sensitivity {causal.decomp}

Sensitivity Analysis Using R-Squared Values for Causal Decomposition Analysis

Description

The function 'sensitivity' is used to implement sensitivity analysis for the causal decomposition analysis, using R-squared values as sensitivity parameters.

Usage

sensitivity(boot.res, fit.y, fit.m = NULL, mediator = NULL, covariates, treat,
            sel.lev.treat, conf.level = 0.95, max.rsq = 0.3)

Arguments

boot.res

bootstrap results from an object fitted by the 'smi' function.

fit.y

outcome model used in fitting the 'smi' function. Can be of class 'lm' or 'glm'.

fit.m

mediator model used in fitting the 'smi' function. Can be of class 'lm', 'glm', or 'polr'.

mediator

a vector containing the name of mediator used in the models.

covariates

a vector containing the name of the covariate variable(s) used in the models. Each covariate can be categorical with two or more categories (two- or multi-valued factor) or continuous (numeric).

treat

a character string indicating the name of the treatment variable used in the models. The treatment can be categorical with two or more categories (two- or multi-valued factor).

sel.lev.treat

a level of categorical treatment variable which is to be compared with the reference level.

conf.level

level of the returned two-sided confidence intervals, which are estimated by the nonparametric percentile bootstrap method. Default is .95, which returns the 2.5 and 97.5 percentiles of the simulated quantities.

max.rsq

upper limit of the two sensitivity parameters (R-squared values). Once it is set, the R-squared values between 0 and this upper limit are explored to draw the sensitivity contour plots. Default is 0.3.

Details

This function is used to implement sensitivity analysis for the causal decomposition analysis, using two sensitivity parameters: (i) the R-squared value between the outcome and unobserved confounder given the treatment, intermediate confounder, mediator, and covariates; and (ii) the R-squared value between the mediator and unobserved confounder given the treatment, intermediate confounder, and covariates (Park et al., 2023).

As of version 0.1.0, 'boot.res' must be fitted by the 'smi' function with a single mediator, which can be of class 'lm', 'glm', or 'polr'.

Value

call

original function call.

disparity.reduction

a matrix containing the estimated disparity reduction value along with lower and upper limits of the confidence interval, for each combination of the two sensitivity parameters, assuming those two are equal.

disparity.remaining

a matrix containing the estimated disparity remaining value along with lower and upper limits of the confidence interval, for each combination of the two sensitivity parameters, assuming those two are equal.

rm

R-squared values between the mediator and unobserved confounder (first sensitivity parameter), which are explored for the sensitivity analysis.

ry

R-squared values between the outcome and unobserved confounder, (second sensitivity parameter), which are explored for the sensitivity analysis.

red

a matrix containing the estimated disparity reduction values given each combination of the two sensitivity parameters.

lower_red

a matrix containing the lower limit of disparity reduction given each combination of the two sensitivity parameters.

rem

a matrix containing the estimated disparity remaining values given each combination of the two sensitivity parameters.

lower_rem

a matrix containing the lower limit of disparity remaining given each combination of the two sensitivity parameters.

RV_red

robustness value for disparity reduction, which represents the strength of association that will explain away the estimated disparity reduction.

RV_red_alpha

robustness value for disparity reduction, which represents the strength of association that will change the significance of the estimated disparity reduction at the given significance level, assuming an equal association to the mediator and the outcome.

RV_rem

robustness value for disparity remaining, which represents the strength of association that will explain away the estimated disparity remaining.

RV_rem_alpha

robustness value for disparity remaining, which represents the strength of association that will change the significance of the estimated disparity remaining at the given significance level, assuming an equal association to the mediator and the outcome.

Author(s)

Suyeon Kang, University of California, Riverside, [e-mail]; Soojin Park, University of California, Riverside, [e-mail].

References

Park, S., Kang, S., Lee, C., & Ma, S. (2023). Sensitivity analysis for causal decomposition analysis: Assessing robustness toward omitted variable bias, Journal of Causal Inference. Forthcoming.

See Also

smi

Examples

data(sMIDUS)

# Center covariates
sMIDUS$age <- scale(sMIDUS$age, center = TRUE, scale = FALSE)
sMIDUS$stroke <- scale(sMIDUS$stroke, center = TRUE, scale = FALSE)
sMIDUS$T2DM <- scale(sMIDUS$T2DM, center = TRUE, scale = FALSE)
sMIDUS$heart <- scale(sMIDUS$heart, center = TRUE, scale = FALSE)

fit.m <- lm(edu ~ racesex + age + stroke + T2DM + heart, data = sMIDUS)
fit.y <- lm(health ~ racesex + lowchildSES + abuse + edu + racesex:edu +
            age + stroke + T2DM + heart, data = sMIDUS)
smiRes <- smi(fit.m = fit.m, fit.y = fit.y, sims = 40, conf.level = .95,
          covariates = c("age", "stroke", "T2DM", "heart"), treat = "racesex", seed = 227)
sensRes <- sensitivity(boot.res = smiRes, fit.m = fit.m, fit.y = fit.y, mediator = "edu",
                       covariates = c("age", "stroke", "T2DM", "heart"), treat = "racesex",
                       sel.lev.treat = "4", max.rsq = 0.3)

sensRes
names(sensRes) 
# Create sensitivity contour plots
plot(sensRes)