H2x2Factorial

This H2x2Factorial package implements the sample size methods for hierarchical 2x2 factorial trials with unequal cluster sizes. The sample size calculations support five types of hypothesis tests: (A1) test for marginal cluster-level treatment effect, (A2) test for marginal individual-level treatment effect, (B) interaction test for the two treatments, (C) joint test for the two marginal treatment effects, (D) intersection union test for the two marginal treatment effects. Finite-sample considerations are included for the tests involving the marginal 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).

Installation

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

install.packages("H2x2Factorial")

Example

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

library(H2x2Factorial)
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:

example("graph.H2x2Factorial")
#> 
#> g.H22F> #Make a plot under the test for marginal cluster-level treatment effect
#> g.H22F> graph.H2x2Factorial(power=0.9, test="cluster", rho=0.1, verbose=FALSE)