Power calculations {qtlDesign} | R Documentation |
Power, sample size, and minimum detectable effect size calculations are performed for backcross, F2 intercross, and recombinant ingred (RI) lines.
powercalc(cross,n,effect,sigma2,thresh=3,alpha=1,theta=0) detectable(cross,n,effect=NULL,sigma2,power=0.8,thresh=3,alpha=1,theta=0) samplesize(cross,effect,sigma2,power=0.8,thresh=3,alpha=1,theta=0)
cross |
String indicating cross type which is "bc", for backcross, "f2" for intercross, and "ri" for recombinant inbred lines. |
n |
Sample size |
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.
The specification of effect depends on the cross. For
backcross,it is the difference in means the heterozygote and
homozygote. For RI lines it is half the difference in means of the
homozygotes, for intercross, it is a two component vector of the form
c(a,d) , where a is the additive effect (half the
difference between the homozygotes), and d is the dominance
effect (difference between the heterozygote and the average of the
homozygotes). The genotype means will be -a-d/2 , d/2 ,
and a-d/2. For detectable , optionally for the
intercross, one can use a string to specify the QTL effect type.
The strings "add" or "dom" are used to denote an additive or
dominant model respectively for the phenotype. It may be
it can be a numerical vector of the form c(a,d) indicating
the relative magnitudes of the additive and dominance components (as
defined above). The default is "add". |
sigma2 |
Error variance |
power |
Proportion indicating power desired |
thresh |
LOD threshold for declaring significance |
alpha |
Selection fraction |
theta |
Recombination fraction corresponding to a marker interval |
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 alpha
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 which is generally unknown.
The function error.var
estimates the error variance using
estimates of the biological variance and genetic variance. Another
useful input is the effect segregating in a cross, which can be
calculated using gmeans2model
.
For powercalc
the power is returned.
For detectable
the effect size detectable is returned. For
backcross and RI lines this is the effect of an allelic substitution.
For F2 intercross the additive and dominance components are returned.
Saunak Sen, Jaya Satagopan, Karl Broman, and Gary Churchill
Sen S, Satagopan JM, Churchill GA (2005) Quantitative trait locus study design from an information perspective. Genetics, 170:447-64.
uniroot
. error.var
,
gmeans2effect
.
powercalc("bc",100,5,sigma2=1,alpha=1,theta=0) detectable("bc",100,sigma2=1)