# Family age-at-onset data simulation and penetrance estimation Family-based studies are used to characterize the disease risk associated with being a carrier of a major gene. When the disease risk can vary with age of onset, penetrance or disease risk functions need to provide age-dependent estimates of this disease risk over lifetime. This FamEvent package can generate age-at-onset data in the context of familial studies, with correction for ascertainment (selection) bias arising from a specified study design based on proband's mutation and disease statuses. Possible study designs are: `"pop"` for population-based design where families are ascertained through affected probands, `"pop+"` are similar to `"pop"` but probands are also known mutation carriers, `"cli"` for clinic-based design that includes affected probands with at least one parent and one sib affected, `"cli+"` are similar to `"cli"` but probands are also known mutation carrriers. And `"twostage"` for two-stage design that randomly samples families from the population in the first stage and oversamples high risk families that includes at least two affected members in the family at the second stage. Ages at disease onset are generated specific to family members' gender and mutation status according to the specified study design with residual familial correlations induced by a shared frailty, correlated frailties with Kinship matrix, or a second gene. For estimating age at onset risks with family data, an ascertainment corrected prospective likelihood approach is used to account for the population or clinic-based study designs while a composite likelihood approach is used for the two-stage sampling design. The Expectation and Maximization (EM) algorithm has been implemented for inferring missing genotypes conditional on observed genotypes and phenotypes in the families. For family members who have missing genotypes, their carrier probabilities are obtained either from the fitted model or from Mendelian transmission probabilities. This package also provides functions to plot the age-dependent penetrance curves estimated parametrically from the fitted model or non-parametrically from the data, pedigree plots of simulated families and penetrance function curves for carriers and non-carriers of a major and second gene based on specified parameter values. In summary, this package facilitates the following: 1. Family data generations from 1) a shared frailty model or 2) a correlated frailty model with Kinship and/or IBD matrix; 3) a competing risk model. 2. Covariates considered: sex, gene, options for additional covariates. 3. Time-varying covariate generation based on permanent exposure (PE) or the Cox-Oaks model (CO). 3. Model estimation for shared frailty models and competing risk models. package ## Author(s) Yun-Hee Choi, Karen Kopciuk, Laurent Briollais, Wenqing He Maintainer: Yun-Hee Choi < yun-hee.choi@schulich.uwo.ca > ## References Choi, Y.-H., Jung, H., Buys, S., Daly, M., John, E.M., Hopper, J., Andrulis, I., Terry, M.B., Briollais, L. (2021) A Competing Risks Model with Binary Time Varying Covariates for Estimation of Breast Cancer Risks in BRCA1 Families, Statistical Methods in Medical Research 30 (9), 2165-2183. https://doi.org/10.1177/09622802211008945. Choi, Y.-H., Briollais, L., He, W. and Kopciuk, K. (2021) FamEvent: An R Package for Generating and Modeling Time-to-Event Data in Family Designs, Journal of Statistical Software 97 (7), 1-30. doi:10.18637/jss.v097.i07 Choi, Y.-H., Kopciuk, K. and Briollais, L. (2008) Estimating Disease Risk Associated Mutated Genes in Family-Based Designs, Human Heredity 66, 238-251. Choi, Y.-H. and Briollais (2011) An EM Composite Likelihood Approach for Multistage Sampling of Family Data with Missing Genetic Covariates, Statistica Sinica 21, 231-253. ## See Also `simfam`, `summary.simfam`, `plot.simfam`, `simfam2`, `summary.simfam2`, `plot.simfam2`, `simfam_tvc`, `summary.simfam_tvc`, `plot.simfam_tvc`, `penplot`, `carrierprob`, `penmodel`, `penmodelEM`, `print.penmodel`, `summary.penmodel`,`print.summary.penmodel`, `plot.penmodel`, `simfam_cmp`, `summary.simfam_cmp`, `plot.simfam_cmp`, `penplot_cmp`, `penmodel_cmp`, `print.penmodel_cmp`, `summary.penmodel_cmp`, `print.summary.penmodel_cmp`, `plot.penmodel_cmp` ## Examples ```r ## Not run: # Example1: Simulate family data set.seed(4321) fam <- simfam(N.fam = 100, design = "pop+", variation = "none", base.dist = "Weibull", base.parms = c(0.01, 3), vbeta = c(-1.13, 2.35), allelefreq = 0.02) # summary of simulated family data summary(fam) # Pedigree plots for family 1 and 2 plot(fam, famid = c(1,2)) # penetrance function plots given model parameter values for Weibull baseline penplot(base.parms = c(0.01, 3), vbeta = c(-1.3, 2.35), base.dist = "Weibull", variation = "none", agemin = 20) # model fit of family data fit <- penmodel(Surv(time, status) ~ gender + mgene, cluster = "famID", design = "pop+", parms=c(0.01, 3, -1.13, 2.35), data = fam, base.dist = "Weibull", robust = TRUE) # summary of estimated model parameters and penetrance estimates summary(fit) # penetrance curves useful for model checking plot(fit) ## Example 2: Simulate family data from a correlated frailty model # with Kinship and IBD matrices given pedigree data. # Inputdata and IBD matrix should be provided; # Inputdata was generated as an example using simfam. data <- simfam(N.fam = 10, design = "noasc", variation = "none", base.dist = "Weibull", base.parms = c(0.016, 3), vbeta = c(1, 1)) IBDmatrix <- diag(1, dim(data)[1]) data <- data[ , c(1:7, 11, 14)] fam2 <- simfam2(inputdata = data, IBD = IBDmatrix, design = "pop", variation = c("kinship","IBD"), depend = c(1, 1), base.dist = "Weibull", base.parms = c(0.016, 3), var_names = c("gender", "mgene"), vbeta = c(1,1), agemin=20) summary(fam2) ### Example 3: Simulate correlated competing risks family data set.seed(4321) fam3 <- simfam_cmp(N.fam = 200, design = "pop+", variation = "frailty", base.dist = "Weibull", frailty.dist = "cgamma", depend=c(1, 2, 0.5), allelefreq = 0.02, base.parms = list(c(0.01, 3), c(0.01, 3)), vbeta = list(c(-1.13, 2.35), c(-1, 2))) # summary of simulated family data summary(fam3) # Pedigree plots for family 1 plot(fam3, famid = 1) # penetrance function plot for event 1 given model parameter values for Weibull baseline penplot_cmp(event = 1, base.parms = list(c(0.01, 3), c(0.01, 3)), vbeta = list(c(-1.3, 2.35), c(-1, 2)), base.dist = "Weibull", variation = "frailty", frailty.dist = "cgamma", depend=c(1,2,0.5), agemin = 20) # Fitting shared correlated gamma frailty Penetrance model for simulated competing risk data fit3 <- penmodel_cmp( formula1 = Surv(time, status==1) ~ gender + mgene, formula2 = Surv(time, status==2) ~ gender + mgene, cluster = "famID", gvar = "mgene", design = "pop+", parms = list(c(0.01, 3, -1, 2), c(0.01, 3, -1, 2), c(0.5, 1, 0.5)), base.dist = "Weibull", frailty.dist = "cgamma", data = fam2, robust = TRUE) # Summary of the model parameter estimates from the model fit summary(fit3) # Plot the lifetime penetrance curves with 95 # gender and mutation status groups along with their nonparametric penetrance curves # based on data excluding probands. plot(fit3, add.CIF = TRUE, conf.int = TRUE, MC = 100) ### Example 4: Simulate family data with a time-varying covariate set.seed(4321) fam4 <- simfam_tvc(N.fam = 10, design = "pop", variation = "frailty", base.dist = "Weibull", frailty.dist = "gamma", depend = 1, add.tvc = TRUE, tvc.type = "CO", tvc.range = c(30,60), tvc.parms = c(1, 0.1, 0), allelefreq = 0.02, base.parms = c(0.01, 3), vbeta = c(-1.13, 2.35)) summary(fam4) ## End(Not run) ```

FamEvent-package