# Generate Synthetic Data In CausalGPS: Matching on Generalized Propensity Scores with Continuous Exposures

knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )  We provide gen_syn_data to generate synthetic data for CausalGPS package ## Usage Input parameters: sample_size Number of data samples seed The seed of R's random number generator outcome_sd Standard deviation used to generate the outcome gps_spec A numerical value (1-7) that indicates the GPS model used to generate synthetic data. See the following section for more details. cova_spec A numerical value (1-2) to modify the covariates. See the code for more details. ## Technical Details for Data Generating Process We generate six confounders$(C_1,C_2,...,C_6), which include a combination of continuous and categorical variables, \begin{align} C_1,\ldots,C_4 \sim N(0,\boldsymbol{I}_4), C_5 \sim U{-2,2}, C_6 \sim U(-3,3), \end{align} and generateW$using six specifications of the generalized propensity score model, 1)$W = 9 {-0.8+ (0.1,0.1,-0.1,0.2,0.1,0.1) \boldsymbol{C}} +17 + N(0,5)$2)$W = 15{-0.8+ (0.1,0.1,-0.1,0.2,0.1,0.1) \boldsymbol{C}} + 22 + T(2)$3)$W = 9 {-0.8+ (0.1,0.1,-0.1,0.2,0.1,0.1) \boldsymbol{C}} + 3/2 C_3^2 + 15 + N(0,5)$4)$W = \frac{49 \exp({-0.8+ (0.1,0.1,-0.1,0.2,0.1,0.1) \boldsymbol{C}})}{1+ \exp({-0.8+ (0.1,0.1,-0.1,0.2,0.1,0.1) \boldsymbol{C}})} -6 + N(0,5)$5)$W = \frac{42}{1+ \exp({-0.8+ (0.1,0.1,-0.1,0.2,0.1,0.1) \boldsymbol{C}})} - 18 + N(0,5)$6)$W = 7 \text{log} ( {-0.8+ (0.1,0.1,-0.1,0.2,0.1,0.1) \boldsymbol{C}}) + 13 + N(0,4)$We generate$Y$from an outcome model which is assumed to be a cubical function of$W$with additive terms for the confounders and interactions between$W$and confounders$\mathbf{C}\$,

$$Y | W, \mathbf{C} \sim N{\mu(W, \mathbf{C}),\text{sd}^2}$$

$$\mu(W, \mathbf{C}) = -10 - (2, 2, 3, -1,2,2)\mathbf{C} - W(0.1 - 0.1C_1 + 0.1C_4 + 0.1C_5 + 0.1C_3^2) + 0.13^2W^3$$

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CausalGPS documentation built on June 22, 2024, 9:31 a.m.