Power results
cmp <- pmap_dfr(list(x = res,
title = c("1. 4 clusters",
"2. 4 clusters, PN",
"3. 12 clusters",
"4. 12 unequal clusters",
"5. Random clusters"),
R = c(1, 1, 1, 50, 100),
cores = c(1, 1, 1, 30, 30)),
compare_power)
kable(cmp, digits = 3)
| 1. 4 clusters |
0.762 |
0.762 |
0.071 |
0.872 |
0.871 |
| 2. 4 clusters, PN |
0.746 |
0.748 |
-0.176 |
0.870 |
0.869 |
| 3. 12 clusters |
0.707 |
0.710 |
-0.298 |
0.746 |
0.744 |
| 4. 12 unequal clusters |
0.572 |
0.573 |
-0.130 |
0.615 |
0.612 |
| 5. Random clusters |
0.913 |
0.911 |
0.192 |
0.924 |
0.924 |
1. 4 clusters
res[[1]]$p
##
## Study setup (three-level)
##
## n1 = 11
## n2 = 50 x 4 (treatment)
## 50 x 4 (control)
## n3 = 4 (treatment)
## 4 (control)
## 8 (total)
## total_n = 200 (treatment)
## 200 (control)
## 400 (total)
## dropout = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (time)
## 0, 11, 15, 18, 20, 22, 24, 26, 27, 29, 30 (%, control)
## 0, 11, 15, 18, 20, 22, 24, 26, 27, 29, 30 (%, treatment)
## icc_pre_subjects = 0.54
## icc_pre_clusters = 0
## icc_slope = 0.1
## var_ratio = 0.03
## cohend = -0.9
summary(res[[1]])
## Model: correct
## Random effects
##
## parameter M_est theta prop_zero
## subject_intercept 7.8404 7.8400 0.0000
## subject_slope 0.1598 0.1600 0.0000
## cluster_slope 0.0181 0.0178 0.0287
## error 6.7616 6.7600 0.0000
## cor_subject -0.1969 -0.2000 0.0000
##
## Fixed effects
##
## parameter M_est theta M_se SD_est Power Power_bw Power_satt
## (Intercept) 37.00338 37.000 0.2290 0.2316 1.000 NA NaN
## treatment -0.00356 -0.640 0.3238 0.3223 0.050 NA NaN
## time -0.64039 0.000 0.0743 0.0765 1.000 NA NaN
## time:treatment -0.34333 -0.344 0.1051 0.1083 0.873 0.871 0.761
## ---
## Number of simulations: 10000 | alpha: 0.05
## Time points (n1): 11
## Subjects per cluster (n2 x n3): 50 x 4 (treatment)
## 50 x 4 (control)
## Total number of subjects: 400
2. 4 clusters, partially nested
res[[2]]$p
##
## Study setup (three-level, partially nested)
##
## n1 = 11
## n2 = 50 x 5 (treatment)
## 250 x 1 (control)
## n3 = 5 (treatment)
## 0 (control)
## 5 (total)
## total_n = 250 (treatment)
## 250 (control)
## 500 (total)
## dropout = No missing data
## icc_pre_subjects = 0.54
## icc_pre_clusters = 0
## icc_slope = 0.1
## var_ratio = 0.03
## cohend = 0.6
summary(res[[2]])
## Model: correct
## Random effects
##
## parameter M_est theta prop_zero
## subject_intercept 7.8415 7.8400 0.0000
## subject_slope 0.1600 0.1600 0.0000
## cluster_slope 0.0177 0.0178 0.0479
## error 6.7611 6.7600 0.0000
## cor_subject -0.1984 -0.2000 0.0000
##
## Fixed effects
##
## parameter M_est theta M_se SD_est Power Power_bw Power_satt
## (Intercept) 36.99954 37.000 0.1998 0.2015 1.0000 NA NaN
## treatment -0.00016 -0.640 0.2826 0.2861 0.0515 NA NaN
## time -0.63978 0.000 0.0297 0.0296 1.0000 NA NaN
## time:treatment 0.23012 0.229 0.0703 0.0727 0.8697 0.869 0.748
## ---
## Number of simulations: 10000 | alpha: 0.05
## Time points (n1): 11
## Subjects per cluster (n2 x n3): 50 x 5 (treatment)
## 250 x 1 (control)
## Total number of subjects: 500
## [Model: correct] 0.01% of the Satterthwaite calculations failed
## [Model: correct] 0.01% of the models threw convergence warnings
3. 12 clusters
res[[3]]$p
##
## Study setup (three-level)
##
## n1 = 11
## n2 = 20 x 12 (treatment)
## 20 x 12 (control)
## n3 = 12 (treatment)
## 12 (control)
## 24 (total)
## total_n = 240 (treatment)
## 240 (control)
## 480 (total)
## dropout = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (time)
## 0, 11, 15, 18, 20, 22, 24, 26, 27, 29, 30 (%, control)
## 0, 11, 15, 18, 20, 22, 24, 26, 27, 29, 30 (%, treatment)
## icc_pre_subjects = 0.54
## icc_pre_clusters = 0
## icc_slope = 0.1
## var_ratio = 0.03
## cohend = 0.5
summary(res[[3]])
## Model: correct
## Random effects
##
## parameter M_est theta prop_zero
## subject_intercept 7.855 7.8400 0.0000
## subject_slope 0.160 0.1600 0.0000
## cluster_slope 0.018 0.0178 0.0083
## error 6.758 6.7600 0.0000
## cor_subject -0.199 -0.2000 0.0000
##
## Fixed effects
##
## parameter M_est theta M_se SD_est Power Power_bw Power_satt
## (Intercept) 37.00660 37.000 0.2092 0.2113 1.0000 NA NaN
## treatment -0.00913 -0.640 0.2959 0.2991 0.0501 NA NaN
## time -0.64074 0.000 0.0514 0.0516 1.0000 NA NaN
## time:treatment 0.19235 0.191 0.0727 0.0732 0.7465 0.744 0.71
## ---
## Number of simulations: 10000 | alpha: 0.05
## Time points (n1): 11
## Subjects per cluster (n2 x n3): 20 x 12 (treatment)
## 20 x 12 (control)
## Total number of subjects: 480
## [Model: correct] 0.01% of the Satterthwaite calculations failed
## [Model: correct] 0.01% of the models threw convergence warnings
4. Unequal clusters
res[[4]]$p
##
## Study setup (three-level)
##
## n1 = 11
## n2 = 5, 5, 5, 6, 7, 10, 10, 15, 20, 20, 25, 30 (treatment)
## 5, 5, 5, 6, 7, 10, 10, 15, 20, 20, 25, 30 (control)
## n3 = 12 (treatment)
## 12 (control)
## 24 (total)
## total_n = 158 (treatment)
## 158 (control)
## 316 (total)
## dropout = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (time)
## 0, 11, 15, 18, 20, 22, 24, 26, 27, 29, 30 (%, control)
## 0, 11, 15, 18, 20, 22, 24, 26, 27, 29, 30 (%, treatment)
## icc_pre_subjects = 0.54
## icc_pre_clusters = 0
## icc_slope = 0.1
## var_ratio = 0.03
## cohend = 0.5
summary(res[[4]])
## Model: correct
## Random effects
##
## parameter M_est theta prop_zero
## subject_intercept 7.8575 7.8400 0.0000
## subject_slope 0.1600 0.1600 0.0000
## cluster_slope 0.0179 0.0178 0.0438
## error 6.7595 6.7600 0.0000
## cor_subject -0.1986 -0.2000 0.0000
##
## Fixed effects
##
## parameter M_est theta M_se SD_est Power Power_bw Power_satt
## (Intercept) 36.99902 37.000 0.2578 0.2579 1.0000 NA NaN
## treatment 0.00631 -0.640 0.3646 0.3623 0.0478 NA NaN
## time -0.64043 0.000 0.0593 0.0607 1.0000 NA NaN
## time:treatment 0.19130 0.191 0.0839 0.0857 0.6151 0.612 0.573
## ---
## Number of simulations: 10000 | alpha: 0.05
## Time points (n1): 11
## Subjects per cluster: 5, 5, 5, 6, 7, 10, 10, 15, 20, 20, 25, 30 (treatment)
## 5, 5, 5, 6, 7, 10, 10, 15, 20, 20, 25, 30 (control)
## Total number of subjects: 316
## [Model: correct] 0.14% of the Satterthwaite calculations failed
## [Model: correct] 0.14% of the models threw convergence warnings
5. Random clusters
res[[5]]$p
##
## Study setup (three-level)
##
## n1 = 11
## n2 = rnorm(18, 5, 15) (treatment)
## rnorm(18, 5, 15) (control)
## n3 = 18 (treatment)
## 18 (control)
## 36 (total)
## total_n = 127 (treatment)
## 127 (control)
## 254 (total)
## dropout = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (time)
## 0, 11, 15, 18, 20, 22, 24, 26, 27, 29, 30 (%, control)
## 0, 11, 15, 18, 20, 22, 24, 26, 27, 29, 30 (%, treatment)
## icc_pre_subjects = 0.54
## icc_pre_clusters = 0
## icc_slope = 0.1
## var_ratio = 0.03
## cohend = 0.7
##
## NOTE: n2 is randomly sampled
summary(res[[5]])
## Model: correct
## Random effects
##
## parameter M_est theta prop_zero
## subject_intercept 7.8373 7.8400 0.0000
## subject_slope 0.1599 0.1600 0.0000
## cluster_slope 0.0179 0.0178 0.0473
## error 6.7609 6.7600 0.0000
## cor_subject -0.1984 -0.2000 0.0000
##
## Fixed effects
##
## parameter M_est theta M_se SD_est Power Power_bw Power_satt
## (Intercept) 36.999483 37.000 0.2418 0.2468 1.000 NA NaN
## treatment -0.000795 -0.640 0.3419 0.3479 0.055 NA NaN
## time -0.640834 0.000 0.0541 0.0556 1.000 NA NaN
## time:treatment 0.267504 0.267 0.0764 0.0786 0.924 0.924 0.911
## ---
## Number of simulations: 10000 | alpha: 0.05
## Time points (n1): 11
## Subjects per cluster: rnorm(18, 5, 15) (treatment)
## rnorm(18, 5, 15) (control)
## Total number of subjects: 371.4 (mean) 366 (median) 78.53 (SD)
## [Model: correct] 0.15% of the Satterthwaite calculations failed
## [Model: correct] 0.15% of the models threw convergence warnings