simulatedDataset: Function to construct a simulated dataset containing...
In PredictABEL: Assessment of Risk Prediction Models

Description Usage Arguments Details Value References Examples

Construct a dataset that contains individual genotype data, genetic risk, and disease status for a hypothetical population. The dataset is constructed using simulation in such a way that the frequencies and odds ratios (ORs) of the genetic variants and the population disease risk computed from this dataset are the same as specified by the input parameters.

1	simulatedDataset(ORfreq, poprisk, popsize, filename)

`ORfreq`	Matrix with ORs and frequencies of the genetic variants. The matrix contains four columns in which the first two describe ORs and the last two describe the corresponding frequencies. The number of rows in this matrix is same as the number of genetic variants included. Genetic variants can be specified as per genotype, per allele, or as dominant/ recessive effect of the risk allele. When per genotype data are used, OR of the heterozygous and homozygous risk genotypes are mentioned in the first two columns and the corresponding genotype frequencies are mentioned in the last two columns. When per allele data are used, the OR and frequency of the risk allele are specified in the first and third column and the remaining two cells are coded as '1'. Similarly, when dominant/ recessive effects of the risk alleles are used, the OR and frequency of the dominant/ recessive variant are specified in the first and third column, and the remaining two cells are coded as '0'.
`poprisk`	Population disease risk (expressed in proportion).
`popsize`	Total number of individuals included in the dataset.
`filename`	Name of the file in which the dataset will be saved. The file is saved in the working directory as a txt file. When no filename is specified, the output is not saved.

The function will execute when the matrix with odds ratios and frequencies, population disease risk and the number of individuals are specified.

The simulation method is described in detail in the references.

The method assumes that (i) the combined effect of the genetic variants on disease risk follows a multiplicative (log additive) risk model; (ii) genetic variants inherit independently, that is no linkage disequilibrium between the variants; (iii) genetic variants have independent effects on the disease risk, which indicates no interaction among variants; and (iv) all genotypes and allele proportions are in Hardy-Weinberg equilibrium. Assumption (ii) and (iv) are used to generate the genotype data, and assumption (ii) and (iii) are used to calculate disease risk.

Simulating the dataset involves three steps: (1) modelling genotype data, (2) modelling disease risks, and (3) modelling disease status. Brief descriptions of these steps are as follows:

(1) Modelling genotype data: For each variant the genotype frequencies are either specified or calculated from the allele frequencies using Hardy-Weinberg equilibrium. Then, the genotypes for each genetic variant are randomly distributed without replacement over all individuals.

(2) Modelling disease risks: For the calculation of the individual disease risk, Bayes' theorem is used, which states that the posterior odds of disease are obtained by multiplying the prior odds by the likelihood ratio (LR) of the individual genotype data. The prior odds are calculated from the population disease risk or disease prevalence (prior odds= prior risk/ (1- prior risk)) and the posterior odds are converted back into disease risk (disease risk= posterior odds/ (1+ posterior odds)). Under the no linkage disequilibrium (LD) assumption, the LR of a genetic profile is obtained by multiplying the LRs of the single genotypes that are included in the risk model. The LR of a single genotype is calculated using frequencies and ORs of genetic variants and population disease risk. See references for more details.

(3) Modelling disease status: To model disease status, we used a procedure that compares the estimated disease risk of each subject to a randomly drawn value between 0 and 1 from a uniform distribution. A subject is assigned to the group who will develop the disease when the disease risk is higher than the random value and to the group who will not develop the disease when the risk is lower than the random value.

This procedure ensures that for each genomic profile, the percentage of people who will develop the disease equals the population disease risk associated with that profile, when the subgroup of individuals with that profile is sufficiently large.

The function returns:

Dataset

A data frame or matrix that includes genotype data, genetic risk and disease status for a hypothetical population. The dataset contains (4 + number of genetic variants included) columns, in which the first column is the un-weighted risk score, which is the sum of the number of risk alleles for each individual, the third column is the estimated genetic risk, the forth column is the individual disease status expressed as '0' or '1', indicating without or with the outcome of interest, and the fifth until the end column are genotype data for the variants expressed as '0', '1' or '2', which indicate the number of risk alleles present in each individual for the genetic variants.

Janssens AC, Aulchenko YS, Elefante S, Borsboom GJ, Steyerberg EW, van Duijn CM. Predictive testing for complex diseases using multiple genes: fact or fiction? Genet Med. 2006;8:395-400.

Kundu S, Karssen LC, Janssens AC: Analytical and simulation methods for estimating the potential predictive ability of genetic profiling: a comparison of methods and results. Eur J Hum Genet. 2012 May 30.

van Zitteren M, van der Net JB, Kundu S, Freedman AN, van Duijn CM, Janssens AC. Genome-based prediction of breast cancer risk in the general population: a modeling study based on meta-analyses of genetic associations. Cancer Epidemiol Biomarkers Prev. 2011;20:9-22.

van der Net JB, Janssens AC, Sijbrands EJ, Steyerberg EW. Value of genetic profiling for the prediction of coronary heart disease. Am Heart J. 2009;158:105-10.

Janssens AC, Moonesinghe R, Yang Q, Steyerberg EW, van Duijn CM, Khoury MJ. The impact of genotype frequencies on the clinical validity of genomic profiling for predicting common chronic diseases. Genet Med. 2007;9:528-35.

# specify the matrix containing the ORs and frequencies of genetic variants 
# In this example we used per allele effects of the risk variants
ORfreq<-cbind(c(1.35,1.20,1.24,1.16), rep(1,4), c(.41,.29,.28,.51),rep(1,4))

# specify the population disease risk
popRisk <- 0.3
# specify size of hypothetical population
popSize <- 10000

# Obtain the simulated dataset
Data <- simulatedDataset(ORfreq=ORfreq, poprisk=popRisk, popsize=popSize)

# Obtain the AUC and produce ROC curve
plotROC(data=Data, cOutcome=4, predrisk=Data[,3])