qtlDesign (version 0.92)

Power calculations: Power, sample size, and detectable effect size calculations

Description

Power, sample size, and minimum detectable effect size calculations are performed for backcross, F2 intercross, and recombinant inbred (RI) lines.

Usage

powercalc(cross,n,effect,sigma2,env.var,gen.var,thresh=3,sel.frac=1,
          theta=0,bio.reps=1)
detectable(cross,n,effect=NULL,sigma2,env.var,gen.var,power=0.8,thresh=3,
           sel.frac=1,theta=0,bio.reps=1)
samplesize(cross,effect,sigma2,env.var,gen.var,power=0.8,thresh=3,
           sel.frac=1,theta=0,bio.reps=1)

Arguments

cross

String indicating cross type which is "bc", for backcross, "f2" for intercross, and "ri" for recombinant inbred lines.

n

Sample size

sigma2

Error variance; if this argument is absent, env.var and gen.var must be specified.

env.var

Environmental (within genotype) variance

gen.var

Genetic (between genotype) variance due to all loci segregating between the parental lines.

effect

The QTL effect we want to detect. For powercalc and samplesize this is a numeric (vector). For detectable it specifies the relative magnitude of the additive and dominance components for the intercross.

power

Proportion indicating power desired

thresh

LOD threshold for declaring significance

sel.frac

Selection fraction

theta

Recombination fraction corresponding to a marker interval

bio.reps

Number of biological replicates per unique genotype. This is usually 1 for backcross and intercross, but may be larger for RI lines.

Value

• For powercalc the power is returned, along with the proportion of variance explained. For detectable the effect size detectable is returned, along with the proportion of variance explained. For backcross and RI lines this is the effect of an allelic substitution. For F2 intercross the additive and dominance components are returned. For samplesize the sample size (rounded up to the nearest integer) is returned along with the proportion of variance explained.

Details

These calculations are done assuming that the asymptotic chi-square regimes apply. A warning message is printed if the effective sample size is less than 30 and either sel.frac is less than 1 or theta is greater than 0. First we calculate the effective sample size using the width of the marker interval and the selection fraction. The QTL is assumed to be in the middle of the marker interval. Then we use the fact that the non-centrality parameter of the likelihood ration test is $m*\delta^2$, where $m$ is the effctive sample size and $\delta$ is the QTL effect measured as the deviation of the genotype means from the overall mean. The chi-squared approximation is used to calculate the power. The minimum detectable effect size is obtained by solving the power equation numerically using uniroot. The theory behind the information calculations is described by Sen et. al. (2005).

A key input is the error variance, sigma2 which is generally unknown. The user can enter the error variance directly, or estimate it using env.var and gen.var. The function error.var is used to the error variance using estimates of the environmental variance and genetic variance. Another key input is the effect segregating in a cross, which can be calculated using gmeans2model.

References

Sen S, Satagopan JM, Churchill GA (2005) Quantitative trait locus study design from an information perspective. Genetics, 170:447-64.

See Also

uniroot. error.var, gmeans2effect.

Examples

powercalc("bc",100,5,sigma2=1,sel.frac=1,theta=0)
powercalc(cross="ri",n=30,effect=5,env.var=64,gen.var=25,bio.rep=6)
detectable("bc",100,sigma2=1)
detectable(cross="ri",n=30,env.var=64,gen.var=25,bio.rep=8)
samplesize(cross="f2",effect=c(5,0),env.var=64,gen.var=25)