Least Square Means (LSM) for incomplete data [Software]
I started a query on Least Square Means (LSM) for unequal sequence several days ago.
In that posting, the method of calculating LSM for unequal sequence data has been pointed out by ElMaestro, thanks to ElMaestro. Although new question on SE for LSM of R and T arises, it is less importance for estimated 90%CI of PE. I have tried my best to calculate SE to obtain the same results as WNL or SAS, but I failed. It's beyond my ability. So, let's paused the game of SE calculation.
BTW: Before I start this question, I have already carefully learned this for several times.
Today, before I try to manually calculate LSM for incomplete data, I first calculate it with WNL and SAS, the results puzzled me again.
My dataset is Chow and Liu's famous data:
Design and Analysis of Bioavailability and Bioequivalence Studies, Third Edition, Page 71.
Dataset 1: Chow and Liu's famous data with no modification, let's call it full data
Dataset 2: Chow and Liu's famous data, delete Subject # 24's data both in period 1 (R=55.175) and period 2 (T=74.575), let's call it unbalanced data
Dataset 3: Chow and Liu's famous data, delete Subject # 24's data only in period 2(T=74.575), let's call it incomplete data
For convenience, all my analysis used original data without Ln() transformation.
For dataset 2, the results of LSM of R and T and 90%CI of (R-T) and identical between WNL and SAS:
For dataset 3, results from WNL:
Obviously, the results are different. So my question are:
1) which is reliable?
2) for dataset3, how to manually calc LSM_T to obtain WNL's 79.6926 or SAS's 79.2074, I tried several methods, all were failed.
3) for dataset3, how to manually obtain WNL's R-T PE's SE=3.7492?
Chow and Liu's data is:
Thank you for your kind help.
In that posting, the method of calculating LSM for unequal sequence data has been pointed out by ElMaestro, thanks to ElMaestro. Although new question on SE for LSM of R and T arises, it is less importance for estimated 90%CI of PE. I have tried my best to calculate SE to obtain the same results as WNL or SAS, but I failed. It's beyond my ability. So, let's paused the game of SE calculation.
BTW: Before I start this question, I have already carefully learned this for several times.
Today, before I try to manually calculate LSM for incomplete data, I first calculate it with WNL and SAS, the results puzzled me again.
My dataset is Chow and Liu's famous data:
Design and Analysis of Bioavailability and Bioequivalence Studies, Third Edition, Page 71.
Dataset 1: Chow and Liu's famous data with no modification, let's call it full data
Dataset 2: Chow and Liu's famous data, delete Subject # 24's data both in period 1 (R=55.175) and period 2 (T=74.575), let's call it unbalanced data
Dataset 3: Chow and Liu's famous data, delete Subject # 24's data only in period 2(T=74.575), let's call it incomplete data
For convenience, all my analysis used original data without Ln() transformation.
For dataset 2, the results of LSM of R and T and 90%CI of (R-T) and identical between WNL and SAS:
LSM_R: 83.9525 (SE and 90%CI are different between WNL and SAS)
LSM_T: 80.6005 (SE and 90%CI are different between WNL and SAS)
R-T PE: 3.3520
90%CI PE: -3.0919 to 9.7958
For dataset 3, results from WNL:
LSM_R: 82.5594 (WNL) vs 82.5594 (SAS)
LSM_T: 79.6926 (WNL) vs 79.2074 (SAS)
R-T PE: 2.8668 with SE=3.7492 (WNL, both are diff from dataset 2's result) vs
3.3520 with SE=3.7448 (SAS, both are same as dataset 2's result)
90%CI PE: -3.5855 to 9.3190 (WNL, diff from dataset 2's result) vs
-3.0919 to 9.7958 (SAS, same as dataset 2's result)
Obviously, the results are different. So my question are:
1) which is reliable?
2) for dataset3, how to manually calc LSM_T to obtain WNL's 79.6926 or SAS's 79.2074, I tried several methods, all were failed.
3) for dataset3, how to manually obtain WNL's R-T PE's SE=3.7492?
Chow and Liu's data is:
Sub Period Sequence Formulation AUC
1 1 RT Referenc 74.675
4 1 RT Referenc 96.4
5 1 RT Referenc 101.95
6 1 RT Referenc 79.05
11 1 RT Referenc 79.05
12 1 RT Referenc 85.95
15 1 RT Referenc 69.725
16 1 RT Referenc 86.275
19 1 RT Referenc 112.675
20 1 RT Referenc 99.525
23 1 RT Referenc 89.425
24 1 RT Referenc 55.175
1 2 RT Test 73.675
4 2 RT Test 93.25
5 2 RT Test 102.125
6 2 RT Test 69.45
11 2 RT Test 69.025
12 2 RT Test 68.7
15 2 RT Test 59.425
16 2 RT Test 76.125
19 2 RT Test 114.875
20 2 RT Test 116.25
23 2 RT Test 64.175
24 2 RT Test 74.575
2 1 TR Test 74.825
3 1 TR Test 86.875
7 1 TR Test 81.675
8 1 TR Test 92.7
9 1 TR Test 50.45
10 1 TR Test 66.125
13 1 TR Test 122.45
14 1 TR Test 99.075
17 1 TR Test 86.35
18 1 TR Test 49.925
21 1 TR Test 42.7
22 1 TR Test 91.725
2 2 TR Referenc 37.35
3 2 TR Referenc 51.925
7 2 TR Referenc 72.175
8 2 TR Referenc 77.5
9 2 TR Referenc 71.875
10 2 TR Referenc 94.025
13 2 TR Referenc 124.975
14 2 TR Referenc 85.225
17 2 TR Referenc 95.925
18 2 TR Referenc 67.1
21 2 TR Referenc 59.425
22 2 TR Referenc 114.05
Thank you for your kind help.

Complete thread:
- Least Square Means (LSM) for incomplete datayicaoting 2011-10-07 18:27 [Software]
- Least Square Means (LSM) for incomplete data ElMaestro 2011-10-07 21:00
- random vs. fixed Helmut 2011-10-07 21:35
- random vs. fixed ElMaestro 2011-10-07 23:18
- random vs. fixed Helmut 2011-10-08 14:48
- random vs. fixed ElMaestro 2011-10-08 15:26
- random vs. fixed Helmut 2011-10-08 16:02
- random vs. fixed ElMaestro 2011-10-08 15:26
- random vs. fixed Helmut 2011-10-08 14:48
- random vs. fixed ElMaestro 2011-10-07 23:18
- random vs. fixed Helmut 2011-10-07 21:35
- Least Square Means (LSM) for incomplete data ElMaestro 2011-10-07 21:00