide an approximate kappa giving that quotient. Value A numeric within interval. Author(s) Chris Salahub Examples chiKappa(0.5, 10, 0.05) chiKappa(0.5, 20, 0.05) chiKappa(0.5, 100, 0.05, interval = c(0, 10)) Chi-squared central rejection level Description Computes the central rejection level for the chi-squared pooled p-value. Usage chiPc(kappa, M, alpha = 0.05) Arguments kappa numeric between 0 and infinity M integer sample size greater than 0 alpha numeric between 0 and 1 Details The central rejection level is the maximum p-value shared among all tests which still results in rejection of the null using a pooled p-value. For the chi-squared pooled p-value, this is an upper tail probability of the chi-squared distribution. This function computes the upper tail probability for a given sample size M, degrees of freedom kappa, and rejection level alpha. Value A numeric between 0 and 1. Author(s) Chris Salahub Examples chiPc(2, 10, 0.05) chiPc(2, 20, 0.05) # increases in sample size Chi-squared p-value pooling Description This implements the chi-squared pooled p-value which can be used to control the centrality quotient when pooling p-values. Usage chiPool(p, kappa) Arguments p numeric vector of p-values between 0 and 1 kappa numeric value between 0 and infinity Details The chi-squared pooled p-value is a quantile transformation pooled p-value based on the chi-squared distribution with degrees of freedom kappa. By setting kappa between 0 and infinity, smooth interpolation is achieved between Tippett's minimum pooled p-value and Stouffer's normal quantile pooled p-value respectively. Choosing a kappa value of 2, Fisher's pooling function is obtained. Tippett's pooled p-value is maximally non-central and Stouffer's is maximally central, while Fisher's presents a balance between marginal and central rejection. Value A pooled p-value between 0 and 1. Author(s) Chris Salahub Examples p <- c(0.1, 0.5, 0.9) chiPool(p, exp(-4)) chiPool(p, 2) chiPool(p, exp(4)) Chi-squared marginal rejection level Description Computes the marginal rejection level for the chi-squared pooled p-value. Usage chiPr(kappa, M, alpha = 0.05) Arguments kappa numeric between 0 and infinity M integer sample size greater than 0 alpha numeric between 0 and 1 Details The marginal rejection level is the maximum p-value in a single test which results in rejection when all other tests produce p-values of one. For the chi-squared pooled p-value, this is an upper tail probability of the chi-squared distribution. This function computes the upper tail probability for a given sample size M, degrees of freedom kappa, and rejection level alpha. Value A numeric between 0 and 1. Author(s) Chris Salahub Examples chiPr(2, 10, 0.05) chiPr(2, 20, 0.05) Chi-squared centrality quotient Description Computes the centrality quotient of the chi-square pooled p-value. Usage chiQ(kappa, M, alpha = 0.05) Arguments kappa numeric between 0 and infinity M integer sample size greater than 0 alpha numeric between 0 and 1 Details The centrality quotient of a pooled p-value measures the relative pref