This is an R toolkit for combining parental history and existing polygenic risk scores for improved prediction of complex traits or disease risks.
The computational scripts in the R folder can be directly downloaded. The only prerequisite is installation of the pracma R pacakge.
We propose a conceptual latent factor model to account for genetic components that are not modelled by polygenic risk scores but could be inferred from parental history. Briefly, for a continuous polygenic trait, we assume that its genetic determinants can be partitioned into two orthogonal genetic components: one component captured by a polygenic risk score used for prediction, and the other component representing under-captured genetic effects. The under-captured genetic component could include the effects of unmeasured common variants, rare variants, gene-by-environment interactions, epistasis, intra-familial shared environmental or lifestyle factors, etc. We suppose that these two genetic components are independently passed on from the parents to the children, and parental measures of the trait may partially inform the under-captured genetic component. This model can be adapted for binary diseases, wherein the parental disease history may inform the underlying genetic liability.
Based on this model, it follows that prediction of a continuous trait or the genetic liability for a disease can be improved by combining a polygenic risk score and family history, requiring only (1) the magnitude of association between a polygenic risk score and the target trait or disease, and (2) the magnitude of association between parents’ trait measures or disease history and the target trait or disease amongst children. Importantly, these estimates can be obtained from separate well-powered cohort studies, without the need to access individual-level information.
Refer to our preprint for detailed descriptions.
Contact:
Tianyuan Lu (tianyuan.lu@mail.mcgill.ca)
Celia Greenwood (celia.greenwood@mcgill.ca)
Predicting a continuous trait for the children requires
(1) an estimate of the proportion of variance explained by a polygenic risk score (h2_PRS);
(2) an estimate of the proportion of variance explained by a mid-parental predictor (h2_midp);
(3) data of the target population.
Both (1) and (2) can be obtained from large cohort studies that have similar genetic ancestries and demographic characteristics as the target population.
In command line:
Rscript /path/to/predict_continuous.R h2_PRS h2_midp /path/to/dataThe data file should be a tab-delimited file and should contain one column with the header PRS corresponding to the children's polygenic risk scores, and at least one column corresponding to the maternal or paternal trait measure, with the header Mother or Father. These columns should be standardized to have zero mean and unit variance.
Mother Father PRS
0.28236405580198 0.0478243107177947 -0.89184382599075
0.759665799839955 -0.00721719819976707 -0.237169912244541
1.01630718554635 0.785608541053388 0.863639182659233
-1.89783916306742 0.713878129174335 0.68661572124903
-1.33398782749324 -0.997270913147984 0.271900690073316
-1.9072137451484 -0.501673356594952 0.855450956488146
-0.199858668999688 0.926516478157096 1.23195377799939
0.571884596761782 -0.527252725302699 -1.60609961780322
0.543640566012509 0.711280253861894 0.00859903139352139
When both Mother and Father columns are supplied, prediction will be based on the children's polygenic risk scores and both parents' trait measures; If only one parental trait measure is supplied, prediction will be based on the children's polygenic risk scores and the provided parental trait measure. Additional columns can be included in the data file, and the order of columns can be flexible.
The joint predictor will be appended to the data file, which will then be stored in an RData with the affix .joint.pred.continuous.RData.
Predicting a binary trait (e.g. a disease outcome) for the children requires
(1) an estimate of the baseline log-odds (mu_0): this should be estimated using a logistic regression model adjusted for covariate effects based on the reference population, but could be approximated by log-[prevalence / (1 - prevalence)] when a regression-based estimate is not available;
(2) an estimate of the log-odds ratio associated with one standard deviation increase in the polygenic risk score based on the reference population (beta_PRS);
(3) an estimate of the log-odds ratio associated with having a parental disease history based on the reference population (beta_parent): when the maternal history-based and the paternal history-based estimates are both available, this should be the average of the two estimates;
(4) an estimate of the log-men-to-women odds ratio based on the reference population (beta_men): this could be set to 0 when only one parent's disease history is provided or when sex has no influence on the disease risk;
(5) data of the target population.
In command line:
Rscript /path/to/predict_binary.R mu_0 beta_PRS beta_parent beta_men /path/to/dataAgain, the data file should a tab-delimited file and should contain one column with the header PRS corresponding to the children's polygenic risk scores, and at least one column corresponding to the maternal or paternal disease history (or binary trait measure), with the header Mother_Disease or Father_Disease. The PRS column should be standardized to have zero mean and unit variance.
Mother_Disease Father_Disease PRS
0 1 -0.89184382599075
0 0 -0.237169912244541
1 0 0.863639182659233
0 0 0.68661572124903
1 0 0.271900690073316
0 0 0.855450956488146
0 0 1.23195377799939
0 0 -1.60609961780322
0 1 0.00859903139352139
When both columns are supplied, prediction will be based on the children's polygenic risk scores and both parents' disease history; If only one parental disease history is supplied, prediction will be based on the children's polygenic risk scores and the provided parental disease history. Additional columns can be included in the data file, and the order of columns can be flexible.
The joint predictor will be appended to the data file, which will then be stored in an RData with the affix .joint.pred.binary.RData.
A simulated toy dataset for estimating parameters is provided here and a simulated toy data for testing prediction is provided here. Scripts used to generate these data are stored here.
Briefly, for a continuous trait, a polygenic risk score was designed to explain 9% of the trait heritability while an orthogonal genetic component was designed to explain 64% of the trait heritability. Based on the reference data, we can find that the score explained 8.9% of the measured trait variance, and that a mid-parental predictor explained 27.2% of the measured trait variance.
> data <- read.table("simulate_phenotype_reference.txt", header = T) ### Reference dataset for parameter estimation
> cor(data$Child, data$PRS)^2 ### Proportion of variance explained by the score
[1] 0.08947465
> data$MidParent <- (data$Mother + data$Father) / 2 ### Mid-parental predictor
> cor(data$Child, data$MidParent)^2 ### Proportion of variance explained by the mid-parental predictor
[1] 0.2719037
We therefore generate a joint predictor with the following command using command line:
Rscript predict_continuous.R 0.089 0.272 simulate_phenotype.txtThis should lead to an RData file similar to the output.
And the joint predictor should explain 31.2% of the measured trait variance in the given dataset.
A binary outcome was simulated based on the above continuous trait with a baseline log-odds designed to be -1. Based on the data, we can find that per one standard deviation increase in the polygenic risk score is associated with a log-odds ratio of 0.233; having a parental disease history is associated with a log-odds ratio of 0.262; and the estimated baseline log-odds is -0.996. We do not consider sex effect in this example.
> data <- read.table("simulate_phenotype_reference.txt", header = T) ### Reference dataset for parameter estimation
> coef(summary(glm(Child_Disease ~ PRS, family = binomial, data = data)))[2,1] ### log-odds ratio associated with one standard deviation increase in the score
[1] 0.233022
> mean(coef(summary(glm(Child_Disease ~ Mother_Disease + Father_Disease, family = binomial, data = data)))[2:3,1]) ### log-odds ratio associated with parental disease history
[1] 0.2622773
> coef(summary(glm(Child_Disease ~ Mother_Disease + Father_Disease, family = binomial, data = data)))[1,1] ### baseline log-odds
[1] -0.9956813
We therefore generate a joint predictor with the following command using command line:
Rscript predict_binary.R -0.996 0.233 0.262 0 simulate_phenotype.txtThis should lead to an RData file similar to the output.
And the joint predictor should achieve an area under the receiver operating characteristic curve of 0.5739, higher than 0.5702 by the polygenic risk score alone.
Disease heritability can be estimated using the estimate_h2 function in this file with
(1) an estimate of the baseline log-odds (mu_0);
(2) an estimate of the log-odds ratio associated with having a parental disease history based on the reference population (beta_parent).
In an R console or RStudio:
estimate_h2(mu_0, beta_parent, degree = 1)Note that this function allows for beta_parent estimates based on 2nd-degree or more distant relatives, which can be specified by the option degree.