Designing Cluster-Randomized Trials with Two Co-Primary Outcomes.
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.
- P-Value Adjustments for Multiple Testing
- Combined Outcomes Approach
- Single 1-Degree of Freedom (DF) Combined Test for Two Outcomes
- Disjunctive 2-DF Test for Two Outcomes
- 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 methodcalc_K_pval_adj()calculates number of clusters per treatment group for this methodcalc_m_pval_adj()calculates cluster size for this method
2. Combined Outcomes Approach
calc_pwr_comb_outcome()calculates power for this methodcalc_K_comb_outcome()calculates number of clusters per treatment group for this methodcalc_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 methodcalc_K_single_1dftest()calculates number of clusters per treatment group for this methodcalc_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 methodcalc_K_disj_2dftest()calculates number of clusters per treatment group for this methodcalc_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 methodcalc_K_conj_test()calculates number of clusters per treatment group for this methodcalc_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 [email protected], or submit an issue to this repository.