Adjusting for expected dropout-rate - Nitpicking [Power / Sample Size]
Dear Helmut.
Should be considered possibility of unbalanced design after adjusting for expected dropout-rate? See example below.
Let's plan 2x2 crossover study with following assumptions/requirements:
CV = 0.262
alpha = 0.05
power >= 0.80
ratio = 0.95
acceptance range: 0.80-1.25
It implies minimum sample size ndes = 30.
Expected dropout-rate = 15%.
nadj=36 (n1=18, n2=18)
Now let's see that all assumptions are respected, but power falls under desired 80% in unbalanced cases.
In the first line of the next table "TR" stands for number of dropouts from sequence TR, "RT" likewise and "Probability" stands for probability of case when exactly 6 dropouts are expected.
In case of 3 dropouts with TR and 3 with RT, the power is 80.1%.
Otherwise the power is supposed to be lower than 80% - not much lower of course. With unbalanced case 4:2 dropouts, the power is 79.9%. Then if it's getting more unbalanced, the power is decreasing (as you know).
So in this example we have 65.8% (100*(1-p_4)) probability that we shoot ourselves in the foot
.
Maybe not so big shot - planned number of subjects finished will be achieved
, but sample size wasn't estimated with option of getting unbalanced in mind. Even though there is almost 2/3 probability that it will ends unbalanced (if assumptions are right, and no better GMR than expected, no lower CV estimated from residual mean square than expected, and no lower dropout-rate than expected).
Best regards,
zizou
"Remember, with great power comes great responsibility."
Should be considered possibility of unbalanced design after adjusting for expected dropout-rate? See example below.
Let's plan 2x2 crossover study with following assumptions/requirements:
CV = 0.262
alpha = 0.05
power >= 0.80
ratio = 0.95
acceptance range: 0.80-1.25
It implies minimum sample size ndes = 30.
Expected dropout-rate = 15%.
nadj=36 (n1=18, n2=18)
Now let's see that all assumptions are respected, but power falls under desired 80% in unbalanced cases.
In the first line of the next table "TR" stands for number of dropouts from sequence TR, "RT" likewise and "Probability" stands for probability of case when exactly 6 dropouts are expected.
TR RT Probability Power
6 0 p_1=0.009530792 <80%
5 1 p_2=0.07917889 <80%
4 2 p_3=0.2403645 <80%
3 3 p_4=0.3418517 >80%
2 4 p_5=0.2403645 <80%
1 5 p_6=0.07917889 <80%
0 6 p_7=0.009530792 <80%
# R code:
p_1=choose(18,6)/choose(36,6)
p_2=(choose(18,5)*choose(18,1))/choose(36,6)
p_3=(choose(18,4)*choose(18,2))/choose(36,6)
p_4=(choose(18,3)*choose(18,3))/choose(36,6)
2*p_1+2*p_2+2*p_3+p_4 # Check that sum of p_i is equal to 1.
In case of 3 dropouts with TR and 3 with RT, the power is 80.1%.
Otherwise the power is supposed to be lower than 80% - not much lower of course. With unbalanced case 4:2 dropouts, the power is 79.9%. Then if it's getting more unbalanced, the power is decreasing (as you know).
So in this example we have 65.8% (100*(1-p_4)) probability that we shoot ourselves in the foot

Maybe not so big shot - planned number of subjects finished will be achieved

Best regards,
zizou
"Remember, with great power comes great responsibility."
Complete thread:
- Adjusting for expected dropout-rate Helmut 2015-06-17 12:33 [Power / Sample Size]
- Percentage calculation d_labes 2015-06-18 09:02
- Adjusting for expected dropout-rate - Nitpickingzizou 2015-08-18 23:34
- Good point! Helmut 2015-08-19 02:20
- Good point! intuitivepharma 2015-08-19 07:47
- Copy paste error d_labes 2015-08-19 10:12
- Copy paste error intuitivepharma 2015-08-19 11:18
- PowerTOST <1.2.7? Helmut 2015-08-19 11:44
- PowerTOST <1.2.7? intuitivepharma 2015-08-26 14:41
- PowerTOST <1.2.7? Helmut 2015-08-19 11:44
- Copy paste error intuitivepharma 2015-08-19 11:18
- Copy paste error d_labes 2015-08-19 10:12
- Good point! intuitivepharma 2015-08-19 07:47
- Good point! Helmut 2015-08-19 02:20