# ARsens.power: Power of the Anderson-Rubin (1949) Test with Sensitivity... In ivmodel: Statistical Inference and Sensitivity Analysis for Instrumental Variables Model

 ARsens.power R Documentation

## Power of the Anderson-Rubin (1949) Test with Sensitivity Analysis

### Description

`ARsens.power` computes the power of sensitivity analysis, which is based on an extension of Anderson-Rubin (1949) test and allows IV be possibly invalid within a certain range.

### Usage

``````ARsens.power(n, k, beta, gamma, Zadj_sq, sigmau, sigmav, rho,
alpha = 0.05, deltarange = deltarange, delta = NULL)
``````

### Arguments

 `n` Sample size. `k` Number of exogenous variables. `beta` True causal effect minus null hypothesis causal effect. `gamma` Regression coefficient for effect of instruments on treatment. `Zadj_sq` Variance of instruments after regressed on the observed variables. `sigmau` Standard deviation of potential outcome under control (structural error for y). `sigmav` Standard deviation of error from regressing treatment on instruments. `rho` Correlation between u (potential outcome under control) and v (error from regressing treatment on instrument). `alpha` Significance level. `deltarange` Range of sensitivity allowance. A numeric vector of length 2. `delta` True value of sensitivity parameter when calculating the power. Usually take delta = 0 for the favorable situation or delta = NULL for unknown delta.

### Value

Power of sensitivity analysis for the proposed study, which extends the Anderson-Rubin (1949) test with possibly invalid IV. The power formula is derived in Jiang, Small and Zhang (2015).

### Author(s)

Yang Jiang, Hyunseung Kang, and Dylan Small

### References

Anderson, T.W. and Rubin, H. (1949), Estimation of the parameters of a single equation in a complete system of stochastic equations, Annals of Mathematical Statistics, 20, 46-63.
Wang, X., Jiang, Y., Small, D. and Zhang, N (2017), Sensitivity analysis and power for instrumental variable studies, (under review of Biometrics).

See also `ivmodel` for details on the instrumental variables model.

### Examples

``````# Assume we calculate the power of sensitivity analysis in a study with
# one IV (l=1) and the only exogenous variable is the intercept (k=1).

# Suppose the difference between the null hypothesis and true causal
# effect is 1 (beta=1).
# The sample size is 250 (n=250), the IV variance is .25 (Zadj_sq =.25).
# The standard deviation of potential outcome is 1(sigmau= 1).
# The coefficient of regressing IV upon exposure is .5 (gamma= .5).
# The correlation between u and v is assumed to be .5 (rho=.5).
# The standard deviation of first stage error is .4 (sigmav=.4).
# The significance level for the study is alpha = .05.

# power of sensitivity analysis under the favorable situation,
# assuming the range of sensitivity allowance is (-0.1, 0.1)
ARsens.power(n=250, k=1, beta=1, gamma=.5, Zadj_sq=.25, sigmau=1,
sigmav=.4, rho=.5, alpha = 0.05, deltarange=c(-0.1, 0.1), delta=0)

# power of sensitivity analysis with unknown delta,
# assuming the range of sensitivity allowance is (-0.1, 0.1)
ARsens.power(n=250, k=1, beta=1, gamma=.5, Zadj_sq=.25, sigmau=1,
sigmav=.4, rho=.5, alpha = 0.05, deltarange=c(-0.1, 0.1))

``````

ivmodel documentation built on April 9, 2023, 5:08 p.m.