This `H2x2Factorial`

package implements the sample size methods for hierarchical 2x2 factorial trials with unequal cluster sizes. The sample size calculations support two types of treatment effect estimands and five types of hypothesis tests based on the two measures. The two estimands are named as the controlled effect and the natural effect, as formally defined in Tian et al. (under review); The hypotheses include (A1) test for the cluster-level controlled effect, (A2) test for the individual-level controlled effect, (B1) test for the cluster-level natural effect, (B2) test for the individual-level natural effect, (C) interaction test for the two treatments, (D1) joint test for the two controlled treatment effects, (D2) joint test for the two natural treatment effects, (E1) intersection-union test for the two controlled treatment effects, (E2) intersection-union test for the two natural treatment effects. Finite-sample considerations are included for the tests involving either cluster-level treatment effect, due to the degree of freedom issues. Three functions are currently contained for predicting the power or sample size based on given design parameters as well as delivering illustrative tables or line plots. Specifically, the `calc.H2x2Factorial`

function calculates required number of clusters for a specific test to achieve a given power, or predicts the actual power given specified sample size resources, with or without finite-sample considerations. The `table.H2x2Factorial`

function creates a data frame to show a series of sample size predictions by providing varying mean cluster sizes, intraclass correlation coefficients, or coefficient of variations of cluster sizes (CV). The `graph.H2x2Factorial`

function plots sample size requirements under different CV in the form of the combinations of mean cluster sizes and number of clusters. All of the hypothesis tests and sample size methodologies are formalized in “Sample size calculation in hierarchical 2x2 factorial trials with unequal cluster sizes” (under review).

The released version of H2x2Factorial can be installed from CRAN with:

This is an example for predicting the required number of clusters based on fixed design parameters:

```
library(H2x2Factorial)
#> Warning: package 'H2x2Factorial' was built under R version 4.0.5
example("calc.H2x2Factorial")
#>
#> c.H22F> #Predict the actual power of a joint test when the number of clusters is 10
#> c.H22F> joint.power <- calc.H2x2Factorial(n_input=10,
#> c.H22F+ delta_x=0.2, delta_z=0.1,
#> c.H22F+ rho=0.1, CV=0.38,
#> c.H22F+ test="joint", correction=TRUE, seed_mix=123456, verbose=FALSE)
#>
#> c.H22F> print(joint.power)
#> [1] 0.2131
```

This is an example for displaying a series of sample size predictions in a table format based on varying design parameters:

```
example("table.H2x2Factorial")
#>
#> t.H22F> #Make a result table by providing three mean cluster sizes, three CV, and three ICC
#> t.H22F> table.cluster <- table.H2x2Factorial(delta_x=0.2, delta_z=0.1,
#> t.H22F+ m_bar=c(10,50,100), CV=c(0, 0.3, 0.5), rho=c(0.01, 0.1),
#> t.H22F+ test="cluster", verbose=FALSE)
#>
#> t.H22F> table.cluster
#> m_bar rho CV n predicted power
#> 1 10 0.01 0.0 86 0.8020410
#> 2 10 0.01 0.3 87 0.8036148
#> 3 10 0.01 0.5 88 0.8027978
#> 4 10 0.10 0.0 150 0.8022800
#> 5 10 0.10 0.3 153 0.8011498
#> 6 10 0.10 0.5 160 0.8023522
#> 7 50 0.01 0.0 24 0.8100115
#> 8 50 0.01 0.3 24 0.8021486
#> 9 50 0.01 0.5 25 0.8036072
#> 10 50 0.10 0.0 93 0.8016170
#> 11 50 0.10 0.3 94 0.8012229
#> 12 50 0.10 0.5 96 0.8011854
#> 13 100 0.01 0.0 16 0.8093656
#> 14 100 0.01 0.3 16 0.8005201
#> 15 100 0.01 0.5 17 0.8078552
#> 16 100 0.10 0.0 86 0.8020410
#> 17 100 0.10 0.3 87 0.8038824
#> 18 100 0.10 0.5 88 0.8035513
```

This is an example for plotting the sample size requirements under varying coefficients of variation of cluster sizes: