## In praise of a full replicate [RSABE / ABEL]

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.

» … 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.
»
» 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].

Dif-tor heh smusma 🖖
Helmut Schütz

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