simfam_c: Generate familial competing risks data
In FamEvent: Family Age-at-Onset Data Simulation and Penetrance Estimation
simfam_c R Documentation
Generate familial competing risks data
Description
Generates familial competing risks data for specified study design, genetic model and source of residual familial correlation; the generated data frame also contains family structure (individual's id, father id, mother id, relationship to proband, generation), gender, current age, genotypes of major or second genes. Similar to the simfam function, except with the addition of the competing option, which provides competing risks data when competing = TURE.
Usage
simfam_c(N.fam, design = "pop+", variation = "none", interaction = FALSE, depend = NULL,
base.dist = c("Weibull", "Weibull"), frailty.dist = "none",
base.parms=list(c(0.016, 3),c(0.016, 3)),
vbeta=list(c(-1.13, 2.35), c(-1, 2)), competing=TRUE,
allelefreq = c(0.02, 0.2), dominant.m = TRUE, dominant.s = TRUE,
mrate = 0, hr = 0, probandage = c(45, 2), agemin = 20, agemax = 100)
Arguments
N.fam
Number of families to generate.
design
Family based study design used in the simulations. Possible choices are: "pop", "pop+", "cli", "cli+" or "twostage", where "pop" is for the population-based design that families are ascertained by affected probands, "pop+" is similar to "pop" but with mutation carrier probands, "cli" is for the clinic-based design that includes affected probands with at least one parent and one sib affected, "cli+" is similar to "cli" but with mutation carrier probands and "twostage" for two-stage design that randomly samples families from the population in the first stage and oversamples high risk families in the second stage that include at least two affected members in the family. Default is "pop+".
variation
Source of residual familial correlation. Possible choices are: "frailty" for frailty shared within families, "secondgene" for second gene variation, or "none" for no residual familial correlation. Default is "none".
interaction
Logical; if TRUE, allows the interaction between gender and mutation status.
For competing=TRUE, two logical values should be specified for each event; if only one logical value is provided, the same logical value will be assumed for both event.
Default is FALSE.
depend
Inverse of variance for the frailty distribution. Dependence within families decreases with depend value. Default is NULL. Positive real values should be specified when variation="frailty". With competing = TRUE, two values shoud be specified for each event when frailty.dist = "gamma" or frailty.dist = "lognormal", three values should be specified with codefrailty.dist = "cgamma" or frailty.dist = "clognormal". The first two values represent the inverse of variance for each event and the thir value represents the correlation between the two events.
base.dist
Choice of baseline hazard distribution. Possible choices are: "Weibull", "loglogistic", "Gompertz", "lognormal" "gamma", "logBurr". Default is "Weibull". When competing = TRUE, two distributions should be specified for each event. If only one distribution is specified, the same distribution will be assumed for both events.
frailty.dist
Choice of frailty distribution. Possible choices are: "gamma" or "lognormal" when variation="frailty". Default is NULL.
When competing = TRUE, possible choices are "gamma" for independent gamma, "lognormal" for independent lognormal, "cgamma" for correlated gamma, or "clognormal" for correlated lognormal distribution.
base.parms
Vector of parameter values for the specified baseline hazard function. base.parms=c(lambda, rho) should be specified for base.dist="Weibull", "loglogistic", "Gompertz", "gamma", and "lognormal". For base.dist="logBurr", three parameters should be specified base.parms = c(lambda, rho, eta).
When codecompeting = TRUE, list of two vectors of baseline parameters for each event should be specified. For example, base.parms=list(c(lambda1, rho1), c(lambda2, rho2)) should be specified for base.dist=c("Weibull", "Weibull").
vbeta
Vector of regression coefficients for gender, majorgene, interaction between gender and majorgene (if interaction = TRUE), and secondgene (if variation = "secondgene").
When codecompeting = TRUE, list of two vectors of regression coefficients for each event should be specified.
competing
Logical; if TRUE, allows to generate two competing events. Default is TRUE.
allelefreq
Vector of population allele frequencies of major and second disease gene alleles. Frequencies must be between 0 and 1. Default frequencies are 0.02 for major gene allele and 0.2 for second gene allele, allelefreq = c(0.02, 0.2).
dominant.m
Logical; if TRUE, the genetic model of major gene is dominant, otherwise recessive.
dominant.s
Logical; if TRUE, the genetic model of second gene is dominant, otherwise recessive.
mrate
Proportion of missing genotypes, value between 0 and 1. Default value is 0.
hr
Proportion of high risk families, which include at least two affected members, to be sampled from the two stage sampling. This value should be specified when design="twostage". Default value is 0. Value should lie between 0 and 1.
probandage
Vector of mean and standard deviation for the proband age. Default values are mean of 45 years and standard deviation of 2 years, probandage = c(45, 2).
agemin
Minimum age of disease onset or minimum age. Default is 20 years of age.
agemax
Maximum age of disease onset or maximum age. Default is 100 years of age.
Details
The design argument defines the type of family based design to be simulated. Two variants of the population-based and clinic-based design can be chosen: "pop" when proband is affected, "pop+" when proband is affected mutation carrier, "cli" when proband is affected and at least one parent and one sibling are affected, "cli+" when proband is affected mutation-carrier and at least one parent and one sibling are affected. The two-stage design, "twostage", is used to oversample high risk families, where the proportion of high risks families to include in the sample is specified by hr. High risk families often include multiple (at least two) affected members in the family.
The ages at onset are generated from the following penetrance models depending on the choice of variation = "none", "frailty", "secondgene".. When variation = "none", the ages at onset are independently generated from the proportional hazard model conditional on the gender and carrier status of major gene mutation, X = c(xs, xg).
The ages at onset correlated within families are generated from the shared frailty model (codevariation = "frailty") or the two-gene model (codevariation = "secondene"), where the residual familial correlation is induced by a frailty or a second gene, respectively, shared within the family.
The proportional hazard model
h(t|X) = h0(t - t0) exp(βs * xs + βg * xg),
where h0(t) is the baseline hazard function, t0 is a minimum age of disease onset, xx and xg indicate male (1) or female (0) and carrier (1) or non-carrier (0) of a main gene of interest, respectively.
The shared frailty model
h(t|X,Z) = h0(t - t0) Z exp(βs * xs + βg * xg),
where h0(t) is the baseline hazard function, t0 is a minimum age of disease onset, Z represents a frailty shared within families and follows either a gamma or log-normal distribution, xx and xg indicate male (1) or female (0) and carrier (1) or non-carrier (0) of a main gene of interest, respectively.
The two-gene model
h(t|X) = h0(t - t0) Z exp(βs * xs + β1 * x2 + β2 * x2),
where x1, x2 indicate carriers (1) and non-carriers (0) of a major gene and of second gene mutation, respectively.
Competing risk model
Event 1:
h1(t|X,Z) = h01(t - t0) Z1 exp(βs1 * xs + βg1 * xg),
Event 2:
h2(t|X,Z) = h02(t - t0) Z2 exp(βs2 * xs + βg2 * xg),
where h01(t) and h02(t) are the baseline hazard functions for event 1 and event 2, respectively, t0 is a minimum age of disease onset, Z1 and Z2 are frailties shared within families for each event and follow either a gamma, log-normal, correlateg gamma, or correlated log-normal distributions, xx and xg indicate male (1) or female (0) and carrier (1) or non-carrier (0) of a main gene of interest, respectively.
Choice of frailty distributions for competing risk models
frailty.dist = "gamma" shares the frailties within families generated from a gamma distribution independently for each competing event, where
Zj follows Gamma(kj, 1/kj).
frailty.dist = "lognormal" shares the frailties within families generated from a log-normal distribution independently for each competing event, where
Zj follows log-normal distribution with mean 0 and variance (1/kj.
frailty.dist = "cgamma" shares the frailties within families generated from a correlated gamma distribution to allow the frailties between two events to be correlated, where the correlated gamma frailties (Z1, Z2) are generated with three independent gamma frailties (Y0, Y1, Y2) as follows:
Z1 = k0/(k0 + k1) Y0 + Y1
Z2 = k0/(k0 + k2) Y0 + Y2
where Y0 from Gamma(k0, 1/k0);
Y1 from Gamma(k1, 1/(k0 + k1));
Y2 from Gamma(k2, 1/(k0 + k2)).
frailty.dist = "clognormal" shares the frailties within families generated from a correlated log-normal distribution where
log(Zj) follows a normal distribution with mean 0, variance 1/kj and correlation between two events k0.
depend should specify the values of related frailty parameters: c(k1, k2) with frailty.dist = "gamma" or frailty.dist = "lognormal"; c(k1, k2, k0) for frailty.dist = "cgamma" or frailty.dist = "clognormal".
The current ages for each generation are simulated assuming normal distributions. However, the probands' ages are generated using a left truncated normal distribution as their ages cannot be less than the minimum age of onset. The average age difference between each generation and their parents is specified as 20 years apart.
Note that simulating family data under the clinic-based designs ("cli" or "cli+") or the two-stage design can be slower since the ascertainment criteria for the high risk families are difficult to meet in such settings. Especially, "cli" design could be slower than "cli+" design since the proband's mutation status is randomly selected from a disease population in "cli" design, so his/her family members are less likely to be mutation carriers and have less chance to be affected, whereas the probands are all mutation carriers, their family members have higher chance to be carriers and affected by disease. Therefore, "cli" design requires more iterations to sample high risk families than "cli+" design. All designs simulations that include variation = "frailty" could be also slower in order to generate families with specific familial correlations induced by the chosen frailty distribution.
Value
Returns an object of class 'simfam', a data frame which contains:
famID
Family identification (ID) numbers.
indID
Individual ID numbers.
gender
Gender indicators: 1 for males, 0 for females.
motherID
Mother ID numbers.
fatherID
Father ID numbers.
proband
Proband indicators: 1 if the individual is the proband, 0 otherwise.
generation
Individuals generation: 1=parents of probands,2=probands and siblings, 3=children of probands and siblings.
majorgene
Genotypes of major gene: 1=AA, 2=Aa, 3=aa where A is disease gene.
secondgene
Genotypes of second gene: 1=BB, 2=Bb, 3=bb where B is disease gene.
ageonset
Ages at disease onset in years.
currentage
Current ages in years.
time
Ages at disease onset for the affected or ages of last follow-up for the unaffected.
status
Disease statuses: 1 for affected, 0 for unaffected (censored).
When competing = TRUE, 1 for affected by event 1, 2 for affected by event 2, 0 for unaffected (censored).
mgene
Major gene mutation indicators: 1 for mutated gene carriers, 0 for mutated gene noncarriers, or NA if missing.
relation
Family members' relationship with the proband:
1 Proband (self)
2 Brother or sister
3 Son or daughter
4 Parent
5 Nephew or niece
6 Spouse
7 Brother or sister in law
fsize
Family size including parents, siblings and children of the proband and the siblings.
naff
Number of affected members within family. When competing = TRUE, naff represents the number of members affected by either event 1 or 2 within family.
df1
Number of members affected by event 1 within family when competing = TRUE.
df2
Number of members affected by event 2 within family when competing = TRUE.
weight
Sampling weights.
Author(s)
Yun-Hee Choi
References
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., 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., 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
summary.simfam_c, plot.simfam_c, penplot_c
Examples
## Example 1: simulate competing risk family data from pop+ design using
# Weibull distribution for both baseline hazards and inducing
# residual familial correlation through a correlated gamma frailty.
set.seed(4321)
fam <- simfam_c(N.fam = 10, 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)))
head(fam)
## Not run:
famID indID gender motherID fatherID proband generation majorgene secondgene ageonset
1 1 1 1 0 0 0 1 3 0 124.23752
2 1 2 0 0 0 0 1 2 0 54.66936
3 1 3 0 2 1 1 2 2 0 32.75208
4 1 4 1 0 0 0 0 3 0 136.44926
5 1 11 1 3 4 0 3 3 0 71.53672
6 1 12 1 3 4 0 3 3 0 152.47073
currentage time status true_status mgene relation fsize naff df1 df2 weight
1 65.30602 65.30602 0 2 0 4 25 2 1 1 1
2 68.62107 54.66936 1 1 1 4 25 2 1 1 1
3 47.07842 32.75208 2 2 1 1 25 2 1 1 1
4 45.09295 45.09295 0 2 0 6 25 2 1 1 1
5 25.32819 25.32819 0 1 0 3 25 2 1 1 1
6 22.95059 22.95059 0 2 0 3 25 2 1 1 1
## End(Not run)
summary(fam)
plot(fam, famid = 1) # pedigree plots for family with ID = 1
FamEvent documentation built on Nov. 17, 2022, 5:06 p.m.
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| simfam_c | R Documentation |
Generate familial competing risks data
Description
Generates familial competing risks data for specified study design, genetic model and source of residual familial correlation; the generated data frame also contains family structure (individual's id, father id, mother id, relationship to proband, generation), gender, current age, genotypes of major or second genes. Similar to the simfam function, except with the addition of the competing option, which provides competing risks data when competing = TURE.
Usage
simfam_c(N.fam, design = "pop+", variation = "none", interaction = FALSE, depend = NULL,
base.dist = c("Weibull", "Weibull"), frailty.dist = "none",
base.parms=list(c(0.016, 3),c(0.016, 3)),
vbeta=list(c(-1.13, 2.35), c(-1, 2)), competing=TRUE,
allelefreq = c(0.02, 0.2), dominant.m = TRUE, dominant.s = TRUE,
mrate = 0, hr = 0, probandage = c(45, 2), agemin = 20, agemax = 100)
Arguments
N.fam |
Number of families to generate. |
design |
Family based study design used in the simulations. Possible choices are: |
variation |
Source of residual familial correlation. Possible choices are: |
interaction |
Logical; if |
depend |
Inverse of variance for the frailty distribution. Dependence within families decreases with depend value. Default is |
base.dist |
Choice of baseline hazard distribution. Possible choices are: |
frailty.dist |
Choice of frailty distribution. Possible choices are: |
base.parms |
Vector of parameter values for the specified baseline hazard function. |
vbeta |
Vector of regression coefficients for gender, majorgene, interaction between gender and majorgene (if |
competing |
Logical; if |
allelefreq |
Vector of population allele frequencies of major and second disease gene alleles. Frequencies must be between 0 and 1. Default frequencies are 0.02 for major gene allele and 0.2 for second gene allele, |
dominant.m |
Logical; if |
dominant.s |
Logical; if |
mrate |
Proportion of missing genotypes, value between 0 and 1. Default value is 0. |
hr |
Proportion of high risk families, which include at least two affected members, to be sampled from the two stage sampling. This value should be specified when |
probandage |
Vector of mean and standard deviation for the proband age. Default values are mean of 45 years and standard deviation of 2 years, |
agemin |
Minimum age of disease onset or minimum age. Default is 20 years of age. |
agemax |
Maximum age of disease onset or maximum age. Default is 100 years of age. |
Details
The design argument defines the type of family based design to be simulated. Two variants of the population-based and clinic-based design can be chosen: "pop" when proband is affected, "pop+" when proband is affected mutation carrier, "cli" when proband is affected and at least one parent and one sibling are affected, "cli+" when proband is affected mutation-carrier and at least one parent and one sibling are affected. The two-stage design, "twostage", is used to oversample high risk families, where the proportion of high risks families to include in the sample is specified by hr. High risk families often include multiple (at least two) affected members in the family.
The ages at onset are generated from the following penetrance models depending on the choice of variation = "none", "frailty", "secondgene".. When variation = "none", the ages at onset are independently generated from the proportional hazard model conditional on the gender and carrier status of major gene mutation, X = c(xs, xg).
The ages at onset correlated within families are generated from the shared frailty model (codevariation = "frailty") or the two-gene model (codevariation = "secondene"), where the residual familial correlation is induced by a frailty or a second gene, respectively, shared within the family.
The proportional hazard model
h(t|X) = h0(t - t0) exp(βs * xs + βg * xg),
where h0(t) is the baseline hazard function, t0 is a minimum age of disease onset, xx and xg indicate male (1) or female (0) and carrier (1) or non-carrier (0) of a main gene of interest, respectively.
The shared frailty model
h(t|X,Z) = h0(t - t0) Z exp(βs * xs + βg * xg),
where h0(t) is the baseline hazard function, t0 is a minimum age of disease onset, Z represents a frailty shared within families and follows either a gamma or log-normal distribution, xx and xg indicate male (1) or female (0) and carrier (1) or non-carrier (0) of a main gene of interest, respectively.
The two-gene model
h(t|X) = h0(t - t0) Z exp(βs * xs + β1 * x2 + β2 * x2),
where x1, x2 indicate carriers (1) and non-carriers (0) of a major gene and of second gene mutation, respectively.
Competing risk model
Event 1:
h1(t|X,Z) = h01(t - t0) Z1 exp(βs1 * xs + βg1 * xg),
Event 2:
h2(t|X,Z) = h02(t - t0) Z2 exp(βs2 * xs + βg2 * xg),
where h01(t) and h02(t) are the baseline hazard functions for event 1 and event 2, respectively, t0 is a minimum age of disease onset, Z1 and Z2 are frailties shared within families for each event and follow either a gamma, log-normal, correlateg gamma, or correlated log-normal distributions, xx and xg indicate male (1) or female (0) and carrier (1) or non-carrier (0) of a main gene of interest, respectively.
Choice of frailty distributions for competing risk models
frailty.dist = "gamma" shares the frailties within families generated from a gamma distribution independently for each competing event, where
Zj follows Gamma(kj, 1/kj).
frailty.dist = "lognormal" shares the frailties within families generated from a log-normal distribution independently for each competing event, where
Zj follows log-normal distribution with mean 0 and variance (1/kj.
frailty.dist = "cgamma" shares the frailties within families generated from a correlated gamma distribution to allow the frailties between two events to be correlated, where the correlated gamma frailties (Z1, Z2) are generated with three independent gamma frailties (Y0, Y1, Y2) as follows:
where Y0 from Gamma(k0, 1/k0);
Y1from Gamma(k1, 1/(k0 + k1));
Y2from Gamma(k2, 1/(k0 + k2)).
frailty.dist = "clognormal" shares the frailties within families generated from a correlated log-normal distribution where
log(Zj) follows a normal distribution with mean 0, variance 1/kj and correlation between two events k0.
depend should specify the values of related frailty parameters: c(k1, k2) with frailty.dist = "gamma" or frailty.dist = "lognormal"; c(k1, k2, k0) for frailty.dist = "cgamma" or frailty.dist = "clognormal".
The current ages for each generation are simulated assuming normal distributions. However, the probands' ages are generated using a left truncated normal distribution as their ages cannot be less than the minimum age of onset. The average age difference between each generation and their parents is specified as 20 years apart.
Note that simulating family data under the clinic-based designs ("cli" or "cli+") or the two-stage design can be slower since the ascertainment criteria for the high risk families are difficult to meet in such settings. Especially, "cli" design could be slower than "cli+" design since the proband's mutation status is randomly selected from a disease population in "cli" design, so his/her family members are less likely to be mutation carriers and have less chance to be affected, whereas the probands are all mutation carriers, their family members have higher chance to be carriers and affected by disease. Therefore, "cli" design requires more iterations to sample high risk families than "cli+" design. All designs simulations that include variation = "frailty" could be also slower in order to generate families with specific familial correlations induced by the chosen frailty distribution.
Value
Returns an object of class 'simfam', a data frame which contains:
famID |
Family identification (ID) numbers. | ||||||||||||||
indID |
Individual ID numbers. | ||||||||||||||
gender |
Gender indicators: 1 for males, 0 for females. | ||||||||||||||
motherID |
Mother ID numbers. | ||||||||||||||
fatherID |
Father ID numbers. | ||||||||||||||
proband |
Proband indicators: 1 if the individual is the proband, 0 otherwise. | ||||||||||||||
generation |
Individuals generation: 1=parents of probands,2=probands and siblings, 3=children of probands and siblings. | ||||||||||||||
majorgene |
Genotypes of major gene: 1=AA, 2=Aa, 3=aa where A is disease gene. | ||||||||||||||
secondgene |
Genotypes of second gene: 1=BB, 2=Bb, 3=bb where B is disease gene. | ||||||||||||||
ageonset |
Ages at disease onset in years. | ||||||||||||||
currentage |
Current ages in years. | ||||||||||||||
time |
Ages at disease onset for the affected or ages of last follow-up for the unaffected. | ||||||||||||||
status |
Disease statuses: 1 for affected, 0 for unaffected (censored).
When | ||||||||||||||
mgene |
Major gene mutation indicators: 1 for mutated gene carriers, 0 for mutated gene noncarriers, or | ||||||||||||||
relation |
Family members' relationship with the proband:
| ||||||||||||||
fsize |
Family size including parents, siblings and children of the proband and the siblings. | ||||||||||||||
naff |
Number of affected members within family. When | ||||||||||||||
df1 |
Number of members affected by event 1 within family when | ||||||||||||||
df2 |
Number of members affected by event 2 within family when | ||||||||||||||
weight |
Sampling weights. |
Author(s)
Yun-Hee Choi
References
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., 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., 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
summary.simfam_c, plot.simfam_c, penplot_c
Examples
## Example 1: simulate competing risk family data from pop+ design using
# Weibull distribution for both baseline hazards and inducing
# residual familial correlation through a correlated gamma frailty.
set.seed(4321)
fam <- simfam_c(N.fam = 10, 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)))
head(fam)
## Not run:
famID indID gender motherID fatherID proband generation majorgene secondgene ageonset
1 1 1 1 0 0 0 1 3 0 124.23752
2 1 2 0 0 0 0 1 2 0 54.66936
3 1 3 0 2 1 1 2 2 0 32.75208
4 1 4 1 0 0 0 0 3 0 136.44926
5 1 11 1 3 4 0 3 3 0 71.53672
6 1 12 1 3 4 0 3 3 0 152.47073
currentage time status true_status mgene relation fsize naff df1 df2 weight
1 65.30602 65.30602 0 2 0 4 25 2 1 1 1
2 68.62107 54.66936 1 1 1 4 25 2 1 1 1
3 47.07842 32.75208 2 2 1 1 25 2 1 1 1
4 45.09295 45.09295 0 2 0 6 25 2 1 1 1
5 25.32819 25.32819 0 1 0 3 25 2 1 1 1
6 22.95059 22.95059 0 2 0 3 25 2 1 1 1
## End(Not run)
summary(fam)
plot(fam, famid = 1) # pedigree plots for family with ID = 1
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