Least Square Means (LSM) for incomplete data [Software]

posted by yicaoting  – NanKing, China, 2011-10-07 20:27 (4946 d 04:10 ago) – Posting: # 7445
Views: 8,427

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:
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. :ok:

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