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

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

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)

An example dataset with competing risks outcomes.

Description

An example dataset with competing risks outcomes that can be used for comprSensitivity.

Usage

data("comprdata")

Format

The format is a list of 5, corresponding to t, d, Z, X, U, respectively.

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

data(comprdata)

A contour plot of sensitivity analysis results.

Description

A contour plot of sensitivity analysis results.

Usage

plotsens(tau.res, coeff0, partialRsq = FALSE)

Arguments

Details

This function gives a contour plot in order to visualize results from either survSensitivity or comprSensitivity. The name of sensitivity parameter in the treatment model needs to be "zetaz", the name of sensitivity parameter in the response model needs to be "zetat1", and the name of estimated treatment effect needs to be "tau1".

Value

A contour plot corresponding to the output from either survSensitivity or comprSensitivity.

Author(s)

Rong Huang

Examples

data(tau.res) #an example output
plotsens(tau.res, coeff0 = 1.131)

Sensitivity analysis of treatment effect to unmeasured confounding with survival outcomes.

Description

survSensitivity performs a dual-parameter sensitivity analysis of treatment effect to unmeasured confounding in observational studies with survival outcomes.

Usage

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

Arguments

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 is modeled using the Cox proportional hazards (PH) regression:

\lambda (t | Z, X, U) = \lambda_{0} (t) exp(\tau Z + X ' \beta + \zeta U).

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

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

Value

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(survdata)
#stochastic EM with regression
tau.sto = survSensitivity(survdata$t, survdata$d, survdata$Z, survdata$X,
"stoEM_reg", zetaT = 0.5, zetaZ = 0.5, B = 3)

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

An example dataset with survival outcomes.

Description

An example dataset with survival outcomes that can be used for survSensitivity.

Usage

data("survdata")

Format

The format is a list of 5, corresponding to t, d, Z, X, U, respectively.

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

data(survdata)

Sensitivity analysis output example

Description

An example output from survSensitivity.

Usage

data("tau.res")

Format

A data frame with 81 observations on the following 7 variables.

zetaz

a numeric vector, corresponding to the sensitivity parameter in the treatment model.

zetat1

a numeric vector, corresponding to the sensitivity parameter in the response model.

tau1

a numeric vector, corresponding to the estimated treatment effect.

tau1.se

a numeric vector, corresponding to the standard error of the estimated treatment effect.

pR2z

a numeric vector, corresponding to the Rsquared in the treatment model.

pR2t1

a numeric vector, corresponding to the Rsquared in the response model.

t

a numeric vector, corresponding to the t statistic.

Examples

data(tau.res)