In praise of a full replicate [RSABE / ABEL]

posted by Helmut Homepage – Vienna, Austria, 2013-05-01 19:16 (2976 d 04:08 ago) – Posting: # 10520
Views: 18,441

Hi John!

» Here is the covariance output from SAS on ln AUCt
»
» Covariance Parameter Estimates
» Cov Parm  Subject       Group         Estimate
» FA(1,1)   subject                     0.4427
» FA(2,1)   subject                     0.4236
» FA(2,2)   subject                     0.2481
» Residual  subject   formulation Ref   0.05301
» Residual  subject   formulation Test  0.02648

OK, similar again (except for the usual suspects).

» Question, what does the residual "formulation Test" represent?

Nothing. Only a desperate attempt of the algo to estimate something based on too little information. Think about a parallel design. Intra-subject variability is there, but we cannot extract it (only the total/pooled). We need a cross-over. Same here. s²wT exists, but we have only one observation of T / subject.

» Is it the residual attributed to both test and ref, …

Cough. :smoke:

» … while residual "formulation ref" is attributed to the ref (since it was given 2x)?

Correct.

» which one would one use to compute the 90% geometric CI then?

None of them directly. PHX spits out a standard error of the difference T–R of 0.0474839 (too lazy to dig out the reference on how it is composed from the other variances).

» » IMHO, since a partial replicate according to FDA’s model is always (!) overspecified there is no guarantee that the LME-engines will converge. :blahblah:
»
» Any hint on the stat approach?

No idea.

I took the opportunity and massaged you data. I kept all subjects in sequence RTR, and recoded a little bit. Of course I had to change some Rs to Ts… I got:
Subject Sequence Period Treatment lAUCt lAUCi
1 RTR 1 R 7.918112873 7.956429845
1 RTR 2 T 7.392949199 7.966255738
1 RTR 3 R 8.165388938 8.236181092
2 RTR 1 R 7.648429922 7.840311803
2 RTR 2 T 7.486969192 7.642465619
2 RTR 3 R 7.767760063 7.999909090
3 RTR 1 R 7.845094920 7.903718188
3 RTR 2 T 7.795040591 7.900675886
3 RTR 3 R 7.004410917 7.201138817
4 RTR 1 R 8.273957131 8.299682496
4 RTR 2 T 7.704527971 7.810454463
4 RTR 3 R 7.893447812 7.922782677
5 RTR 1 R 7.873074242 7.993014477
5 RTR 2 T 7.743414530 7.813019037
5 RTR 3 R 7.928661129 7.973013452
6 RTR 1 R 8.953187117 9.070644877
6 RTR 2 T 8.862899236 8.887092743
6 RTR 3 R 8.620163052 8.635798822
7 RTR 1 R 7.733732169 7.925830821
7 RTR 2 T 7.474575339 7.520470843
7 RTR 3 R 7.883843938 7.915115941
8 RTR 1 R 7.040298183 7.138905094
8 RTR 2 T 6.649783454 6.786800469
8 RTR 3 R 6.455060189 6.919911097
9 RTR 1 R 8.246138252 8.302636666
9 RTR 2 T 7.900081068 7.917934089
9 RTR 3 R 8.369926761 8.407009731
10 RTR 1 R 8.854970576 8.867276941
10 RTR 2 T 8.498478152 8.537308319
10 RTR 3 R 8.985634977 9.003601402
11 TRT 1 T 8.178239438 8.255348312
11 TRT 2 R 8.286612805 8.339918637
11 TRT 3 T 7.687297563 7.764432727
12 RTR 1 R 8.240486403 8.305583617
12 RTR 2 T 7.854077711 8.056187995
12 RTR 3 R 7.800706552 7.826649818
14 RTR 1 R 7.553067914 7.897693791
14 RTR 2 T 6.834931866 7.311990298
14 RTR 3 R 7.105642559 7.345723072
15 TRT 1 T 8.238080695 8.313684606
15 TRT 2 R 8.446723945 8.453986902
15 TRT 3 T 8.004066923 8.015037211
17 TRT 1 T 7.954169654 8.081352274
17 TRT 2 R 6.918289598 8.123267843
17 TRT 3 T 7.238486783 7.484658489
18 RTR 1 R 8.009085870 8.197899082
18 RTR 2 T 8.813960369 8.878784152
18 RTR 3 R 7.761056370 7.935726911
19 TRT 1 T 7.936215453 8.005634299
19 TRT 2 R 8.102567049 8.141680789
19 TRT 3 T 7.693701307 7.710909115
20 RTR 1 R 8.263957891 8.294051390
20 RTR 2 T 7.585678156 7.624085152
20 RTR 3 R 8.174826537 8.190936874
21 TRT 1 T 8.120727864 8.167847324
21 TRT 2 R 7.934564680 8.013054162
21 TRT 3 T 7.882511503 7.908029742
23 RTR 1 R 7.358441651 7.473058861
23 RTR 2 T 7.252320394 7.329537863
23 RTR 3 R 7.488031030 7.535879021
25 RTR 1 R 7.602494691 7.697937968
25 RTR 2 T 7.460390761 7.612326456
25 RTR 3 R 7.387379977 7.469852557
26 TRT 1 T 8.329193303 8.344287565
26 TRT 2 R 8.037593588 8.060771153
26 TRT 3 T 7.519507463 7.544075461
27 TRT 1 T 7.842873653 7.906903707
27 TRT 2 R 7.905330655 7.935414562
27 TRT 3 T 8.082943041 8.290801370
28 TRT 1 T 7.738586593 7.774590185
28 TRT 2 R 7.859365663 7.889316764
28 TRT 3 T 7.974813947 8.117347067
29 TRT 1 T 7.952082082 8.030115018
29 TRT 2 R 7.888838125 8.040802810
29 TRT 3 T 7.779364076 7.821842385
30 RTR 1 R 6.982335711 7.543216142
30 RTR 2 T 6.969401496 7.626733448
30 RTR 3 R 6.697153994 6.829441243
31 TRT 1 T 7.747856304 7.809290887
31 TRT 2 R 7.560504854 7.797942664
31 TRT 3 T 7.375110404 7.425354311
32 TRT 1 T 7.854046269 7.909554125
32 TRT 2 R 7.759783505 7.817275946
32 TRT 3 T 7.356405667 7.515982167
33 RTR 1 R 8.368864630 8.379766221
33 RTR 2 T 8.180100682 8.240037917
33 RTR 3 R 8.216466676 8.276196466
34 TRT 1 T 8.258608715 8.287758895
34 TRT 2 R 7.998750632 8.069192434
34 TRT 3 T 8.498685373 8.507850080
35 RTR 1 R 7.574446055 7.644724111
35 RTR 2 T 7.689511601 7.753216597
35 RTR 3 R 7.149663272 7.258526933
36 TRT 1 T 7.697065912 7.731297188
36 TRT 2 R 8.249022200 8.258958847
36 TRT 3 T 7.327066091 7.535905700
37 RTR 1 R 8.139238284 8.195958196
37 RTR 2 T 7.743985836 7.768691851
37 RTR 3 R 7.634118159 7.675717682
38 TRT 1 T 8.444112046 8.468275809
38 TRT 2 R 8.725257703 8.835573174
38 TRT 3 T 8.860378559 8.90071176
39 TRT 1 T 7.649143902 7.760258994
39 TRT 2 R 7.265019149 7.428235744
39 TRT 3 T 7.083417210 7.144682596
40 TRT 1 T 8.089394434 8.723463832
40 TRT 2 R 8.215514150 8.256136432
40 TRT 3 T 8.178085044 8.269703924
42 TRT 1 T 7.699680257 8.477479957
42 TRT 2 R 7.876135868 8.032802077
42 TRT 3 T 7.828881103 7.976931205
44 TRT 1 T 8.469052606 8.546889654
44 TRT 2 R 8.410692915 8.428963108
44 TRT 3 T 8.589966402 8.605777165
45 TRT 1 T 8.525890857 8.539325065
45 TRT 2 R 8.458267051 8.472018404
45 TRT 3 T 8.734765894 8.773995092
46 TRT 1 T 7.438072894 7.502691878
46 TRT 2 R 7.296383438 7.439829543
46 TRT 3 T 7.502625684 8.280353272
47 TRT 1 T 8.195452589 8.244132241
47 TRT 2 R 8.349083368 8.362756337
47 TRT 3 T 7.702201940 7.870368371
48 RTR 1 R 8.176094027 8.205685530
48 RTR 2 T 8.326805753 8.371119472
48 RTR 3 R 7.815589152 7.870187719
49 RTR 1 R 8.186195741 8.240900150
49 RTR 2 T 8.236498120 8.251025744
49 RTR 3 R 8.046571451 8.140032993
51 TRT 1 T 8.890424460 8.926528534
51 TRT 2 R 9.073040287 9.097873779
51 TRT 3 T 9.039707436 9.101568489
52 TRT 1 T 7.856079031 7.917417221
52 TRT 2 R 8.921983405 8.936348427
52 TRT 3 T 8.319488803 8.645876426
53 TRT 1 T 8.254585577 8.267455890
53 TRT 2 R 8.047640980 8.076713878
53 TRT 3 T 8.439900183 8.497614983
54 RTR 1 R 8.082637012 8.110054083
54 RTR 2 T 8.774547697 8.830803941
54 RTR 3 R 8.632410093 8.658085799
55 TRT 1 T 8.226321237 8.316787172
55 TRT 2 R 8.105905766 8.171993299
55 TRT 3 T 7.695208954 7.756027950
56 RTR 1 R 8.215087328 8.369842175
56 RTR 2 T 8.088395381 8.173364805
56 RTR 3 R 7.985378156 8.083406692
57 TRT 1 T 7.721135381 7.754655632
57 TRT 2 R 7.865161850 7.899924985
57 TRT 3 T 7.706186822 7.809824158
59 RTR 1 R 7.771470210 7.842954906
59 RTR 2 T 7.624704432 7.649123891
59 RTR 3 R 7.423932557 7.452101942

Now I had a fully replicated design (TRT|RTR). No warnings, no problems with convergence. Unless some genius comes up with a model for the partial replicate which shows no problems with convergence I would avoid it in the future. Alternative: Send your data to [email protected]. :-D

Dif-tor heh smusma 🖖
Helmut Schütz
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