dreamer_data: Generate Data from Dose Response Models

Description

See the model definitions below for specifics for each model.

Usage

dreamer_data_linear(
  n_cohorts,
  doses,
  b1,
  b2,
  sigma,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_linear_binary(
  n_cohorts,
  doses,
  b1,
  b2,
  link,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_quad(
  n_cohorts,
  doses,
  b1,
  b2,
  b3,
  sigma,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_quad_binary(
  n_cohorts,
  doses,
  b1,
  b2,
  b3,
  link,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_loglinear(
  n_cohorts,
  doses,
  b1,
  b2,
  sigma,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_loglinear_binary(
  n_cohorts,
  doses,
  b1,
  b2,
  link,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_logquad(
  n_cohorts,
  doses,
  b1,
  b2,
  b3,
  sigma,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_logquad_binary(
  n_cohorts,
  doses,
  b1,
  b2,
  b3,
  link,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_emax(
  n_cohorts,
  doses,
  b1,
  b2,
  b3,
  b4,
  sigma,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_emax_binary(
  n_cohorts,
  doses,
  b1,
  b2,
  b3,
  b4,
  link,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_exp(
  n_cohorts,
  doses,
  b1,
  b2,
  b3,
  sigma,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_exp_binary(
  n_cohorts,
  doses,
  b1,
  b2,
  b3,
  link,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_beta(
  n_cohorts,
  doses,
  b1,
  b2,
  b3,
  b4,
  scale,
  sigma,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_beta_binary(
  n_cohorts,
  doses,
  b1,
  b2,
  b3,
  b4,
  scale,
  link,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_independent(
  n_cohorts,
  doses,
  b1,
  sigma,
  times,
  t_max,
  longitudinal = NULL,
  ...
)
dreamer_data_independent_binary(
  n_cohorts,
  doses,
  b1,
  link,
  times,
  t_max,
  longitudinal = NULL,
  ...
)

Value

A dataframe of random subjects from the specified model and parameters.

Arguments

n_cohorts: a vector listing the size of each cohort.
doses: a vector listing the dose for each cohort.
b1, b2, b3, b4: parameters in the models. See sections below for each parameter's interpretation in a given model.
sigma: standard deviation.
times: the times at which data should be simulated if a longitudinal model is specified.
t_max: the t_max parameter used in the longitudinal model.
longitudinal: a string indicating the longitudinal model to be used. Can be "linear", "itp", or "idp".
...: additional longitudinal parameters.
link: character vector indicating the link function for binary models.
scale: a scaling parameter (fixed, specified by the user) for the beta models.

Functions

dreamer_data_linear(): generate data from linear dose response.
dreamer_data_linear_binary(): generate data from linear binary dose response.
dreamer_data_quad(): generate data from quadratic dose response.
dreamer_data_quad_binary(): generate data from quadratic binary dose response.
dreamer_data_loglinear(): generate data from log-linear dose response.
dreamer_data_loglinear_binary(): generate data from binary log-linear dose response.
dreamer_data_logquad(): generate data from log-quadratic dose response.
dreamer_data_logquad_binary(): generate data from log-quadratic binary dose response.
dreamer_data_emax(): generate data from EMAX dose response.
dreamer_data_emax_binary(): generate data from EMAX binary dose response.
dreamer_data_exp(): generate data from exponential dose response.
dreamer_data_exp_binary(): generate data from exponential binary dose response.
dreamer_data_beta(): generate data from Beta dose response.
dreamer_data_beta_binary(): generate data from binary Beta dose response.
dreamer_data_independent(): generate data from an independent dose response.
dreamer_data_independent_binary(): generate data from an independent dose response.

Linear

$$y \sim N(f(d), \sigma^2)$$ $$f(d) = b_1 + b_2 * d$$ $$b_1 \sim N(mu_b1, sigma_b1 ^ 2)$$ $$b_2 \sim N(mu_b2, sigma_b2 ^ 2)$$ $$1 / \sigma^2 \sim Gamma(shape, rate)$$

Quadratic

$$y \sim N(f(d), \sigma^2)$$ $$f(d) = b_1 + b_2 * d + b_3 * d^2$$ $$b_1 \sim N(mu_b1, sigma_b1 ^ 2)$$ $$b_2 \sim N(mu_b2, sigma_b2 ^ 2)$$ $$b_3 \sim N(mu_b3, sigma_b3 ^ 2)$$ $$1 / \sigma^2 \sim Gamma(shape, rate)$$

Log-linear

$$y \sim N(f(d), \sigma^2)$$ $$f(d) = b_1 + b_2 * log(d + 1)$$ $$b_1 \sim N(mu_b1, sigma_b1 ^ 2)$$ $$b_2 \sim N(mu_b2, sigma_b2 ^ 2)$$ $$1 / \sigma^2 \sim Gamma(shape, rate)$$

Log-quadratic

$$y \sim N(f(d), \sigma^2)$$ $$f(d) = b_1 + b_2 * log(d + 1) + b_3 * log(d + 1)^2$$ $$b_1 \sim N(mu_b1, sigma_b1 ^ 2)$$ $$b_2 \sim N(mu_b2, sigma_b2 ^ 2)$$ $$b_3 \sim N(mu_b3, sigma_b3 ^ 2)$$ $$1 / \sigma^2 \sim Gamma(shape, rate)$$

EMAX

$$y \sim N(f(d), \sigma^2)$$ $$f(d) = b_1 + (b_2 - b_1) * d ^ b_4 / (exp(b_3 * b_4) + d ^ b_4)$$ $$b_1 \sim N(mu_b1, sigma_b1 ^ 2)$$ $$b_2 \sim N(mu_b2, sigma_b2 ^ 2)$$ $$b_3 \sim N(mu_b3, sigma_b3 ^ 2)$$ $$b_4 \sim N(mu_b4, sigma_b4 ^ 2), (Truncated above 0)$$ $$1 / \sigma^2 \sim Gamma(shape, rate)$$ Here, $b_1$ is the placebo effect (dose = 0), $b_2$ is the maximum treatment effect, $b_3$ is the $log(ED50)$, and $b_4$ is the hill or rate parameter.

Exponential

$$y \sim N(f(d), \sigma^2)$$ $$f(d) = b_1 + b_2 * (1 - exp(- b_3 * d))$$ $$b_1 \sim N(mu_b1, sigma_b1 ^ 2)$$ $$b_2 \sim N(mu_b2, sigma_b2 ^ 2)$$ $$b_3 \sim N(mu_b3, sigma_b3 ^ 2), (truncated to be positive)$$ $$1 / \sigma^2 \sim Gamma(shape, rate)$$

Linear Binary

$$y \sim Binomial(n, f(d))$$ $$link(f(d)) = b_1 + b_2 * d$$ $$b_1 \sim N(mu_b1, sigma_b1 ^ 2)$$ $$b_2 \sim N(mu_b2, sigma_b2 ^ 2)$$

Quadratic Binary

$$y \sim Binomial(n, f(d))$$ $$link(f(d)) = b_1 + b_2 * d + b_3 * d^2$$ $$b_1 \sim N(mu_b1, sigma_b1 ^ 2)$$ $$b_2 \sim N(mu_b2, sigma_b2 ^ 2)$$ $$b_3 \sim N(mu_b3, sigma_b3 ^ 2)$$

Log-linear Binary

$$y \sim Binomial(n, f(d))$$ $$link(f(d)) = b_1 + b_2 * log(d + 1)$$ $$b_1 \sim N(mu_b1, sigma_b1 ^ 2)$$ $$b_2 \sim N(mu_b2, sigma_b2 ^ 2)$$

Log-quadratic Binary

$$y \sim Binomial(n, f(d))$$ $$link(f(d)) = b_1 + b_2 * log(d + 1) + b_3 * log(d + 1)^2$$ $$b_1 \sim N(mu_b1, sigma_b1 ^ 2)$$ $$b_2 \sim N(mu_b2, sigma_b2 ^ 2)$$ $$b_3 \sim N(mu_b3, sigma_b3 ^ 2)$$

EMAX Binary

$$y \sim Binomial(n, f(d))$$ $$link(f(d)) = b_1 + (b_2 - b_1) * d ^ b_4 / (exp(b_3 * b_4) + d ^ b_4)$$ $$b_1 \sim N(mu_b1, sigma_b1 ^ 2)$$ $$b_2 \sim N(mu_b2, sigma_b2 ^ 2)$$ $$b_3 \sim N(mu_b3, sigma_b3 ^ 2)$$ $$b_4 \sim N(mu_b4, sigma_b4 ^ 2), (Truncated above 0)$$ Here, on the $link(f(d))$ scale, $b_1$ is the placebo effect (dose = 0), $b_2$ is the maximum treatment effect, $b_3$ is the $log(ED50)$, and $b_4$ is the hill or rate parameter.

Exponential Binary

$$y \sim Binomial(n, f(d))$$ $$link(f(d)) = b_1 + b_2 * (exp(b_3 * d) - 1)$$ $$b_1 \sim N(mu_b1, sigma_b1 ^ 2)$$ $$b_2 \sim N(mu_b2, sigma_b2 ^ 2)$$ $$b_3 \sim N(mu_b3, sigma_b3 ^ 2), (Truncated below 0)$$

Independent

$$y \sim N(f(d), \sigma^2)$$ $$f(d) = b_{1d}$$ $$b_{1d} \sim N(mu_b1[d], sigma_b1[d] ^ 2)$$ $$1 / \sigma^2 \sim Gamma(shape, rate)$$

Independent Binary

$$y \sim Binomial(n, f(d))$$ $$link(f(d)) = b_{1d}$$ $$b_{1d} \sim N(mu_b1[d], sigma_b1[d]) ^ 2$$

Longitudinal Linear

Let $f(d)$ be a dose response model. The expected value of the response, y, is: $$E(y) = g(d, t)$$ $$g(d, t) = a + (t / t_max) * f(d)$$ $$a \sim N(mu_a, sigma_a)$$

Longitudinal ITP

Let $f(d)$ be a dose response model. The expected value of the response, y, is: $$E(y) = g(d, t)$$ $$g(d, t) = a + f(d) * ((1 - exp(- c1 * t))/(1 - exp(- c1 * t_max)))$$ $$a \sim N(mu_a, sigma_a)$$ $$c1 \sim Uniform(a_c1, b_c1)$$

Longitudinal IDP

Increasing-Decreasing-Plateau (IDP).

Let $f(d)$ be a dose response model. The expected value of the response, y, is: $$E(y) = g(d, t)$$ $$g(d, t) = a + f(d) * (((1 - exp(- c1 * t))/(1 - exp(- c1 * d1))) * I(t < d1) + (1 - gam * ((1 - exp(- c2 * (t - d1))) / (1 - exp(- c2 * (d2 - d1))))) * I(d1 <= t <= d2) + (1 - gam) * I(t > d2))$$ $$a \sim N(mu_a, sigma_a)$$ $$c1 \sim Uniform(a_c1, b_c1)$$ $$c2 \sim Uniform(a_c2, b_c2)$$ $$d1 \sim Uniform(0, t_max)$$ $$d2 \sim Uniform(d1, t_max)$$ $$gam \sim Uniform(0, 1)$$

Examples

Run this code

set.seed(888)
data <- dreamer_data_linear(
  n_cohorts = c(20, 20, 20),
  dose = c(0, 3, 10),
  b1 = 1,
  b2 = 3,
  sigma = 5
)

head(data)

plot(data$dose, data$response)
abline(a = 1, b = 3)

# longitudinal data
set.seed(889)
data_long <- dreamer_data_linear(
  n_cohorts = c(10, 10, 10, 10), # number of subjects in each cohort
  doses = c(.25, .5, .75, 1.5), # dose administered to each cohort
  b1 = 0, # intercept
  b2 = 2, # slope
  sigma = .5, # standard deviation,
  longitudinal = "itp",
  times = c(0, 12, 24, 52),
  t_max = 52, # maximum time
  a = .5,
  c1 = .1
)

if (FALSE) {
  ggplot(data_long, aes(time, response, group = dose, color = factor(dose))) +
    geom_point()
}

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