# Saddle_Prob: Calculate Saddlepoint p values (for external libraries) In SPAtest: Score Test and Meta-Analysis Based on Saddlepoint Approximation

## Description

Function to calculate the SPA p value from score function. Intended to be used by external libraries.

## Usage

 1 2 3 Saddle_Prob(q, mu, g, Cutoff=2,alpha,output="P",nodes.fixed,nodes.init,log.p=FALSE) Saddle_Prob_fast(q, g,mu,gNA,gNB,muNA,muNB,Cutoff=2,alpha,output,nodes.fixed, nodes.init,log.p=FALSE) 

## Arguments

 q Numeric scalar, score statistic. mu Numeric vector, fitted probabilities from the null model. g Numeric vector, covariate adjusted genotypes. gNA Numeric vector, covariate adjusted genotypes where the observed genotype is zero. gNB Numeric vector, covariate adjusted genotypes where the observed genotype is non-zero. muNA Numeric vector, fitted probabilities from the null model where the observed genotype is zero. muNB Numeric vector, fitted probabilities from the null model where the observed genotype is non-zero. Cutoff An integer or the string "BE" denoting the standard deviation cutoff to be used. If Cutoff = "BE", the level-specific cutoff based on Berry-Esseen theorem is calculated. If the test statistic lies within the standard deviation cutoff of the mean, p-value based on traditional score test is returned. Default value is 2. alpha Significance level for the test(s), default value is 5\times 10^{-8}. Used only if Cutoff = "BE". output String specifying the output required. Possible values are "P" (default), "metaZ", "metaGC", and "metaspline". nodes.fixed Vector denoting the spline nodes for the spline based summary statistics, if you do not want to provide a fixed set of nodes instead of estimating the optimal set of nodes. Only applicable when the output is "metaspline". nodes.init Vector denoting the initial values of the spline nodes when you want to estimate the optimal set of spline nodes using the coordinate descent algorithm. Only applicable when the output is "metaspline". Ignored if nodes.fixed is provided. The node at 0 will be automatically added, no need to provide that. The number of finally selected nodes will be the same as in nodes.init. log.p Whether to return natural log-transformed p-values, default value is FALSE.

## Value

 p.value p-value or natural log-transformed p-value based on the saddlepoint approximation. If output = "P", it is unsigned. For all other choice of output, it is signed. p.value.NA p-value or natural log-transformed p-value based on the normal approximation (traditional score test). If output = "P", it is unsigned. For all other choice of output, it is signed. Is.converge "TRUE" or "FALSE" denoting whether the root-finding algorithm for the saddlepoint equation has converged. Score Centered score statistic. splfun Outputs from fitting the CGF-Spline method, if output = "metaspline". var Variance of the score test statistic, if output = "metaspline".

ScoreTest_SPA
ScoreTest_SPA_wMeta
 1 2 3 4 5 ## Not run: Saddle_Prob(q, mu, g, Cutoff=2,alpha,output="P",nodes.fixed,nodes.init,log.p=FALSE) Saddle_Prob_fast(q, g,mu,gNA,gNB,muNA,muNB,Cutoff=2,alpha,output,nodes.fixed,nodes.init,log.p=FALSE) ## End(Not run)