pwr.normtest {hscovar}

Probability under alternative hypothesis (power)

Description

Calculation of power is based on normal distribution. At each selected QTL position, the probability of the corresponding regression coefficient being different from zero is calculated using a t-like test statistic which has normal distribution with mean E(beta_k)/sqrt{Var(beta_k)} and variance 1. Under the null hypothesis beta_k = 0, E(beta_k) = 0. Then, the mean value is returned as power.

Usage

pwr.normtest(R, n, betaSE, lambda, pos, weights = 1, alpha = 0.01)

Arguments

R

(p x p) matrix containing theoretical correlation between SNP pairs

n

sample size

betaSE

effect size relative to residual standard deviation

lambda

shrinkage parameter

pos

vector (LEN nqtl) of SNP indices for assumed QTL positions

weights

weights vector (LEN p) of SNP-specific weights or scalar if weights are equal for all SNPs; default value 1

alpha

type-I error level; default value 0.01

Value

result

mean power at selected QTL positions

h2.le

QTL heritability under linkage-equilibrium assumption

h2.ld

QTL heritability under linkage-disequilibrium assumption

References

Wittenburg, Bonk, Doschoris, Reyer (2020) Design of Experiments for Fine-Mapping Quantitative Trait Loci in Livestock Populations. BMC Genetics 21:66. doi: 10.1186/s12863-020-00871-1

Examples

  ### correlation matrix (should depend on sire haplotypes)
  R <- AR1(100, rho = 0.1)
  ### positions of putative QTL signals
  pos <- c(14, 75)
  ### power at given sample size and other parameters
  pwr.normtest(R, 100, 0.35, 1200, pos)