Generate simulated dataset with two exposure mixtures — sim_mixture

Generates a dataset for simulation studies involving two mixtures of correlated exposures and their interaction. Exposures are generated from a multivariate normal distribution with user-specified within-mixture and between-mixture correlations, then discretized into quantiles. The outcome is generated from family- and estimand-scale-specific models where the parameters correspond to simultaneous one-quantile increases in each mixture.

Usage

sim_mixture_data(
  n,
  pA,
  pB,
  rho_within_A,
  rho_within_B,
  rho_between,
  psi1,
  psi2,
  psi12,
  sigma_eps = 1,
  q = 4,
  return_quantized = FALSE,
  seed = NULL,
  family = stats::gaussian(),
  estimand_scale = NULL,
  baseline_mean = 0,
  baseline_risk = 0.2,
  baseline_rate = 1,
  beta_C = 1
)

Arguments

n: Number of observations.
pA: Number of components in mixture A.
pB: Number of components in mixture B.
rho_within_A: Correlation between components within mixture A.
rho_within_B: Correlation between components within mixture B.
rho_between: Correlation between components across mixtures.
psi1: Effect of a one-quantile increase in mixture A.
psi2: Effect of a one-quantile increase in mixture B.
psi12: Interaction effect representing the change in the effect of mixture A when mixture B increases by one quantile.
sigma_eps: Standard deviation of the outcome error term for Gaussian generation.
q: Number of quantiles used to discretize exposures.
return_quantized: Logical; if TRUE returns quantized exposures, otherwise returns the original continuous exposures.
seed: Optional random seed for reproducibility.
family: Outcome family. Supported families are gaussian(), binomial(), and poisson().
estimand_scale: Optional outcome-generating estimand scale. Supported values mirror the fitting API: "mean_difference", "risk_difference", "odds_ratio", and "rate_ratio". If omitted, defaults follow the 0.5.0 fitting conventions.
baseline_mean: Baseline mean used for Gaussian generation.
baseline_risk: Baseline risk used for binomial generation.
baseline_rate: Baseline rate used for Poisson generation.
beta_C: Effect of covariate C in the outcome-generating model.

Value

A data frame containing the simulated outcome Y, mixture exposures (X1...XpA and W1...WpB), and covariate C.

Details

The exposure summaries are:

$$S_A = \textrm{rowMeans}(X_q), \qquad S_B = \textrm{rowMeans}(W_q)$$

where X_q and W_q are the quantized mixture components. The outcome is then generated from one of the following models:

Gaussian mean-difference generation: $$Y = \mu_0 + \psi_1 S_A + \psi_2 S_B + \psi_{12} S_A S_B + \beta_C C + \epsilon$$
Binomial odds-ratio generation: $$\textrm{logit}\{P(Y = 1)\} = \textrm{logit}(p_0) + \log(\psi_1) S_A + \log(\psi_2) S_B + \log(\psi_{12}) S_A S_B + \beta_C C$$
Binomial risk-difference generation: $$P(Y = 1) = p_0 + \psi_1 S_A + \psi_2 S_B + \psi_{12} S_A S_B + \beta_C C$$
Poisson rate-ratio generation: $$\log\{E(Y)\} = \log(\lambda_0) + \log(\psi_1) S_A + \log(\psi_2) S_B + \log(\psi_{12}) S_A S_B + \beta_C C$$
Poisson mean-difference generation: $$E(Y) = \lambda_0 + \psi_1 S_A + \psi_2 S_B + \psi_{12} S_A S_B + \beta_C C$$

Ratio-valued inputs are accepted on their natural scale. For example, psi1 = 1.5 with family = poisson() and estimand_scale = "rate_ratio" means that a one-quantile increase in mixture A corresponds to a rate ratio of 1.5 before any interaction modification by mixture B.

Continuous exposures are generated from a multivariate normal distribution with a block correlation structure. Exposures are then discretized into quantile categories ranging from 0 to q - 1. The outcome is always generated from the quantized mixture summaries so that the requested parameters psi1, psi2, and psi12 correspond directly to the intended one-quantile mixture effects on the chosen generating scale.

Additive binary-risk and additive Poisson-mean generation are supported, but the requested baseline and effect values must imply valid probabilities or strictly positive means for all simulated observations.

Examples

dat_gaussian <- sim_mixture_data(
  n = 1000,
  pA = 4,
  pB = 4,
  rho_within_A = 0.5,
  rho_within_B = 0.5,
  rho_between = 0.3,
  psi1 = 0.5,
  psi2 = 0.3,
  psi12 = 0.2,
  return_quantized = TRUE,
  seed = 123
)

dat_binomial <- sim_mixture_data(
  n = 1000,
  pA = 3,
  pB = 3,
  rho_within_A = 0.4,
  rho_within_B = 0.4,
  rho_between = 0.2,
  psi1 = 1.5,
  psi2 = 1.2,
  psi12 = 1.1,
  family = binomial(),
  baseline_risk = 0.2,
  beta_C = 0.25,
  seed = 123
)

dat_poisson <- sim_mixture_data(
  n = 1000,
  pA = 3,
  pB = 3,
  rho_within_A = 0.4,
  rho_within_B = 0.4,
  rho_between = 0.2,
  psi1 = 1.5,
  psi2 = 1.2,
  psi12 = 1.1,
  family = poisson(),
  baseline_rate = 1,
  beta_C = 0.15,
  seed = 123
)