# survSensitivity: Sensitivity analysis of treatment effect to unmeasured... In survSens: Sensitivity Analysis with Time-to-Event Outcomes

## Description

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

## Usage

 ```1 2``` ```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

 `t` survival outcomes. `d` indicator of occurrence of event, with `d == 0` denotes right censoring. `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 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(π) (default 0.5). Given Z, X and U, the hazard rate is modeled using the Cox proportional hazards (PH) regression:

λ (t | Z, X, U) = λ_{0} (t) exp(τ Z + X ' β + ζ U).

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

P( Z=1 | X,U ) = Φ(X' β_z + ζ_z U).

## Value

 `tau` a data.frame with zetaz, zetat, tau1, tau1.se and t statistic.

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

 ```1 2 3 4 5 6 7 8 9``` ```#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) ```

### Example output

```
```

survSens documentation built on April 29, 2020, 5:07 p.m.