# Calibration for Gaussian Outcomes Calibrates the naive estimates to account for unobserved confounding when outcome variables are Gaussian. The calibration can be done with user-specific sensitivity parameters or with our pre-provided calibration methods, the worst-case calibration for a single contrast or multivariate calibration for multiple contrasts. ```r gcalibrate( y, tr, t1, t2, calitype = c("worstcase", "multicali", "null"), mu_y_dt = NULL, sigma_y_t = NULL, mu_u_dt = NULL, cov_u_t = NULL, nU = NULL, R2 = 1, gamma = NULL, R2_constr = 1, nc_index = NULL, ... ) ``` ## Arguments - `y`: `data.frame`, `matrix` or `vector`. Gaussian outcome variable. - `tr`: `data.frame`. Treatment variables with rows corresponding to observations and columns to variables. - `t1`: `data.frame`. First treatment arms of interest. May contain a single or multiple treatments in rows. - `t2`: `data.frame`. Second treatment arms of interest, which has same number of row as `t1`. - `calitype`: character. The calibration method to be applied. Can be one of: "worstcase" - apply worst-case calibration when considering a single contrast. "multicali" - apply mutlivariate calibration when considering multiple contrasts. "null" - apply calibration with user-specified sensitivity parameter, $\gamma$. - `mu_y_dt`: an optional scalar or vector that contains naive estimates of treatment effects ignoring confounding. - `sigma_y_t`: an optional scalar of the standard deviation of outcome conditional on treatments. - `mu_u_dt`: an optional matrix of difference in conditional confounder means, $E(U \mid t1) - E(U \mid t2)$, with latent variables in columns. - `cov_u_t`: an optional covariance matrix of confounders conditional on treatments. - `nU`: Number of latent confounders to consider. - `R2`: an optional scalar or vector specifying the proportion of residual variance in outcome given the treatment that can be explained by confounders. - `gamma`: sensitivity parameter vector. Must be given when `calitype = "null"`. - `R2_constr`: an optional scalar or vector specifying the upper limit constraint on $R^2$ . By default, `R2_constr = 1`. - `nc_index`: an optional vector containing indexes of negative control treatments. If not `NULL`, worstcase calibration will be executed with constraints imposed by negative control treatments. - `...`: further arguments passed to `kEstimate`, `pca` or `get_opt_gamma`. ## Returns `gcalibrate` returns a list containing the following components: - **`est_df`**: a `data.frame` with naive and calibrated estimates of average treatment effects. - **`R2`**: a vector of $R^2$ with elements corresponding to columns of `est_df`. - **`gamma`**: a matrix returned when `calitype = "multicali"` or `"worstcase"`. If `calitype = "multicali"`, optimized gamma are in columns, respectively resulting in estimates in columns of `est_df`. If `calitype = "worstcase"`, gamma are in rows, which respectively lead to the worstcase ignorance region with $R^2=1$ for each contrast of interest. - **`rv`**: a `numeric vector` returned when `calitype = "worstcase"`, with elements being the robustness value or `NA` if the ignorance region doesn't contains 0 for each contrast of interest. ## Examples ```r # load the example data # y <- GaussianT_GaussianY$y tr <- subset(GaussianT_GaussianY, select = -c(y)) # worst-case calibration # t1 <- data.frame(diag(ncol(tr))) t2 <- data.frame(matrix(0, nrow = ncol(tr), ncol = ncol(tr))) colnames(t1) = colnames(t2) <- colnames(tr) est_g1 <- gcalibrate(y = y, tr = tr, t1 = t1, t2 = t2, nU = 3, calitype = "worstcase", R2 = c(0.3, 1)) plot_estimates(est_g1) # with negative conotrls # est_g1_nc <- gcalibrate(y = y, tr = tr, t1 = t1, t2 = t2, nU = 3, calitype = "worstcase", R2 = c(0.3, 1), nc_index = c(3, 6)) plot_estimates(est_g1_nc) # multivariate calibration # est_g2 <- gcalibrate(y = y, tr = tr, t1 = tr[1:10,], t2 = tr[11:20,], nU = 3, calitype = "multicali", R2_constr = c(1, 0.15)) plot_estimates(est_g2) # user-specified calibration # est_g3 <- gcalibrate(y = y, tr = tr, t1 = tr[1:2,], t2 = tr[3:4,], nU = 3, calitype = "null", gamma = c(0.96, -0.29, 0), R2 = c(0.2, 0.6, 1)) plot_estimates(est_g3) # apply gamma that maximizes the bias for the first contrast considered in est_g1 # est_g4 <- gcalibrate(y = y, tr = tr, t1 = tr[1:2,], t2 = tr[3:4,], nU = 3, calitype = "null", gamma = est_g1$gamma[1,], R2 = c(0.2, 0.6, 1)) plot_estimates(est_g4) ```

gcalibrate function