R: Generate familial time-to-event data with a time-varying...

simfam_tvc {FamEvent}

R Documentation

Generate familial time-to-event data with a time-varying covariate

Description

Generates familial time-to-event data with a time-varying covariate 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.

Usage

simfam_tvc(N.fam, design = "pop", variation = "none", interaction = FALSE, 
       add.x = FALSE, x.dist = NULL, x.parms = NULL, depend = NULL, 
       add.tvc = FALSE, tvc.type = "PE", tvc.range = NULL, tvc.parms = 1,
       base.dist = "Weibull", frailty.dist = NULL, base.parms = c(0.016, 3), 
       vbeta = c(1, 1), 
       allelefreq = 0.02, 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+"`, `"twostage"`, or `"noasc"`, 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, `"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, and `"noasc"` for no ascertainment correction that families are from simple random sampling. Default is `"pop"`.
`variation`	Source of residual familial correlation. Possible choices are: `"frailty"` for frailty shared within families, `"secondgene"` for second gene variation, `"kinship"` for correlated frailties within families with kinship matrix, or `"none"` for no residual familial correlation. Default is `"none"`.
`interaction`	Logical; if `TRUE`, allows the interaction between gender and mutation status. Default is `FALSE`.
`add.x`	Logical; if `TRUE`, generates a covariate in addition to gender and majorgene. Default is `FALSE`.
`x.dist`	Distribution of the covairate. Possible choices to generate the covariate are: `"normal"` from normal distribution and `"binomial"` from binominal distribution. Default is `NULL`.
`x.parms`	Parameter values for the specified distribution of the covariate. `x.parms = c(mean, sd)` should be specified for `x.dist = "normal"` and `x.parms = c(size, probs)` should be specified for `"binomial"`; when `size = 1`, it generates binary covariate. Default is `NULL`.
`depend`	Inverse of variance of the frailty distribution. Dependence within families decreases with depend value. Default is `NULL`. Value should be specified as a positive real number when `variation = "frailty"` or `variation = "kinship"`.
`add.tvc`	Logical; if `TRUE`, generates a time varying covariate. Default is `FALSE`.
`tvc.type`	Choice of time-varying covariate model. Possible choices are: `"PE"` and `"CO"`. Default is `"PE"`.
`tvc.range`	Range of ages at which the time-varying covariate occurs. Default is `NULL`.
`tvc.parms`	Vector of parameter values used for the time-varying covariate model. Default value is 1.
`base.dist`	Choice of baseline hazard distribution. Possible choices are: `"Weibull"`, `"loglogistic"`, `"Gompertz"`, `"lognormal"` `"gamma"`, `"logBurr"`. Default is `"Weibull"`.
`frailty.dist`	Choice of frailty distribution. Possible choices are: `"gamma"` or `"lognormal"` when `variation="frailty"`. Default is `NULL`.
`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)`. Default value is `base.parms = c(0.016, 3)` for `base.dist = "Weibull"`.
`vbeta`	Vector of regression coefficients for gender, majorgene, interaction between gender and majorgene (if `interaction = TRUE`), secondgene (if `variation = "secondgene"`), and additional covariate (if `add.x = TRUE`).
`allelefreq`	Population allele frequencies of major disease gene. Value should be between 0 and 1. Vector of population allele frequencies of major and second disease genes should be provided when `variation = "secondgene"`. Default value is `allelefreq = 0.02`.
`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

Time-varying covariate

When add.tvc = TRUE, the time at which the time-varying covariate (TVC) occurs, tvc.age, is generated from a uniform distribution with the range specified by tvc.range. A vector of minimum and maximum ages for the TVC should be specified in tve.range. When tvc.range = NULL, agemin and agemax are used as the range. In addition, tvc.type should be either "PE" or "CO" and the parameter values for the specified TVC type should be provided in tvc.parms.

tvc.type = "PE" represents a permanent exposure model for TVC which assumes that the effect of the TVC stays constant after tvc.age. The tvc.parms for the PE model should be specified as a single value, which represents log hazard ratio.

tvc.type = "CO" represents the Cox and Oaks model for TVC which assumes that the effect of the TVC decays exponentially over time in the form β exp(-(t - t*) η) + η₀, where t* is the time at which the TVC occurs. The tvc.parms for the CO model should be specified by a vector of three parameters consisting of c(beta, eta, eta0).

Family-based study design

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. design = "noasc" is to be used for no ascertainment correction.

Penetrance model

The ages at onset are generated from the following penetrance models depending on the choice of variation = "none", "frailty", "secondgene", "kinship".. 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(x_s, x_g).

The ages at onset correlated within families are generated from the shared frailty model (variation = "frailty") , the correlated shared frailty model with kinship matrix (variation = "kinship"), or the two-gene model (variation = "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(β_s * x_s + β_g * x_g),

where h₀(t) is the baseline hazard function, t₀ is a minimum age of disease onset, x_x and x_g 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(β_s * x_s + β_g * x_g),

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, x_x and x_g indicate male (1) or female (0) and carrier (1) or non-carrier (0) of a main gene of interest, respectively.

The correlated shared frailty model with kinship matrix

h(t|X,Z) = h₀(t - t₀) Z exp(β_s * x_s + β_g * x_g),

where h₀(t) is the baseline hazard function, t₀ is a minimum age of disease onset, Z represents a vector of frailties following a multivariate log-normal distribution with mean 0 and variance 2*K*depend, where K represents the kinship matrix, x_x and x_g 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(β_s * x_s + β₁ * x₂ + β₂ * x₂),

where x₁, x₂ indicate carriers (1) and non-carriers (0) of a major gene and of second gene mutation, respectively.

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.

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).

mgene

Major gene mutation indicators: 1 for mutated gene carriers, 0 for mutated gene noncarriers, or NA if missing.

newx

Additional covariate when add.x = TRUE.

tvc.age

Age at which the time-varying covariate occurs when add.tvc = TRUE.

tvc.status

TVC status: 1 if tvc.age < time, 0 otherwise.

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 in family.

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., 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.

Examples


## Example: simulate family data with TVC based on CO model.

set.seed(4321)
fam <- 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))

## Not run: 
> head(fam) 
  famID indID gender motherID fatherID proband generation majorgene secondgene ageonset
1     1     1      1        0        0       0          1         2          0 61.80566
2     1     2      0        0        0       0          1         3          0 61.56996
3     1     3      0        2        1       1          2         2          0 39.42050
4     1     4      1        0        0       0          0         3          0 90.17320
5     1    13      0        3        4       0          3         3          0 51.49538
6     1    14      0        3        4       0          3         3          0 75.97238
  currentage     time status mgene  tvc.age tvc.status relation fsize naff weight
1   68.26812 61.80566      1     1 59.16387          1        4    29    3      1
2   68.60174 61.56996      1     0 39.45786          1        4    29    3      1
3   47.05410 39.42050      1     1 35.01941          1        1    29    3      1
4   44.86501 44.86501      0     0 58.67013          0        6    29    3      1
5   22.73075 22.73075      0     0 30.19254          0        3    29    3      1
6   22.71399 22.71399      0     0 40.66258          0        3    29    3      1

> summary(fam) 
Study design:           pop: population-based study with affected probands 
Baseline distribution:  Weibull 
Frailty distribution:   gamma 
Number of families:                     10 
Average number of affected per family:  3.1 
Average number of carriers per family:  3.4 
Average family size:                    16.3 
Average age of onset for affected:      48.19 
Average number of TVC event per family: 4 
Sampling weights used:                  1

## End(Not run)

[Package FamEvent version 3.2 Index]