Confidence interval expected widths {qtlDesign}

Calculating expected QTL confidence interval widths

Description

Provides expected confidence interval widths for QTL location when we have dense markers.

Usage

ci.length(cross,n,effect,p=0.95,sigma2=1,env.var,gen.var,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

p

Confidence level for desired confidence interval

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; 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.

bio.reps

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

Details

With dense markers, the log likelihood follows a compound process. Approximate expected confidence intervals can be calculated by pretending the log likelihood decays linearly with a drift rate that depends on the effect size and cross type.

Value

Returns the expected confidence interval width (scalar) in cM assuming dense markers.

Author(s)

Saunak Sen

References

Dupuis J and Siegmund D (1999) Statistical methods for mapping quantitative trait loci from a dense set of markers. Genetics 151:373-386.

Darvasi A (1998) Experimental strategies for the genetic dissection of complex traits in animal models. Nature Genetics 18:19-24.

Kong A and Wright FA (1994) Asymptotic theory for gene mapping. Proceedings of the National Academy of Sciences of the USA 91:9705-9709.

See Also

powercalc.

Examples

ci.length(cross="bc",n=400,effect=5,p=0.95,sigma2=1)