comprSensitivity {survSens}

Sensitivity analysis of treatment effect to unmeasured confounding with competing risks outcomes.

Description

comprSensitivity performs a dual-parameter sensitivity analysis of treatment effect to unmeasured confounding in observational studies with competing risks outcomes.

Usage

comprSensitivity(t, d, Z, X, method, zetaT = seq(-2,2,by=0.5),
zetat2 = 0, zetaZ = seq(-2,2,by=0.5), theta = 0.5, B = 50, Bem = 200)

Arguments

t

survival outcomes with competing risks.

d

indicator of occurrence of event, with d == 0 denotes right censoring, d==1 denotes event of interest, d==2 denotes competing risk.

Z

indicator of treatment.

X

pre-treatment covariates that will be included in the model as measured confounders.

method

needs to be one of "stoEM_reg", "stoEM_IPW" and "EM_reg".

zetaT

range of coefficient of U in the event of interest response model.

zetat2

value of coefficient of U in the competing risk response model

zetaZ

range of coefficient of U in the treatment model.

theta

marginal probability of U=1.

B

iteration in the stochastic EM algorithm.

Bem

iteration used to estimate the variance-covariance matrix in the EM algorithm.

Details

This function performs a dual-parameter sensitivity analysis of treatment effect to unmeasured confounding by either drawing simulated potential confounders U from the conditional distribution of U given observed response, treatment and covariates or the Expectation-Maximization algorithm. We assume U is following Bernoulli(\pi) (default 0.5). Given Z, X and U, the hazard rate of the jth type of failure is modeled using the Cox proportional hazards (PH) regression:

\lambda_j (t | Z, X, U) = \lambda_{j0} (t) exp( \tau_j Z + X' \beta_j + \zeta_j U).

Given X and U, Z follows a generalized linear model:

P(Z=1 | X, U) = \Phi(X' \beta_z + \zeta_z U).

Value

tau1

a data.frame with zetaz, zetat1, zetat2, tau1, tau1.se and t statistic in the event of interest response model.

tau2

a data.frame with zetaz, zetat, zetat2, tau2, tau2.se and t statistic in the competing risks response model.

Author(s)

Rong Huang

References

Huang, R., Xu, R., & Dulai, P. S. (2019). Sensitivity Analysis of Treatment Effect to Unmeasured Confounding in Observational Studies with Survival and Competing Risks Outcomes. arXiv preprint arXiv:1908.01444.

Examples

#load the dataset included in the package
data(comprdata)
#stochastic EM with regression
tau.sto = comprSensitivity(comprdata$t, comprdata$d, comprdata$Z, comprdata$X,
"stoEM_reg", zetaT = 0.5, zetaZ = 0.5, B = 3)

#EM with regression
tau.em = comprSensitivity(comprdata$t, comprdata$d, comprdata$Z, comprdata$X,
"EM_reg", zetaT = 0.5, zetaZ = 0.5, Bem = 50)