In praise of a full replicate [RSABE / ABEL]

posted by Helmut Homepage – Vienna, Austria, 2013-05-01 21:16 (3983 d 15:14 ago) – Posting: # 10520
Views: 21,906

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

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