ARsens.size: Sample Size Calculator for the Power of the Anderson-Rubin... In ivmodel: Statistical Inference and Sensitivity Analysis for Instrumental Variables Model

Description

`ARsens.size` computes the minimum sample size required for achieving certain 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

 ```1 2``` ```ARsens.size(power, k, beta, gamma, Zadj_sq, sigmau, sigmav, rho, alpha = 0.05, deltarange = deltarange, delta = NULL) ```

Arguments

 `power` The desired power over a constant. `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 covariates. `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 instruments). `alpha` Significance level. `deltarange` Range of sensitivity allowance. A numeric vector of length 2. `delta` True value of sensitivity parameter when calculating power. Usually take delta = 0 for the favorable situation or delta = NULL for unknown delta.

Value

Minimum sample size required for achieving certain 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.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```# Assume we performed a sensitivity analysis in a study with one # IV (l=1) and the only exogenous variable is the intercept (k=1). # We want to calculate the minimum sample size needed for this # sensitivity analysis to have an at least 0.8 power. # Suppose the difference between the null hypothesis and true causal # effect is 1 (beta=1). # 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. # minimum sample size for sensitivity analysis under the favorable # situation, assuming the range of sensitivity allowance is (-0.1, 0.1) ARsens.size(power=0.8, 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) # minimum sample size for sensitivity analysis with unknown delta, # assuming the range of sensitivity allowance is (-0.1, 0.1) ARsens.size(power=0.8, k=1, beta=1, gamma=.5, Zadj_sq=.25, sigmau=1, sigmav=.4, rho=.5, alpha = 0.05, deltarange=c(-0.1, 0.1)) ```