modelSim: Data simulation from different survival models
In survMS: Survival Model Simulation
Description
Usage
Arguments
Details
Value
Author(s)
See Also
Examples
Description
Data simulation from different survival models
Usage
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Arguments
model
Survival model: "cox", "AFT", "AFTshift" or "AH"
matDistr
Distribution of matrix
matParam
Parameters of matrix
n
size of sample
p
number of parameters
pnonull
number of partinent covariates
betaDistr
Distribution of beta or vector of beta
hazDistr
distribution of baseline hazard
hazParams
Parameters of baseline hazard
seed
seed
Phi
nonlinearity (not coded)
d
censorship
pourc
pourcents
Details
This function simulates survival data from different models: Cox model, AFT model and AH model.
1. The Cox model is defined as:
λ(t|X) = α_0(t) \exp(β^T X_{i.}),
with α_0(t) is the baseline risk and β is the vector of coefficients.
Two distributions are considered for the baseline risk:
Weibull: α_0(t) = λ a t^{(a-1)};
Log-normal: α_0(t) = (1/(σ√(2π t) \exp[-(\log t - μ)^2 /2 σ^2]))/(1 - Φ[(\log t - μ)/σ]);
Exponential: α_0(t) = λ;
Gompertz: α_0(t) = λ \exp(α t).
To Simulate the covariates, two distributions are also proposed:
Uniform
Normal
and the choice of parameters
The Phi parameter enables to simulate survival data in a linear framework with no interaction, but its future implementation will take into account a non-linear framework with interactions. If the parameter Phi is NULL (to complete...).
2. The AFT model is defined from a linear regression of the interest covariate:
Y_i = X_{i.} β + W_i,
with X_{i.} the covariates, β the vector of regression coefficients et ε_i the error term
AFT model can also be defined from the baseline survival function S_0(t), corresponding distribution tail \exp(ε_i). Survival function of AFT model is written as:
S(t|{X_{i.}}) = S_0(t\exp{(β^T X_{i.})}),
and the expression of hazard risk is the form of:
λ(t|X_{i.}) = \exp(β^T X_{i.}) α_0(t\exp(β^T X_{i.})). \label{eq:riskAFT}
with α_0(t) is the baseline risk and β is the vector of coefficients.
The advantage of AFT model is that the variables have a multiplicative effect on t rather than on the risk function, as is the case in Cox model.
Two distributions are considered for the baseline risk:
Weibull: α_0(t) = λ a t^{(a-1)};
Log-normal: α_0(t) = (1/(σ√(2π t) \exp[-(\log t - μ)^2 /2 σ^2]))/(1 - Φ[(\log t - μ)/σ])
.
To Simulate the covariates, two distributions are also proposed:
Uniform
Normal
and the choice of parameters
The Phi parameter enables to simulate survival data in a linear framework with no interaction, but its future implementation will take into account a non-linear framework with interactions. If the parameter Phi is NULL (to complete...).
3. The hazard risk of the AH model is defined for an individual i as:
λ_{AH}(t|X_{i.}) = α_0(t\exp(β^T X_{i.})),
with α_0 the baseline risk and β the vector of regression parameters. In a model with only one binary variable considered that corresponds to the treatment, the hazard risk is written as follows:
λ_1(t) = α_0(β t).
with α_0 the baseline risk and β the vector of regression parameters. In a model with only one binary variable considered that corresponds to the treatment, the hazard risk is written as follows:
λ_1(t) = α_0(β t).
The regression vector β characterizes the influence of variables on the survival time of individuals, and \exp(β^TX_{i.}) is a factor altering the time scale on hazard risk.
The positive or negative value of β^T X_{i.} will respectively imply an acceleration or deceleration of the risk.The AH model is defined from a linear regression of the interest covariate:
Two distributions are considered for the baseline risk:
Weibull: α_0(t) = λ a t^{(a-1)};
Log-normal: α_0(t) = (1/(σ√(2π t) \exp[-(\log t - μ)^2 /2 σ^2]))/(1 - Φ[(\log t - μ)/σ]).
To Simulate the covariates, two distributions are also proposed:
Uniform
Normal
and the choice of parameters
The Phi parameter enables to simulate survival data in a linear framework with no interaction, but its future implementation will take into account a non-linear framework with interactions. If the parameter Phi is NULL (to complete...).
sim$model <- model
Value
modelSim returns a list containing:
model model (Cox, AFT, AFTshift, AH)
Z Matrix of covariates
Y random covariates
TC Vector of survival times
delta Vector of censorship indicator
betanorm Vector of normalized regression parameter
crate Censorship rate
crate_delta Censorship rate
vecY Vector of number of individuals at risk at time t_i
hazParams Vector of parameter distribution of the baseline hazard function
hazDistr Distribution of the baseline hazard function
St Matrix of survival functions
ht Matrix of hazard risk functions
grilleTi Time grid
Author(s)
Mathilde Sautreuil
See Also
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
library(survMS)
### Survival data simulated from Cox model
res_paramW = get_param_weib(med = 2228, mu = 2325)
listCoxSim_n500_p1000 <- modelSim(model = "cox", matDistr = "unif", matParam = c(-1,1), n = 500,
p = 1000, pnonull = 20, betaDistr = 1, hazDistr = "weibull",
hazParams = c(res_paramW$a, res_paramW$lambda), seed = 1, d = 0)
print(listCoxSim_n500_p1000)
hist(listCoxSim_n500_p1000)
plot(listCoxSim_n500_p1000, ind = sample(1:500, 5))
plot(listCoxSim_n500_p1000, ind = sample(1:500, 5), type = "hazard")
df_p1000_n500 = data.frame(time = listCoxSim_n500_p1000$TC,
event = listCoxSim_n500_p1000$delta,
listCoxSim_n500_p1000$Z)
df_p1000_n500[1:6,1:10]
dim(df_p1000_n500)
### Survival data simulated from AFT model
res_paramLN = get_param_ln(var = 200000, mu = 1134)
listAFTSim_n500_p1000 <- modelSim(model = "AFT", matDistr = "unif", matParam = c(-1,1), n = 500,
p = 100, pnonull = 100, betaDistr = 1, hazDistr = "log-normal",
hazParams = c(res_paramLN$a, res_paramLN$lambda),
Phi = 0, seed = 1, d = 0)
hist(listAFTSim_n500_p1000)
plot(listAFTSim_n500_p1000, ind = sample(1:500, 5))
df_p1000_n500 = data.frame(time = listAFTSim_n500_p1000$TC,
event = listAFTSim_n500_p1000$delta,
listAFTSim_n500_p1000$Z)
df_p1000_n500[1:6,1:10]
dim(df_p1000_n500)
### Survival data simulated from AH model
res_paramLN = get_param_ln(var=170000, mu=2325)
listAHSim_n500_p1000 <- modelSim(model = "AH", matDistr = "unif", matParam = c(-1,1), n = 500,
p = 100, pnonull = 100, betaDistr = 1.5, hazDistr = "log-normal",
hazParams = c(res_paramLN$a*4, res_paramLN$lambda),
Phi = 0, seed = 1, d = 0)
print(listAHSim_n500_p1000)
hist(listAHSim_n500_p1000)
plot(listAHSim_n500_p1000, ind = sample(1:500, 5))
plot(listAHSim_n500_p1000, ind = sample(1:500, 5), type = "hazard")
survMS documentation built on April 16, 2021, 9:07 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Details Value Author(s) See Also Examples
Description
Data simulation from different survival models
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
Arguments
model |
Survival model: "cox", "AFT", "AFTshift" or "AH" |
matDistr |
Distribution of matrix |
matParam |
Parameters of matrix |
n |
size of sample |
p |
number of parameters |
pnonull |
number of partinent covariates |
betaDistr |
Distribution of beta or vector of beta |
hazDistr |
distribution of baseline hazard |
hazParams |
Parameters of baseline hazard |
seed |
seed |
Phi |
nonlinearity (not coded) |
d |
censorship |
pourc |
pourcents |
Details
This function simulates survival data from different models: Cox model, AFT model and AH model. 1. The Cox model is defined as: λ(t|X) = α_0(t) \exp(β^T X_{i.}), with α_0(t) is the baseline risk and β is the vector of coefficients. Two distributions are considered for the baseline risk:
Weibull: α_0(t) = λ a t^{(a-1)};
Log-normal: α_0(t) = (1/(σ√(2π t) \exp[-(\log t - μ)^2 /2 σ^2]))/(1 - Φ[(\log t - μ)/σ]);
Exponential: α_0(t) = λ;
Gompertz: α_0(t) = λ \exp(α t).
To Simulate the covariates, two distributions are also proposed:
Uniform
Normal
and the choice of parameters The Phi parameter enables to simulate survival data in a linear framework with no interaction, but its future implementation will take into account a non-linear framework with interactions. If the parameter Phi is NULL (to complete...).
2. The AFT model is defined from a linear regression of the interest covariate: Y_i = X_{i.} β + W_i, with X_{i.} the covariates, β the vector of regression coefficients et ε_i the error term AFT model can also be defined from the baseline survival function S_0(t), corresponding distribution tail \exp(ε_i). Survival function of AFT model is written as: S(t|{X_{i.}}) = S_0(t\exp{(β^T X_{i.})}), and the expression of hazard risk is the form of: λ(t|X_{i.}) = \exp(β^T X_{i.}) α_0(t\exp(β^T X_{i.})). \label{eq:riskAFT} with α_0(t) is the baseline risk and β is the vector of coefficients. The advantage of AFT model is that the variables have a multiplicative effect on t rather than on the risk function, as is the case in Cox model. Two distributions are considered for the baseline risk:
Weibull: α_0(t) = λ a t^{(a-1)};
Log-normal: α_0(t) = (1/(σ√(2π t) \exp[-(\log t - μ)^2 /2 σ^2]))/(1 - Φ[(\log t - μ)/σ])
.
To Simulate the covariates, two distributions are also proposed:
Uniform
Normal
and the choice of parameters The Phi parameter enables to simulate survival data in a linear framework with no interaction, but its future implementation will take into account a non-linear framework with interactions. If the parameter Phi is NULL (to complete...). 3. The hazard risk of the AH model is defined for an individual i as: λ_{AH}(t|X_{i.}) = α_0(t\exp(β^T X_{i.})), with α_0 the baseline risk and β the vector of regression parameters. In a model with only one binary variable considered that corresponds to the treatment, the hazard risk is written as follows: λ_1(t) = α_0(β t). with α_0 the baseline risk and β the vector of regression parameters. In a model with only one binary variable considered that corresponds to the treatment, the hazard risk is written as follows: λ_1(t) = α_0(β t). The regression vector β characterizes the influence of variables on the survival time of individuals, and \exp(β^TX_{i.}) is a factor altering the time scale on hazard risk. The positive or negative value of β^T X_{i.} will respectively imply an acceleration or deceleration of the risk.The AH model is defined from a linear regression of the interest covariate: Two distributions are considered for the baseline risk:
Weibull: α_0(t) = λ a t^{(a-1)};
Log-normal: α_0(t) = (1/(σ√(2π t) \exp[-(\log t - μ)^2 /2 σ^2]))/(1 - Φ[(\log t - μ)/σ]).
To Simulate the covariates, two distributions are also proposed:
Uniform
Normal
and the choice of parameters The Phi parameter enables to simulate survival data in a linear framework with no interaction, but its future implementation will take into account a non-linear framework with interactions. If the parameter Phi is NULL (to complete...).
sim$model <- model
Value
modelSim returns a list containing:
model model (Cox, AFT, AFTshift, AH)
Z Matrix of covariates
Y random covariates
TC Vector of survival times
delta Vector of censorship indicator
betanorm Vector of normalized regression parameter
crate Censorship rate
crate_delta Censorship rate
vecY Vector of number of individuals at risk at time t_i
hazParams Vector of parameter distribution of the baseline hazard function
hazDistr Distribution of the baseline hazard function
St Matrix of survival functions
ht Matrix of hazard risk functions
grilleTi Time grid
Author(s)
Mathilde Sautreuil
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 | library(survMS)
### Survival data simulated from Cox model
res_paramW = get_param_weib(med = 2228, mu = 2325)
listCoxSim_n500_p1000 <- modelSim(model = "cox", matDistr = "unif", matParam = c(-1,1), n = 500,
p = 1000, pnonull = 20, betaDistr = 1, hazDistr = "weibull",
hazParams = c(res_paramW$a, res_paramW$lambda), seed = 1, d = 0)
print(listCoxSim_n500_p1000)
hist(listCoxSim_n500_p1000)
plot(listCoxSim_n500_p1000, ind = sample(1:500, 5))
plot(listCoxSim_n500_p1000, ind = sample(1:500, 5), type = "hazard")
df_p1000_n500 = data.frame(time = listCoxSim_n500_p1000$TC,
event = listCoxSim_n500_p1000$delta,
listCoxSim_n500_p1000$Z)
df_p1000_n500[1:6,1:10]
dim(df_p1000_n500)
### Survival data simulated from AFT model
res_paramLN = get_param_ln(var = 200000, mu = 1134)
listAFTSim_n500_p1000 <- modelSim(model = "AFT", matDistr = "unif", matParam = c(-1,1), n = 500,
p = 100, pnonull = 100, betaDistr = 1, hazDistr = "log-normal",
hazParams = c(res_paramLN$a, res_paramLN$lambda),
Phi = 0, seed = 1, d = 0)
hist(listAFTSim_n500_p1000)
plot(listAFTSim_n500_p1000, ind = sample(1:500, 5))
df_p1000_n500 = data.frame(time = listAFTSim_n500_p1000$TC,
event = listAFTSim_n500_p1000$delta,
listAFTSim_n500_p1000$Z)
df_p1000_n500[1:6,1:10]
dim(df_p1000_n500)
### Survival data simulated from AH model
res_paramLN = get_param_ln(var=170000, mu=2325)
listAHSim_n500_p1000 <- modelSim(model = "AH", matDistr = "unif", matParam = c(-1,1), n = 500,
p = 100, pnonull = 100, betaDistr = 1.5, hazDistr = "log-normal",
hazParams = c(res_paramLN$a*4, res_paramLN$lambda),
Phi = 0, seed = 1, d = 0)
print(listAHSim_n500_p1000)
hist(listAHSim_n500_p1000)
plot(listAHSim_n500_p1000, ind = sample(1:500, 5))
plot(listAHSim_n500_p1000, ind = sample(1:500, 5), type = "hazard")
|
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.