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Simulate from continuous outcome model given covariates

Source: R/outcome_models.R
outcome_continuous.Rd

Simulate from continuous outcome model with mean $$g(\text{par}^\top X)$$ where \(X\) is the design matrix specified by the formula, and \(g\) is the link function specified by the family argument

Usage

outcome_continuous(
  data,
  mean = NULL,
  par = NULL,
  sd = 1,
  het = 0,
  outcome.name = "y",
  remove = c("id", "num"),
  family = gaussian(),
  ...
)

Arguments

data

(data.table) Covariate data, usually the output of the covariate model of a Trial object.

mean

formula specifying design from 'data' or a function that maps x to the mean value. If NULL all main-effects of the covariates will be used

par

(numeric) Regression coefficients (default zero). Can be given as a named list corresponding to the column names of model.matrix

sd

(numeric) standard deviation of Gaussian measurement error

het

Introduce variance hetereogeneity by adding a residual term \(het \cdot \mu_x \cdot e\), where \(\mu_x\) is the mean given covariates and \(e\) is an independent standard normal distributed variable. This term is in addition to the measurement error introduced by the sd argument.

outcome.name

Name of outcome variable ("y")

remove

variables that will be removed from input data (if formula is not specified)

family

exponential family (default gaussian(identity))

...

Additional arguments passed to mean function (see examples)

See also

outcome_count outcome_binary outcome_lp

Examples

trial <- Trial$new(
  covariates = \(n) data.frame(a = rbinom(n, 1, 0.5), x = rnorm(n)),
  outcome = outcome_continuous
)
est <- function(data) glm(y ~ a + x, data = data)
trial$simulate(1e4, mean = ~ 1 + a + x, par = c(1, 0.5, 2)) |> est()
#> 
#> Call:  glm(formula = y ~ a + x, data = data)
#> 
#> Coefficients:
#> (Intercept)            a            x  
#>      0.9816       0.5331       2.0119  
#> 
#> Degrees of Freedom: 9999 Total (i.e. Null);  9997 Residual
#> Null Deviance:	    51370 
#> Residual Deviance: 10160 	AIC: 28550

# default behavior is to set all regression coefficients to 0
trial$simulate(1e4, mean = ~ 1 + a + x) |> est()
#> 
#> Call:  glm(formula = y ~ a + x, data = data)
#> 
#> Coefficients:
#> (Intercept)            a            x  
#>     0.01652     -0.01496      0.01026  
#> 
#> Degrees of Freedom: 9999 Total (i.e. Null);  9997 Residual
#> Null Deviance:	    10130 
#> Residual Deviance: 10130 	AIC: 28510

# intercept defaults to 0 and regression coef for a takes the provided value
trial$simulate(1e4, mean = ~ 1 + a, par = c(a = 0.5)) |> est()
#> 
#> Call:  glm(formula = y ~ a + x, data = data)
#> 
#> Coefficients:
#> (Intercept)            a            x  
#>  -0.0004711    0.4985070   -0.0028209  
#> 
#> Degrees of Freedom: 9999 Total (i.e. Null);  9997 Residual
#> Null Deviance:	    10360 
#> Residual Deviance: 9734 	AIC: 28120
# trial$simulate(1e4, mean = ~ 1 + a, par = c("(Intercept)" = 0.5)) |> est()

# define mean model that directly works on whole covariate data, incl id and
# num columns
trial$simulate(1e4, mean = \(x) with(x, -1 + a * 2 + x * -3)) |>
  est()
#> 
#> Call:  glm(formula = y ~ a + x, data = data)
#> 
#> Coefficients:
#> (Intercept)            a            x  
#>      -1.009        2.005       -3.019  
#> 
#> Degrees of Freedom: 9999 Total (i.e. Null);  9997 Residual
#> Null Deviance:	    110900 
#> Residual Deviance: 9956 	AIC: 28340

# par argument is not passed on to mean function
trial$simulate(1e4,
  mean = \(x,  reg.par) with(x, reg.par[1] + reg.par[2] * a),
  reg.par = c(1, 5)
) |> est()
#> 
#> Call:  glm(formula = y ~ a + x, data = data)
#> 
#> Coefficients:
#> (Intercept)            a            x  
#>    0.979250     5.016445    -0.008517  
#> 
#> Degrees of Freedom: 9999 Total (i.e. Null);  9997 Residual
#> Null Deviance:	    73030 
#> Residual Deviance: 10120 	AIC: 28510