crt2power

Overview

crt2power is an R package that allows users to calculate the statistical power or sample size of their cluster randomized trials (CRTs) with two co-primary outcomes, given a set of input parameters. The motivation for this package is to aid in the design of hybrid 2 studies. Hybrid 2 studies are studies where there are two co-primary outcomes, namely an implementation outcome (such as fidelity or reach) and a health outcome (such as infection rates, or change from baseline health scores). When powering these studies, cluster correlations and the inflation of the Type I error rate must be accounted for.

The five key study design approaches are included in this package that can be used to power hybrid 2 CRTs.

1. P-Value Adjustments for Multiple Testing
2. Combined Outcomes Approach
3. Single 1-Degree of Freedom (DF) Combined Test for Two Outcomes
4. Disjunctive 2-DF Test for Two Outcomes
5. Conjunctive Intersection-Union Test for Two outcomes

For details on the methods listed above, please refer to the publication that discusses these methods, available here. (Add link)

Installation

install.packages("devtools")
require(devtools)
install_github("https://github.com/melodyaowen/crt2power")
require(crt2power)

Required Input Parameters

Table of Key Required Input Parameters:

Parameter	Statistical Notation	Variable Name	Description
Statistical power	$\pi$	power	Probability of detecting a true effect under $H_A$
Number of clusters	$K$	K	Number of clusters in each treatment arm
Cluster size	$m$	m	Number of individuals in each cluster
Family-wise false positive rate	$\alpha$	alpha	Probability of one or more Type I error(s)
Effect for $Y_1$	$\beta_1^*$	beta1	Estimated intervention effect on the first outcome ($Y_1$)
Effect for $Y_2$	$\beta_2^*$	beta2	Estimated intervention effect on the second outcome ($Y_2$)
Total variance of $Y_1$	$\sigma_1^2$	varY1	Total variance of the first outcome, $Y_1$
Total variance of $Y_2$	$\sigma_2^2$	varY2	Total variance of the second outcome, $Y_2$
Endpoint-specific ICC for $Y_1$	$\rho_0^{(1)}$	rho01	Correlation for $Y_1$ for two different individuals in the same cluster
Endpoint-specific ICC for $Y_2$	$\rho_0^{(2)}$	rho02	Correlation for $Y_2$ for two different individuals in the same cluster
Inter-subject between-endpoint ICC	$\rho_1^{(1,2)}$	rho1	Correlation between $Y_1$ and $Y_2$ for two different individuals in the same cluster
Intra-subject between-endpoint ICC	$\rho_2^{(1,2)}$	rho2	Correlation between $Y_1$ and $Y_2$ for the same individual
Treatment allocation ratio	$r$	r	Treatment allocation ratio; $K_2 = rK_1$ where $K_1$ is number of clusters in experimental group

Function Description

Each method has a set of functions for calculating the statistical power ($\pi$), required number of clusters per treatment group ($K$), or cluster size ($m$) given a set of input parameters. The names of all functions offered in this package are listed below, organized by study design method.

1. P-Value Adjustments for Multiple Testing

• calc_pwr_pval_adj() calculates power for this method
• calc_K_pval_adj() calculates number of clusters per treatment group for this method
• calc_m_pval_adj() calculates cluster size for this method

2. Combined Outcomes Approach

• calc_pwr_comb_outcome() calculates power for this method
• calc_K_comb_outcome() calculates number of clusters per treatment group for this method
• calc_m_comb_outcome() calculates cluster size for this method

3. Single 1-Degree of Freedom (DF) Combined Test for Two Outcomes

• calc_pwr_single_1dftest() calculates power for this method
• calc_K_single_1dftest() calculates number of clusters per treatment group for this method
• calc_m_single_1dftest() calculates cluster size for this method

4. Disjunctive 2-DF Test for Two Outcomes

• calc_pwr_disj_2dftest() calculates power for this method
• calc_K_disj_2dftest() calculates number of clusters per treatment group for this method
• calc_m_disj_2dftest() calculates cluster size for this method

5. Conjunctive Intersection-Union Test for Two outcomes

• calc_pwr_conj_test() calculates power for this method
• calc_K_conj_test() calculates number of clusters per treatment group for this method
• calc_m_conj_test() calculates cluster size for this method

Usage

# Example of using Method 1 for a power calculation
calc_pwr_pval_adj(K = 15, m = 300, alpha = 0.05,
                  beta1 = 0.1, beta2 = 0.1,
                  varY1 = 0.23, varY2 = 0.25,
                  rho01 = 0.025, rho02 = 0.025,
                  rho2  = 0.05, r = 1)

# Example of using Method 3 for number of clusters in treatment group (K) calculation
calc_K_single_1dftest(power = 0.8, m = 300, alpha = 0.05,
                      beta1 = 0.1, beta2 = 0.1,
                      varY1 = 0.23, varY2 = 0.25,
                      rho01 = 0.025, rho02 = 0.025,
                      rho1 = 0.01, rho2  = 0.05, r = 1)

# Example of using Method 5 for cluster size (m) calculation
calc_m_conj_test(power = 0.8, K = 15, alpha = 0.05,
                 beta1 = 0.1, beta2 = 0.1,
                 varY1 = 0.23, varY2 = 0.25,
                 rho01 = 0.025, rho02 = 0.025,
                 rho1 = 0.01, rho2  = 0.05, r = 1)

# Example of calculating power based on all five methods
run_crt2_design(output = "power", K = 15, m = 300, alpha = 0.05,
                beta1 = 0.1, beta2 = 0.1,
                varY1 = 0.23, varY2 = 0.25,
                rho01 = 0.025, rho02 = 0.025,
                rho1 = 0.01, rho2 = 0.05, r = 1)

Contact

For questions or comments, please email Melody Owen at melody.owen@yale.edu, or submit an issue to this repository.