This is the function that calculates profileLikelihood for a single SNP. The main function evian calls this function repeatedly to obtain results for multiple SNPs.
calculateEvianMLE(snp, formula_tofit, model, data, bim, lolim, hilim,
m, bse, k, robust, family, plinkCC)a string specifying the SNP of interests to be calculated.
a formula object of the genetic model. The model should be formatted as y~nuisance parameters. The parameter of interest should not be included here.
a string specifying the mode of inheritance parameterization: additive, dominant, recessive, or overdominance. See details.
data frame; read from the argument data in the main function evian. It should contain the SNP ID specified in the snp argument as a column name.
data frame; read from from the argument bim in the main function evian. Provides allele information (base pair, effect/reference alleles) for the SNP of interest.
numeric; the lower limit for the grid or the minimum value of the regression parameter \(\beta\) used to calculate the likelihood function.
numeric; the upper limit for the grid or the maximum value of the regression parameter \(\beta\) used to calculate the likelihood funciton.
numeric; the density of the grid at which to compute the standardized likelihood function. A beta grid is defined as the grid of values for the SNP parameter used to evaluate the likelihood function.
numeric; the number of beta standard errors to utilize in constraining the beta grid limits. Beta grid is evaluated at \(\beta\) +/- bse*s.e.
numeric or numeric vector; The strength of evidence criterion k. Reads from the input of kcutoff from the main evian function
logical; if TRUE, then a robust adjustment is applied to the likelihood function to account for the cluster nature in the data. See robust_forCluster.
the link function for glm.
A boolean type that specifies how case/control are coded. case/control were coded 1/0 if it is FALSE, and were coded 2/1 if TRUE.
This function outputs a list containg 4 elements that can be directly accessed using '$' operator.
numeric vector; It stores all m \(\beta\) values that used to estimate the standardized profile likelihood.
numeric vector; the corresponding m standardized profile likelihood value at each of the \(\beta\) values in theta. If robust=TRUE, then the values will be adjusted by the robust factor.
numeric vector; It specifies which k-cutoff had been used in the calculation, ordered from the smallest k to the largest k.
data frame; contains the summary statistics of the profile likelihood calculation. It contains the following columns:
mle: the estimates for SNP effect with respect to the effective allele
maxlr: maximum likelihood ratio in the beta grid defined by lolim and hilim
AF: allele frequency for the effective allele
SNP: SNP ID
bp: base pair position from the bim input
effect, ref: the effective allele and the other allele from the bim input
robustFactor: robust factor calculated, set to 1 if robust=FALSE.
lo_1, hi_1, lo_2, hi_2...: the lower and upper bound of the likelihood intervals for the kth cut-off in k_cutoff.
calculateEvianMLE calculates the profile likelihood for a single SNP. A proper grid range is first established for \(\beta\) then the standardized profile likelihood is evaluated at each of the m cuts uniformly spread across the grid. Based on the standardized profile likelihood, the MLE for \(\beta\) is computed as well as the likelihood intervals for each value of k provided.
For different genetic models, their coding schemes are shown as below:
Additive AA 0 AB 1 BB 2Dominant AA 0 AB 1 BB 1
Recessive AA 0 AB 0 BB 1
Overdominance model A D AA 0 0 AB 1 1 BB 2 0
Specifically for the overdominance model, the column of interest is the D column.
Strug, L. J., Hodge, S. E., Chiang, T., Pal, D. K., Corey, P. N., & Rohde, C. (2010). A pure likelihood approach to the analysis of genetic association data: an alternative to Bayesian and frequentist analysis. Eur J Hum Genet, 18(8), 933-941. doi:10.1038/ejhg.2010.47
Strug, L. J., & Hodge, S. E. (2006). An alternative foundation for the planning and evaluation of linkage analysis. I. Decoupling "error probabilities" from "measures of evidence". Hum Hered, 61(3), 166-188. doi:10.1159/000094709
Royall, R. (1997). Statistical Evidence: A Likelihood Paradigm. London, Chapman and Hall.