# IVsize: Calculating minimum sample size for achieving a certain power In ivmodel: Statistical Inference and Sensitivity Analysis for Instrumental Variables Model

 IVsize R Documentation

## Calculating minimum sample size for achieving a certain power

### Description

`IVsize` calculates the minimum sample size needed for achieving a certain power in one of the following tests: two stage least square estimates; Anderson-Rubin (1949) test; Sensitivity analysis.

### Usage

``````IVsize(ivmodel, power, alpha = 0.05, beta = NULL, type = "TSLS",
deltarange = NULL, delta = NULL)
``````

### Arguments

 `ivmodel` `ivmodel` object. `power` The power threshold to achieve. `alpha` The significance level for hypothesis testing. Default is 0.05. `beta` True causal effect minus null hypothesis causal effect. If missing, will use the beta calculated from the input `ivmodel` object. `type` Determines which test will be used for power calculation. "TSLS" for two stage least square estimates; "AR" for Anderson-Rubin test; "ARsens" for sensitivity analysis. `deltarange` Range of sensitivity allowance. A numeric vector of length 2. If missing, will use the deltarange from the input `ivmodel` object. `delta` True value of sensitivity parameter when calculating the power. Usually take delta = 0 for the favorable situation or delta = NULL for unknown delta.

### Details

`IVsize` calculates the minimum sample size needed for achieving a certain power for one of the following tests: two stage least square estimates; Anderson-Rubin (1949) test; Sensitivity analysis. The related value of parameters will be inferred from the input of `ivmodel` object.

### Value

minimum sample size needed for achieving a certain power

### Author(s)

Yang Jiang, Hyunseung Kang, Dylan Small

### References

Freeman G, Cowling BJ, Schooling CM (2013). Power and Sample Size Calculations for Mendelian Randomization Studies Using One Genetic Instrument. International journal of epidemiology, 42(4), 1157-1163.
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.
ang, 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. See also `TSLS.size`, `AR.size`, `ARsens.size` for calculation details.

### Examples

``````data(card.data)
Y=card.data[,"lwage"]
D=card.data[,"educ"]
Z=card.data[,"nearc4"]
Xname=c("exper", "expersq", "black", "south", "smsa", "reg661",
"reg662", "reg663", "reg664", "reg665", "reg666", "reg667",
"reg668", "smsa66")
X=card.data[,Xname]
card.model = ivmodel(Y=Y,D=D,Z=Z,X=X, deltarange=c(-0.01, 0.01))

IVsize(card.model, power=0.8)
IVsize(card.model, power=0.8, type="AR")
IVsize(card.model, power=0.8, type="ARsens", deltarange=c(-0.01, 0.01))

``````

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