heatmap_ate: Visualize ATE Estimates by Heatmap
In JiajingZ/TukeySens: Sensitivity Analysis Based on Tukey's Factorization

Description Usage Arguments Details Examples

Visualize Average Treatment Effect (ATE) estimates for a grid of sensitivity parameters. "NS" is used to denote "not significant", meaning that the 95% posterior credible interval of the ATE contains 0.

1 2	heatmap_ate(x_trt, y_trt, x_ctrl, y_ctrl, largest_effect, gamma_length = 11)

`x_trt`	a `tibble` or data frame with observed pre-treatment variables for the treatment group
`y_trt`	a vector with outcomes for the treatment group
`x_ctrl`	a `tibble` or data frame with observed pre-treatment variables for the control group
`y_ctrl`	a vector with outcomes for the control group
`largest_effect`	the largest magnitude of sensitivity parameter to be considered, chosen from `caliplot`
`gamma_length`	chosen length of sensitivity parameter sequence, which needs to be an odd integer
`joint`	logical. If TURE, the mean surface and residual variance will be estimated jointly for both treatment groups; if FALSE (default), the mean surface and residual variance will be estimated independently for each treatment group.

The Average Treatment Effect is defined as:

τ^{ATE} := E[Y(1) - Y(0)] = E[Y(1)] - E(Y(0))

For each t, the complete-data distribution for each potential outcome can be written as a mixture of the distribution of observed and missing outcomes:

f(Y(t) \mid X) = f(T = t \mid X)f_t^{obs}(Y(t) \mid T = t, X) + f(T = 1-t \mid X)f_t^{mis}(Y(t) \mid T = 1 - t, X).

The logistic selection with mixtures of exponential families (logistic-mEF models) have been considered, the marginal selection functions in each arm are specified as logistic in the potential outcomes, and the observed data is modeled with a mixture of exponential family distributions, which can be identified using flexible nonparametric or machine learning method. Specifically, the treatment assignment model is posited as:

f(T=1 \mid Y(t),X) = \text{logit}^{-1}\{ α_t(X)+γ_t's_t(Y(t)) \},

where \text{logit}^{-1}(x) = (1 + exp(-x))^{-1}. This specification has sensitivity parameters γ = (γ_0, γ_1), which describe how treatment assignment depends marginally on each potential outcome, and a parmeter α_t(X) in each arm that is identified by the observed data once gamma_t is specified.
Under these settings, the missing outcome distribution can be infered as a tilt of the observed outcome distribution.

# Observed data in treatment group
NHANES_trt <- NHANES %>% dplyr::filter(trt_dbp == 1)
x_trt <- NHANES_trt %>% select(-one_of("trt_dbp", "ave_dbp"))
y_trt <- NHANES_trt %>% select(ave_dbp)

# Observed data in control group 
NHANES_ctrl <- NHANES %>% dplyr::filter(trt_dbp == 0)
x_ctrl <- NHANES_ctrl %>% select(-one_of("trt_dbp", "ave_dbp"))
y_ctrl <- NHANES_ctrl %>% select(ave_dbp)

# ATE Heatmap 
heatmap_ate(x_trt, y_trt, x_ctrl, y_ctrl, largest_effect = 0.05)
heatmap_ate(x_trt, y_trt, x_ctrl, y_ctrl, largest_effect = 0.05, joint = TRUE)