Code to accompany the paper: Dreyfuss JM$, Levner D$, Galagan JE, Church GM, Ramoni MF. How accurate can genetic predictions be? BMC Genomics. 2012 Jul 24;13:340. doi: 10.1186/1471-2164-13-340. PubMed PMID: 22827772; PubMed Central PMCID: PMC3534619 [$Equal contribution]. http://bmcgenomics.biomedcentral.com/articles/10.1186/1471-2164-13-340.

To use these algorithms, call the functions: maxAUC, optSe, and/or optSp.

maxAUC returns the maximal AUC given:
k=prevalence
pve=proportion of variance explained (e.g. heritability)
n.bins=number of bins (default: 100)

optSe returns the optimal (maximal or minimal) sensitivity given:
k=prevalence
pve=proportion of variance explained (e.g. heritability)
sp=specificity
n.bins=number of bins (default: 1000)
direction="max" or "min" (default: "max")
thresh.vector=vector of thresholds in terms of bins (default: integer sequence from 1 to n.bins by 10)

optSp returns the optimal (maximal or minimal) specificity given:
k=prevalence
pve=proportion of variance explained (e.g. heritability)
se=sensitivity
n.bins=number of bins (default: 1000)
direction="max" or "min" (default: "max")
thresh.vector=vector of thresholds in terms of bins (default: integer sequence from 1 to n.bins by 10)

PARAMETERS
k=prevalence. 0<=k<=1.
pve=proportion of variance explained (e.g. heritability). 0<=pve<=1.
se=sensitivity. 0<=se<=1.
sp=specificity. 0<=sp<=1.
n.bins=number of bins. Positive integer corresponding to ‘b’ in Detailed methods.
direction="max" or "min". Maximize or minimize sensitivity or specificity.
thresh.vector=vector of thresholds in terms of bins (default: integer sequence from 1 to n.bins by 10). This corresponds to ‘t’ in Detailed methods; people whose risk is >= threshold/n.bins test positive. Thresholds should be positive integers <= n.bins.

EXAMPLES
Two examples follow. The commented-out numbers on the right-hand side are the numerical results I got when using: R version 2.12.1 (2010-12-16)

##R code
#breast cancer
k <- 0.04; pve <- 0.11; sp <- 0.99; se <- 0.2429554
maxAUC(k=k, pve=pve) #0.8935785
optSe(k=k, pve=pve, sp=sp) #0.2429554
optSp(k=k, pve=pve, se=se) #0.99

#T2D
k <- 0.13; pve <- 0.26; sp <- 0.99; se <- 0.3553533
maxAUC(k=k, pve=pve) #0.8882527
optSe(k=k, pve=pve, sp=sp) #0.3553533
optSp(k=k, pve=pve, se=se) #0.99
##end R code