survSens

This package performs a dual-parameter sensitivity analysis of treatment effect to unmeasured confounding in observational studies with either survival or competing risks outcomes.

Release Note

12/27/2022 Version 1.1.0

Motivated by Cinelli, C., & Hazlett, C. (2020), we introduce partial $R_{T \sim U | X, Z}^{2}$ and partial $R_{Z \sim U | X}^{2}$ to measure the dependency between the unmeasured confounder $U$ and the outcome $T$ , and between $U$ and the treatment $Z$ , respectively.

In the outcome model, suppose the full model $T \sim X + Z + U$ has a log likelihood $l_{1}$ , and the reduced model $T \sim X + Z$ has a log likelihood $l_{0}$ , with $k$ events, we calculate partial $R_{T \sim U | X, Z}^{2}$ similar to $R^{2}$ in O’Quigley, J., Xu, R., & Stare, J. (2005) $R_{T \sim U | X, Z}^{2} = 1 - e^{- 2 (l_{1} - l_{0}) / k} .$

In the treatment model, according to Cox, D. R., & Snell, E. J. (1989), the full model $Z \sim X + U$ has deviance $D E V_{1}$ , $D E V_{1} = - 2 \sum [z_{i} \log ({\hat{p}}_{i}) + (1 - z_{i}) \log (1 - {\hat{p}}_{i})]$ where ${\hat{p}}_{i} = P (z_{i} = 1 | x_{i}, u_{i})$ and the reduced model $Z \sim X$ has deviance $D E V_{0}$ , $D E V_{0} = - 2 \sum [z_{i} \log ({\hat{p}}_{i}) + (1 - z_{i}) \log (1 - {\hat{p}}_{i})]$ where ${\hat{p}}_{i} = P (z_{i} = 1 | x_{i})$ then $R_{Z \sim U | X}^{2} = 1 - e^{(D E V_{1} - D E V_{0}) / n} .$

The returned partial $R^{2}$ has a sign, which indicates whether the association is positive or negative. Its absolute value is calculated as above.

04/29/2020 Version 0.1.0

Performs a dual-parameter sensitivity analysis of treatment effect to unmeasured confounding in observational studies with either survival or competing risks outcomes as described in Huang, R., Xu, R., & Dulai, P. S. (2020).

Install package from GitHub

if(!require(devtools))install.packages("devtools")
devtools::install_github("Rong0707/survSens")

Usage examples

For survival outcomes,

# Load the dataset included in the package.
data(survdata)
# Stochastic EM with regression
tau.res = survSensitivity(survdata$t, survdata$d, survdata$Z, survdata$X, "stoEM_reg", B = 5)
# EM with regression
tau.res = survSensitivity(survdata$t, survdata$d, survdata$Z, survdata$X, "EM_reg", Bem = 50)

# Contour plot with coefficients as axes.
plotsens(tau.res, coeff0 = 1.131)
# Contour plot with partial R-squared as axes.
plotsens(tau.res, coeff0 = 1.131, TRUE)

For competing risks outcomes,

# Load the dataset included in the package
data(comprdata)
# Stochastic EM with regression
tau.res = comprSensitivity(comprdata$t, comprdata$d, comprdata$Z, comprdata$X, "stoEM_reg", B = 5)
# EM with regression
tau.res = comprSensitivity(comprdata$t, comprdata$d, comprdata$Z, comprdata$X, "EM_reg", Bem = 50)

# Contour plot with coefficients as axes.
plotsens(tau.res$tau1, coeff0 = 1.244)
# Contour plot with partial R-squared as axes.
plotsens(tau.res$tau1, coeff0 = 1.244, TRUE)

Output consists of dataframe(s) for estimated treatment effect(s), as well as a contour plot for visualization.

Reference

Cinelli, C., & Hazlett, C. (2020). Making sense of sensitivity: Extending omitted variable bias. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 82(1), 39-67.
Huang, R., Xu, R., & Dulai, P. S. (2020). Sensitivity analysis of treatment effect to unmeasured confounding in observational studies with survival and competing risks outcomes. Statistics in Medicine, 39(24), 3397-3411.
O’Quigley, J., Xu, R., & Stare, J. (2005). Explained randomness in proportional hazards models. Statistics in medicine, 24(3), 479-489.
Cox, D. R., & Snell, E. J. (1989). The analysis of binary data, 2nd ed. London: Chapman and Hall.