pwr.snpblup {hscovar}

Wrapper function for sample size calculation

Description

Given parameters specified by the experimenter, optimal sample size is estimated by repeatedly applying search.best.n.bisection.

Usage

pwr.snpblup(
  nfathers,
  nqtl,
  h2,
  R,
  rep = 10,
  nmax = 5000,
  weights = 1,
  typeII = 0.2,
  alpha = 0.01
)

Arguments

nfathers

number of half-sib families

nqtl

number of QTL assumed

h2

heritability captured by QTL

R

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

rep

number of repetitions; default value 10

nmax

maximum value for grid search; default value 5000

weights

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

typeII

type-II error level; default value 0.2

alpha

type-I error level; default value 0.01

Details

Sample size depends on parameters specified by the experimenter (number of half-sib families, number of QTL, heritability, correlation matrix). These values are converted into parameters required for the probability density function under the alternative hypothesis (beta_k !=0, for k selected QTL positions). As power depends on the selected QTL positions, these are sampled at random and power calculations are repeated. Afterwards the mean value is a plausible estimate of optimal sample size.

Linear model for SNP-BLUP approach: y = X beta + e with t(beta) = (beta_1, ldots, beta_p) Ridge approach: hat{beta} = (Xt X + I lambda)^{-1} Xt y

The identity matrix I can be replaced by a diagonal matrix containing SNP-specific weights yielding a generalised ridge approach.

Value

vector of optimal sample size over all repetitions

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

  ### input parameters specified by experimenter
  # number of half-sib families
  nfathers <- 10
  # number of assumed QTL
  nqtl <- 2
  # QTL heritability
  h2 <- 0.2
  ### correlation matrix (should depend on sire haplotypes)
  R <- AR1(100, rho = 0.1)
  ### optimal sample size in a multi-marker approach
  set.seed(11)
  pwr.snpblup(nfathers, nqtl, h2, R, rep = 1)