Create Design Comparison Table for Two Co-Primary Endpoints
Source:R/design_table.R
design_table.RdGenerates a comprehensive table comparing sample sizes or power across different parameter combinations and correlation values. This function is useful for sensitivity analyses and exploring how design parameters affect statistical properties.
Arguments
- param_grid
A data.frame containing parameter combinations. Required columns depend on endpoint_type and calculation_mode:
For continuous endpoints (sample size): delta1, delta2, sd1, sd2
For continuous endpoints (power): n1, n2, delta1, delta2, sd1, sd2
For binary endpoints (sample size): p11, p12, p21, p22
For binary endpoints (power): n1, n2, p11, p12, p21, p22
For mixed continuous-binary (sample size): delta, sd, p1, p2
For mixed continuous-binary (power): n1, n2, delta, sd, p1, p2
For mixed count-continuous (sample size): r1, r2, nu, t, mu1, mu2, sd
For mixed count-continuous (power): n1, n2, r1, r2, nu, t, mu1, mu2, sd
- rho_values
Numeric vector of correlation values to evaluate. Default is c(0, 0.3, 0.5, 0.8).
- r
Allocation ratio (n1/n2). Required for sample size calculation. Default is 1.
- alpha
One-sided significance level. Default is 0.025.
- beta
Type II error rate (1 - power). Required for sample size calculation. Default is 0.2 (power = 0.8).
- endpoint_type
Character string specifying endpoint type: "continuous", "binary", "mixed_cont_binary", or "mixed_count_cont".
- Test
Test method. For
endpoint_type = "binary"the four asymptotic methods "AN" (asymptotic normal), "ANc" (with continuity correction), "AS" (arcsine) and "ASc" (arcsine with continuity correction) route to the approximate functions, while "Chisq", "Fisher", "Fisher-midP", "Z-pool" and "Boschloo" route to the exact functions and are substantially more expensive. Forendpoint_type = "mixed_cont_binary"the four asymptotic methods and "Fisher" are available. Default is "AN". Not used for the continuous and mixed count-continuous endpoint types.- known_var
Logical indicating whether variance is known for continuous endpoints. Default is TRUE.
- nMC
Number of Monte Carlo simulations for certain calculations. Default is 1000.
- output_var
Character string specifying which variable to output in the result columns: "N" (total sample size, default for sample size calculation) or "powerCoprimary" (co-primary power, default for power calculation).
- n_grid
Number of grid points used to maximize the null tail probability over the nuisance parameter in the two exact unconditional tests, that is
"Z-pool"and"Boschloo"(default is 100). The other three tests read their p-values off a distribution and ignore this argument. A finer grid locates the maximum more accurately at a proportionally higher computational cost, and the default reproduces the results of earlier versions of the package.
Value
A data.frame of class "twoCoprimary_table" with:
Parameter columns (from param_grid)
Result columns for each correlation value (rho_0.0, rho_0.3, etc.)
Details
This function performs systematic calculations across all combinations of parameters specified in param_grid and correlation values in rho_values.
The calculation mode (sample size vs power) is automatically determined:
If param_grid contains n1 and n2: calculates power
Otherwise: calculates sample size (requires r, alpha, beta)
For binary endpoints with two correlations (rho1, rho2), both are set to the same value from rho_values for each calculation.
The output format follows the style of Sozu et al. (2011), with parameters displayed in the leftmost columns and results for each correlation in subsequent columns.
References
Sozu, T., Sugimoto, T., & Hamasaki, T. (2011). Sample size determination in superiority clinical trials with multiple co-primary correlated endpoints. Journal of Biopharmaceutical Statistics, 21(4), 650-668.
Examples
# Sample size calculation for continuous endpoints
param_grid <- expand.grid(
delta1 = c(0.3, 0.5),
delta2 = c(0.1, 0.2, 0.3),
sd1 = c(1.0, 1.5),
sd2 = c(1.0, 1.5)
)
result <- design_table(
param_grid = param_grid,
rho_values = c(0, 0.3, 0.5, 0.8),
r = 1,
alpha = 0.025,
beta = 0.2,
endpoint_type = "continuous"
)
print(result)
#>
#> Design Comparison Table for Two Co-Primary Endpoints
#> ======================================================
#>
#> delta1 delta2 sd1 sd2 rho_0.0 rho_0.3 rho_0.5 rho_0.8
#> 0.3 0.1 1.0 1.0 3140 3140 3140 3140
#> 0.5 0.1 1.0 1.0 3140 3140 3140 3140
#> 0.3 0.2 1.0 1.0 804 798 794 786
#> 0.5 0.2 1.0 1.0 786 786 786 786
#> 0.3 0.3 1.0 1.0 460 448 436 408
#> 0.5 0.3 1.0 1.0 352 352 350 350
#> 0.3 0.1 1.5 1.0 3142 3140 3140 3140
#> 0.5 0.1 1.5 1.0 3140 3140 3140 3140
#> 0.3 0.2 1.5 1.0 1032 1006 980 916
#> 0.5 0.2 1.5 1.0 792 790 788 786
#> 0.3 0.3 1.5 1.0 804 798 794 786
#> 0.5 0.3 1.5 1.0 418 408 398 374
#> 0.3 0.1 1.0 1.5 7064 7064 7064 7064
#> 0.5 0.1 1.0 1.5 7064 7064 7064 7064
#> 0.3 0.2 1.0 1.5 1768 1768 1766 1766
#> 0.5 0.2 1.0 1.5 1766 1766 1766 1766
#> 0.3 0.3 1.0 1.5 804 798 794 786
#> 0.5 0.3 1.0 1.5 786 786 786 786
#> 0.3 0.1 1.5 1.5 7064 7064 7064 7064
#> 0.5 0.1 1.5 1.5 7064 7064 7064 7064
#> 0.3 0.2 1.5 1.5 1808 1794 1784 1768
#> 0.5 0.2 1.5 1.5 1766 1766 1766 1766
#> 0.3 0.3 1.5 1.5 1032 1006 980 916
#> 0.5 0.3 1.5 1.5 792 790 788 786
# Power calculation for continuous endpoints
param_grid_power <- expand.grid(
n1 = c(50, 100),
n2 = c(50, 100),
delta1 = 0.5,
delta2 = 0.5,
sd1 = 1.0,
sd2 = 1.0
)
result_power <- design_table(
param_grid = param_grid_power,
rho_values = c(0, 0.3, 0.5, 0.8),
alpha = 0.025,
endpoint_type = "continuous"
)
print(result_power)
#>
#> Design Comparison Table for Two Co-Primary Endpoints
#> ======================================================
#>
#> n1 n2 delta1 delta2 sd1 sd2 rho_0.0 rho_0.3 rho_0.5 rho_0.8
#> 50 50 0.5 0.5 1 1 0.4976088 0.5352018 0.5634879 0.6173565
#> 100 50 0.5 0.5 1 1 0.6772986 0.7002326 0.7190959 0.7573394
#> 50 100 0.5 0.5 1 1 0.6772986 0.7002326 0.7190959 0.7573394
#> 100 100 0.5 0.5 1 1 0.8881885 0.8938066 0.8997323 0.9141060
# Binary endpoints
param_grid_binary <- expand.grid(
p11 = c(0.6, 0.7),
p12 = c(0.4, 0.5),
p21 = c(0.4, 0.5),
p22 = c(0.2, 0.3)
)
result_binary <- design_table(
param_grid = param_grid_binary,
rho_values = c(0.3, 0.5, 0.7),
r = 1,
alpha = 0.025,
beta = 0.2,
endpoint_type = "binary",
Test = "AN"
)
print(result_binary)
#>
#> Design Comparison Table for Two Co-Primary Endpoints
#> ======================================================
#>
#> p11 p12 p21 p22 rho_0.3 rho_0.5 rho_0.7
#> 0.6 0.4 0.4 0.2 230 224 NA
#> 0.7 0.4 0.4 0.2 168 166 NA
#> 0.6 0.5 0.4 0.2 196 196 NA
#> 0.7 0.5 0.4 0.2 104 100 NA
#> 0.6 0.4 0.5 0.2 776 776 NA
#> 0.7 0.4 0.5 0.2 224 218 NA
#> 0.6 0.5 0.5 0.2 776 776 NA
#> 0.7 0.5 0.5 0.2 188 188 NA
#> 0.6 0.4 0.4 0.3 714 712 NA
#> 0.7 0.4 0.4 0.3 712 712 NA
#> 0.6 0.5 0.4 0.3 244 238 228
#> 0.7 0.5 0.4 0.3 190 188 NA
#> 0.6 0.4 0.5 0.3 952 928 NA
#> 0.7 0.4 0.5 0.3 714 712 NA
#> 0.6 0.5 0.5 0.3 776 776 NA
#> 0.7 0.5 0.5 0.3 238 232 NA