simulate_under_LTM simulates families and thresholds under
the liability threshold model for a given family structure and a
variable number of phenotypes.Please note that it is not possible
to simulate different family structures.
simulate_under_LTM(
fam_vec = c("m", "f", "s1", "mgm", "mgf", "pgm", "pgf"),
n_fam = NULL,
add_ind = TRUE,
h2 = 0.5,
genetic_corrmat = NULL,
full_corrmat = NULL,
phen_names = NULL,
n_sim = 1000,
pop_prev = 0.1
)A vector of strings holding the different family members. All family members must be represented by strings from the following list:
m (Mother)
f (Father)
c[0-9]*.[0-9]* (Children)
mgm (Maternal grandmother)
mgf (Maternal grandfather)
pgm (Paternal grandmother)
pgf (Paternal grandfather)
s[0-9]* (Full siblings)
mhs[0-9]* (Half-siblings - maternal side)
phs[0-9]* (Half-siblings - paternal side)
mau[0-9]* (Aunts/Uncles - maternal side)
pau[0-9]* (Aunts/Uncles - paternal side).
Defaults to c("m","f","s1","mgm","mgf","pgm","pgf").
A named vector holding the desired number of family members.
See setNames.
All names must be picked from the list mentioned above. Defaults to NULL.
A logical scalar indicating whether the genetic
component of the full liability as well as the full
liability for the underlying target individual should be included in
the covariance matrix. Defaults to TRUE.
Either a number or a numeric vector holding the liability-scale
heritability(ies) for one or more phenotypes. All entries in h2 must
be non-negative. Note that under the liability threshold model, the
heritabilities must also be at most 1. Defaults to 0.5.
Either NULL or a numeric matrix holding the
genetic correlations between the desired phenotypes. Must be specified, if
length(h2)\(>0\), and will be ignored if h2 is a number.
All diagonal entries in genetic_corrmat must be equal to one,
while all off-diagonal entries must be between -1 and 1. In addition,
the matrix must be symmetric.
Defaults to NULL.
Either NULL or a numeric matrix holding the
full correlations between the desired phenotypes. Must be specified, if
length(h2)\(>0\), and will be ignored if h2 is a number.
All diagonal entries in full_corrmat must be equal to one, while
all off-diagonal entries must be between -1 and 1. In addition, the
matrix must be symmetric.
Defaults to NULL.
Either NULL or character vector holding the
phenotype names. These names will be used to create the row and column
names for the covariance matrix. Must be specified, if length(h2)
\(> 0\), and will be ignored if h2 is a number.
If it is not specified, the names will default to phenotype1, phenotype2, etc.
Defaults to NULL.
A positive number representing the number of simulations. Defaults to 1000.
Either a number or a numeric vector holding the population
prevalence(s), i.e. the overall prevalence(s) in the population.
All entries in pop_prev must be positive
and smaller than 1. Defaults to 0.1.
If either fam_vec or n_fam is used as the argument,
if it is of the required format, if the liability-scale heritability h2
is a number satisfying \(0 \leq h^2\), n_sim is a strictly positive number,
and pop_prev is a positive number that is at most one,
then the output will be a list containing two tibbles.
The first tibble, sim_obs, holds the simulated liabilities, the disease
status and the current age/age-of-onset for all family members in each of the
n_sim families.
The second tibble, thresholds, holds the family identifier, the personal
identifier, the role (specified in fam_vec or n_fam) as well as the lower and
upper thresholds for all individuals in all families. Note that this tibble has
the format required in estimate_liability.
If either fam_vec or n_fam is used as the argument and if it is of the
required format, if genetic_corrmat and full_corrmat are two numeric
and symmetric matrices satisfying that all diagonal entries are one and that all
off-diagonal entries are between -1 and 1, if the liability-scale heritabilities in
h2_vec are numbers satisfying \(0 \leq h^2_i\) for all \(i \in \{1,...,n_pheno\}\),
n_sim is a strictly positive number, and pop_prev is a positive numeric
vector such that all entries are at most one, then the output will be a list containing
the following lists.
The first outer list, which is named after the first phenotype in phen_names,
holds the tibble sim_obs, which holds the simulated liabilities, the
disease status and the current age/age-of-onset for all family members in each of
the n_sim families for the first phenotype.
As the first outer list, the second outer list, which is named after the second
phenotype in phen_names, holds the tibble sim_obs, which holds
the simulated liabilities, the disease status and the current age/age-of-onset
for all family members in each of the n_sim families for the second phenotype.
There is a list containing sim_obs for each phenotype in phen_names.
The last list entry, thresholds, holds the family identifier, the personal
identifier, the role (specified in fam_vec or n_fam) as well as the lower and
upper thresholds for all individuals in all families and all phenotypes.
Note that this tibble has the format required in estimate_liability.
Finally, note that if neither fam_vec nor n_fam are specified, the function
returns the disease status, the current age/age-of-onset, the lower and upper
thresholds, as well as the personal identifier for a single individual, namely
the individual under consideration (called o).
If both fam_vec and n_fam are defined, the user is asked to '
decide on which of the two vectors to use.
This function can be used to simulate the case-control status, the current
age and age-of-onset as well as the lower and upper thresholds for
a variable number of phenotypes for all family members in each of
the n_sim families.
If h2 is a number, simulate_under_LTM simulates the case-
control status, the current age and age-of-onset as well as thresholds
for a single phenotype.
However, if h2 is a numeric vector, if genetic_corrmat and
full_corrmat are two symmetric correlation matrices, and if
phen_names and pop_prev are to numeric vectors holding
the phenotype names and the population prevalences, respectively, then
simulate_under_LTM simulates the case-control status, the current
age and age-of-onset as well as thresholds for two or more (correlated)
phenotypes.
The family members can be specified using one of two possible formats.
simulate_under_LTM()
#> $sim_obs
#> # A tibble: 1,000 × 26
#> fam_ID g o m f s1 mgm mgf pgm
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 fam_ID_1 0.108 -0.521 -0.643 -0.390 0.919 -2.77 0.462 -0.885
#> 2 fam_ID_2 -0.648 -0.577 0.0365 1.16 -0.0330 -0.0978 -0.132 2.01
#> 3 fam_ID_3 0.897 0.0153 1.31 0.333 0.123 0.500 0.671 0.0854
#> 4 fam_ID_4 -1.36 -2.12 -1.96 -1.50 -1.02 0.0177 -0.433 -0.518
#> 5 fam_ID_5 -0.563 -0.151 -0.259 -0.313 -0.182 -2.15 -0.806 0.0901
#> 6 fam_ID_6 0.00290 0.166 0.383 -0.384 0.246 -0.284 1.39 0.850
#> 7 fam_ID_7 0.429 0.285 0.716 0.0402 0.659 -0.714 -1.01 -0.266
#> 8 fam_ID_8 -0.955 -0.547 -0.368 0.627 0.0231 0.690 -1.08 -1.11
#> 9 fam_ID_9 0.185 0.501 1.70 0.978 1.59 -1.11 0.0535 0.812
#> 10 fam_ID_10 0.109 -0.204 -0.126 -0.103 -0.501 1.26 0.924 -1.96
#> # ℹ 990 more rows
#> # ℹ 17 more variables: pgf <dbl>, o_status <lgl>, m_status <lgl>,
#> # f_status <lgl>, s1_status <lgl>, mgm_status <lgl>, mgf_status <lgl>,
#> # pgm_status <lgl>, pgf_status <lgl>, o_aoo <dbl>, m_aoo <dbl>, f_aoo <dbl>,
#> # s1_aoo <dbl>, mgm_aoo <dbl>, mgf_aoo <dbl>, pgm_aoo <dbl>, pgf_aoo <dbl>
#>
#> $thresholds
#> # A tibble: 8,000 × 5
#> fam_ID indiv_ID role lower upper
#> <chr> <chr> <chr> <dbl> <dbl>
#> 1 fam_ID_1 fam_ID_1_1 o -Inf 3.24
#> 2 fam_ID_2 fam_ID_2_1 o -Inf 3.45
#> 3 fam_ID_3 fam_ID_3_1 o -Inf 2.91
#> 4 fam_ID_4 fam_ID_4_1 o -Inf 2.43
#> 5 fam_ID_5 fam_ID_5_1 o -Inf 2.68
#> 6 fam_ID_6 fam_ID_6_1 o -Inf 3.17
#> 7 fam_ID_7 fam_ID_7_1 o -Inf 2.83
#> 8 fam_ID_8 fam_ID_8_1 o -Inf 2.68
#> 9 fam_ID_9 fam_ID_9_1 o -Inf 3.10
#> 10 fam_ID_10 fam_ID_10_1 o -Inf 3.38
#> # ℹ 7,990 more rows
#>
genetic_corrmat <- matrix(0.4, 3, 3)
diag(genetic_corrmat) <- 1
full_corrmat <- matrix(0.6, 3, 3)
diag(full_corrmat) <- 1
simulate_under_LTM(fam_vec = NULL, n_fam = stats::setNames(c(1,1,1,2,2),
c("m","mgm","mgf","s","mhs")))
#> $sim_obs
#> # A tibble: 1,000 × 26
#> fam_ID g o m mgm mgf s1 s2 mhs1 mhs2
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 fam_ID_1 0.0568 0.223 1.44 0.973 2.02 1.11 1.44 1.08 0.302
#> 2 fam_ID_2 0.0991 0.839 -0.709 -0.375 0.365 -1.50 0.0962 -0.908 -0.874
#> 3 fam_ID_3 0.540 0.771 1.16 -0.592 1.20 0.127 -0.159 1.09 0.974
#> 4 fam_ID_4 1.18 1.26 0.249 -1.64 0.216 -0.724 -0.260 -1.13 -1.19
#> 5 fam_ID_5 -0.0394 0.412 2.37 -1.15 -0.0778 0.446 0.688 0.940 0.268
#> 6 fam_ID_6 -0.107 0.523 -1.77 -1.93 0.840 -0.697 0.519 0.823 0.912
#> 7 fam_ID_7 -0.803 -0.638 -0.422 -1.44 -1.50 -1.44 -0.634 -2.15 0.472
#> 8 fam_ID_8 -0.136 0.212 0.783 0.521 0.514 -0.0401 0.601 0.609 -0.525
#> 9 fam_ID_9 -0.999 -1.74 -0.249 -0.212 0.0313 -0.839 -1.60 1.15 -0.221
#> 10 fam_ID_10 0.379 0.802 -0.999 -1.41 1.13 0.0237 -0.117 -0.245 -0.499
#> # ℹ 990 more rows
#> # ℹ 16 more variables: o_status <lgl>, m_status <lgl>, mgm_status <lgl>,
#> # mgf_status <lgl>, s1_status <lgl>, s2_status <lgl>, mhs1_status <lgl>,
#> # mhs2_status <lgl>, o_aoo <dbl>, m_aoo <dbl>, mgm_aoo <dbl>, mgf_aoo <dbl>,
#> # s1_aoo <dbl>, s2_aoo <dbl>, mhs1_aoo <dbl>, mhs2_aoo <dbl>
#>
#> $thresholds
#> # A tibble: 8,000 × 5
#> fam_ID indiv_ID role lower upper
#> <chr> <chr> <chr> <dbl> <dbl>
#> 1 fam_ID_1 fam_ID_1_1 o -Inf 3.45
#> 2 fam_ID_2 fam_ID_2_1 o -Inf 2.99
#> 3 fam_ID_3 fam_ID_3_1 o -Inf 3.38
#> 4 fam_ID_4 fam_ID_4_1 o -Inf 3.48
#> 5 fam_ID_5 fam_ID_5_1 o -Inf 2.95
#> 6 fam_ID_6 fam_ID_6_1 o -Inf 2.68
#> 7 fam_ID_7 fam_ID_7_1 o -Inf 2.59
#> 8 fam_ID_8 fam_ID_8_1 o -Inf 2.83
#> 9 fam_ID_9 fam_ID_9_1 o -Inf 2.91
#> 10 fam_ID_10 fam_ID_10_1 o -Inf 3.38
#> # ℹ 7,990 more rows
#>
simulate_under_LTM(fam_vec = c("m","f","s1"), n_fam = NULL, add_ind = FALSE,
genetic_corrmat = genetic_corrmat, full_corrmat = full_corrmat, n_sim = 200)
#> $sim_obs
#> # A tibble: 200 × 10
#> fam_ID m f s1 m_status f_status s1_status m_aoo f_aoo s1_aoo
#> <chr> <dbl> <dbl> <dbl> <lgl> <lgl> <lgl> <dbl> <dbl> <dbl>
#> 1 fam_ID_1 0.912 -0.832 -2.12 FALSE FALSE FALSE 56 61 31
#> 2 fam_ID_2 -1.65 -0.696 -0.0462 FALSE FALSE FALSE 47 51 22
#> 3 fam_ID_3 -0.879 -0.164 0.721 FALSE FALSE FALSE 35 32 11
#> 4 fam_ID_4 -1.86 0.502 0.464 FALSE FALSE FALSE 70 67 40
#> 5 fam_ID_5 -0.796 -0.530 0.968 FALSE FALSE FALSE 57 52 27
#> 6 fam_ID_6 0.679 1.78 1.35 FALSE TRUE TRUE 57 56 76
#> 7 fam_ID_7 -0.569 1.24 0.987 FALSE FALSE FALSE 59 64 40
#> 8 fam_ID_8 -0.831 2.26 1.01 FALSE TRUE FALSE 47 44 23
#> 9 fam_ID_9 0.315 0.304 -0.223 FALSE FALSE FALSE 38 37 15
#> 10 fam_ID_… -0.214 1.31 0.333 FALSE TRUE FALSE 64 84 36
#> # ℹ 190 more rows
#>
#> $thresholds
#> # A tibble: 600 × 5
#> fam_ID indiv_ID role lower upper
#> <chr> <chr> <chr> <dbl> <dbl>
#> 1 fam_ID_1 fam_ID_1_1 m -Inf 1.78
#> 2 fam_ID_2 fam_ID_2_1 m -Inf 2.13
#> 3 fam_ID_3 fam_ID_3_1 m -Inf 2.63
#> 4 fam_ID_4 fam_ID_4_1 m -Inf 1.42
#> 5 fam_ID_5 fam_ID_5_1 m -Inf 1.74
#> 6 fam_ID_6 fam_ID_6_1 m -Inf 1.74
#> 7 fam_ID_7 fam_ID_7_1 m -Inf 1.68
#> 8 fam_ID_8 fam_ID_8_1 m -Inf 2.13
#> 9 fam_ID_9 fam_ID_9_1 m -Inf 2.51
#> 10 fam_ID_10 fam_ID_10_1 m -Inf 1.54
#> # ℹ 590 more rows
#>
simulate_under_LTM(fam_vec = c(), n_fam = NULL, add_ind = TRUE, h2 = 0.5,
n_sim = 200, pop_prev = 0.05)
#> Warning message:
#> Neither fam_vec nor n_fam is specified...
#> $sim_obs
#> # A tibble: 200 × 5
#> fam_ID g o o_status o_aoo
#> <chr> <dbl> <dbl> <lgl> <dbl>
#> 1 fam_ID_1 -0.510 -0.921 FALSE 30
#> 2 fam_ID_2 -0.565 0.886 FALSE 19
#> 3 fam_ID_3 -0.274 -0.760 FALSE 12
#> 4 fam_ID_4 -0.473 -0.448 FALSE 11
#> 5 fam_ID_5 1.01 1.39 FALSE 18
#> 6 fam_ID_6 0.00167 -0.0850 FALSE 30
#> 7 fam_ID_7 0.0621 -0.0607 FALSE 19
#> 8 fam_ID_8 1.20 1.35 FALSE 22
#> 9 fam_ID_9 0.820 2.34 TRUE 48
#> 10 fam_ID_10 0.136 1.07 FALSE 17
#> # ℹ 190 more rows
#>
#> $thresholds
#> # A tibble: 200 × 5
#> fam_ID indiv_ID role lower upper
#> <chr> <chr> <chr> <dbl> <dbl>
#> 1 fam_ID_1 fam_ID_1_1 o -Inf 3.05
#> 2 fam_ID_2 fam_ID_2_1 o -Inf 3.44
#> 3 fam_ID_3 fam_ID_3_1 o -Inf 3.67
#> 4 fam_ID_4 fam_ID_4_1 o -Inf 3.70
#> 5 fam_ID_5 fam_ID_5_1 o -Inf 3.47
#> 6 fam_ID_6 fam_ID_6_1 o -Inf 3.05
#> 7 fam_ID_7 fam_ID_7_1 o -Inf 3.44
#> 8 fam_ID_8 fam_ID_8_1 o -Inf 3.33
#> 9 fam_ID_9 fam_ID_9_1 o 2.36 2.36
#> 10 fam_ID_10 fam_ID_10_1 o -Inf 3.50
#> # ℹ 190 more rows
#>