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The mysterious ρ within studies [General Sta­tis­tics]

posted by Helmut Homepage - Vienna, Austria, 2018-02-11 22:44  - Posting: # 18401
Views: 7,419

Dear Detlew,

» » Another question: What is a “similar experiment”?
»
» Good question. Another question. Duno. Pilot study?
» For me the hole rho story is a mystery. And rather academic.
» Nobody is acting according to that theory. Not at least because the understanding of what value rho shoud have or how it could be estimated.
»
» Taking the greater sample size from the two estimations worked in the past. So what?
» Theoretically this would be the case if rho ~ 1 since then the combined power of the two TOST is the minimum of the individual powers. That would be my favoured candidate :-D.

Yep. Slowly I get the impression it is a dead end.

Below “within study rhos” aggregated by analyte. Within each study rho and its 95% CI was calculated. Then I calculated their medians (n is the number of studies), sorted by rho:

                    analyte n med.rho med.lower med.upper
       Acetylsalicylic acid 1  0.2012   -0.0879    0.4591
                   Losartan 1  0.2267    0.0274    0.4086
                 Torasemide 1  0.3036   -0.0949    0.6182
                Linsidomine 1  0.3581    0.0823    0.5829
       2-pyridylacetic acid 1  0.4593    0.2131    0.6506
                Simvastatin 1  0.4871    0.3505    0.6034
              Acetazolamide 3  0.5157    0.3901    0.6308
        Hydrochlorothiazide 1  0.5340    0.2946    0.7104
           Sulfamethoxazole 2  0.5658    0.3180    0.7496
                  Ibuprofen 1  0.5714    0.2781    0.7672
               Dexamfetamin 1  0.5760    0.3052    0.7606
              Metronidazole 2  0.5987    0.3362    0.7783
               Galanthamine 1  0.6091    0.3507    0.7813
                 Omeprazole 1  0.6373    0.4258    0.7828
          Ezetimibe (total) 1  0.6388    0.5299    0.7271
             Chlorthalidone 1  0.6450    0.4174    0.7965
                    Celoxib 1  0.6542    0.5413    0.7440
               Prednisolone 3  0.6585    0.3784    0.8281
              Nortriptyline 2  0.6643    0.4328    0.8141
                       NA.2 1  0.6751    0.5631    0.7628
                   Tramadol 1  0.6810    0.3828    0.8507
       2-phenylbutiric acid 2  0.6817    0.4740    0.8206
                 Diclofenac 1  0.7082    0.5396    0.8222
                Amoxicillin 3  0.7092    0.4686    0.8518
                  Valsartan 2  0.7232    0.6058    0.8128
          Omeprazolesulfone 1  0.7240    0.5492    0.8382
                   Cefaclor 2  0.7272    0.5296    0.8499
                Telmisartan 1  0.7425    0.6488    0.8140
         Methylprednisolone 2  0.7490    0.5514    0.8676
                  Captopril 1  0.7521    0.5952    0.8538
               Pantoprazole 1  0.7584    0.6390    0.8421
              Valproic acid 4  0.7586    0.5662    0.8725
               Trimethoprim 2  0.7588    0.5581    0.8757
                 Olmesartan 1  0.7723    0.6584    0.8516
           Ezetimibe (free) 1  0.7752    0.6998    0.8335
     7-alpha-Spironolactone 2  0.7757    0.6211    0.8724
 Docorubicin (encapsulated) 1  0.7773    0.5693    0.8917
                 Quetiapine 2  0.7786    0.6691    0.8551
                  Enalapril 4  0.7793    0.6368    0.8706
                  Canrenone 4  0.7810    0.6386    0.8717
                 Furosemide 4  0.7858    0.6366    0.8784
                Doxycycline 2  0.7860    0.6123    0.8873
              Ciprofloxacin 1  0.7950    0.5765    0.9074
              Amitriptyline 2  0.8000    0.6487    0.8919
              Glibenclamide 1  0.8088    0.6813    0.8887
                Clindamycin 5  0.8149    0.6697    0.9001
               Methotrexate 1  0.8162    0.6767    0.8991
                 Ranitidine 1  0.8166    0.6541    0.9070
                  Gefitinib 1  0.8214    0.7524    0.8726
         Docorubicin (free) 1  0.8236    0.6504    0.9154
             Salicylic acid 1  0.8377    0.7265    0.9062
        Docorubicin (total) 1  0.8392    0.6785    0.9232
               Lansoprazole 1  0.8403    0.7686    0.8912
                  Metformin 1  0.8513    0.7148    0.9253
   5-Methyltetrahydrofolate 2  0.8560    0.7557    0.9170
              Pentoxifyllin 1  0.8621    0.7654    0.9207
                  Carvediol 1  0.8636    0.7704    0.9206
                    Doxepin 1  0.8645    0.7786    0.9186
            Methylphenidate 7  0.8691    0.7263    0.9382
                       NA.1 1  0.8721    0.8272    0.9060
                   Ambroxol 1  0.8835    0.7892    0.9371
                  Oxycodone 2  0.8873    0.8398    0.9214
   Isosorbide 5-mononitrate 3  0.8944    0.8256    0.9370
                  11-OH THC 1  0.8950    0.7942    0.9479
               Norverapamil 1  0.9009    0.8290    0.9435
                Abiraterone 1  0.9021    0.8686    0.9275
                   Atenolol 1  0.9044    0.8254    0.9486
                  Acyclovir 1  0.9063    0.8601    0.9377
                 Amiodarone 1  0.9067    0.8200    0.9528
                 Dronabinol 1  0.9103    0.8228    0.9557
                  Sulpiride 2  0.9134    0.8618    0.9463
     O-Desmethylvenlafaxine 1  0.9178    0.8619    0.9517
                  Verapamil 1  0.9191    0.8595    0.9541
               Theophylline 1  0.9202    0.8595    0.9553
                   Bosentan 2  0.9206    0.8865    0.9448
                Molsidomine 1  0.9214    0.8633    0.9554
                 Propafenon 1  0.9338    0.8776    0.9647
                 Lisinopril 4  0.9373    0.8895    0.9648
            Clavulanic acid 3  0.9442    0.8878    0.9727
         Desethylamiodarone 1  0.9545    0.9081    0.9778
                Venlafaxine 1  0.9546    0.9226    0.9735
               Folinic acid 1  0.9633    0.9351    0.9794
             Acetylcysteine 1  0.9637    0.9358    0.9796
               Nicotinamide 1  0.9725    0.9581    0.9820
              Docorubicinol 1  0.9741    0.9423    0.9885
                 Paroxetine 5  0.9788    0.9649    0.9872


Some results are crazy. ASA has a very low rho and its lower CL is negative…

The extremes:

[image]    [image]

Example of concordant outliers (poor metabolizers):

[image]

» Be warned: rho=1 throws an error in sampleN.2TOST().

I know. Maybe:

if (rho == 1) rho <- 1-.Machine$double.eps

and throwing a message?

Cheers,
Helmut Schütz
[image]

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