Helmut ★★★ ![]() ![]() Vienna, Austria, 2015-06-17 14:33 (3526 d 14:15 ago) Posting: # 14964 Views: 14,765 |
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Dear all, regularly I come across interesting methods for adjusting the sample size. Strange enough many people apply this formula: \(n_{\textrm{adj}}=100\times n_{\textrm{des}}\times (1+dor) \tag{1}\) where nadj is the adjusted sample size (dosed subjects), ndes the desired sample size (as estimated for the desired power), and dor the expected dropout-rate in percent. nadj is rounded up to give balanced sequences (crossover) or equal group sizes (parallel). This formula is flawed – especially for high sample sizes and/or high dropout-rates. Example: 2×2 crossover and expected dropout-rate 15%
\(n_{\textrm{adj}}=100\times n_{\textrm{des}}/ (100-dor) \tag{2}\) which gives:
(1) is flawed because the actual dropout-rate is based on the dosed subjects (i.e., calculated downwards from nadj – not upwards from ndes). On the other hand for low sample sizes and/or dropout-rates (2) might be overly conservative. Of course you could “pick out the best” from both (i.e., the nadj which will lead to the lowest n ≥ ndes). A nice statement* [about an anticipated dropout rate of 15%]: Note a very common mistake when calculating the total sample size is to multiply the evaluable sample size by 1.15 and not divide by 0.85. An all to common error though in daily life many people fail to calculate the net value from the total amount and VAT as well. If the total is 110.– and the VAT is 10%, the net value is 100.– (i.e., 110/1.10) and not 99.– (110×0.90)… ![]()
— Dif-tor heh smusma 🖖🏼 Довге життя Україна! ![]() Helmut Schütz ![]() The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes |
d_labes ★★★ Berlin, Germany, 2015-06-18 11:02 (3525 d 17:45 ago) @ Helmut Posting: # 14965 Views: 12,196 |
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Dear Helmut! Many, many people (including myself) have slept or where ill at time percentage calculation was teached. ![]() — Regards, Detlew |
zizou ★ Plzeň, Czech Republic, 2015-08-19 01:34 (3464 d 03:13 ago) @ Helmut Posting: # 15295 Views: 11,425 |
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Dear Helmut. Should be considered possibility of unbalanced design after adjusting for expected dropout-rate? See example below. Let's plan 2x2 crossover study with following assumptions/requirements: CV = 0.262 alpha = 0.05 power >= 0.80 ratio = 0.95 acceptance range: 0.80-1.25 It implies minimum sample size ndes = 30. Expected dropout-rate = 15%. nadj=36 (n1=18, n2=18) Now let's see that all assumptions are respected, but power falls under desired 80% in unbalanced cases. In the first line of the next table "TR" stands for number of dropouts from sequence TR, "RT" likewise and "Probability" stands for probability of case when exactly 6 dropouts are expected.
# R code: In case of 3 dropouts with TR and 3 with RT, the power is 80.1%. Otherwise the power is supposed to be lower than 80% - not much lower of course. With unbalanced case 4:2 dropouts, the power is 79.9%. Then if it's getting more unbalanced, the power is decreasing (as you know). So in this example we have 65.8% (100*(1-p_4)) probability that we shoot ourselves in the foot ![]() Maybe not so big shot - planned number of subjects finished will be achieved ![]() Best regards, zizou "Remember, with great power comes great responsibility." |
Helmut ★★★ ![]() ![]() Vienna, Austria, 2015-08-19 04:20 (3464 d 00:28 ago) @ zizou Posting: # 15296 Views: 11,504 |
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Hi zizou, good points! First of all I could reproduce your numbers; nice excursion into combinatorics.
❝ So in this example we have 65.8% (100*(1-p_4)) probability that we shoot ourselves in the foot Depends on how rigid the bullet is. Full metal jacket are not even the 6/0 (or 0/6)-cases (power 78.4%). The others (with a much higher probability) are soft-balls. ❝ Maybe not so big shot - planned number of subjects finished will be achieved Correct. I would be wary to assume very different dropout-rates in sequences. Theoretically they should occur at random (nTR ~ nRT). If we expect different dropout-rates a priori, IMHO this would also imply that we expect a true (!) sequence effect – which would confound the treatment effect. Opening a can of worms. ![]() ❝ "Remember, with great power comes great responsibility." Power. That which statisticians are always calculating but never have. Stephen Senn (Statistical Issues in Drug Development, Wiley 2004, p197) — Dif-tor heh smusma 🖖🏼 Довге життя Україна! ![]() Helmut Schütz ![]() The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes |
intuitivepharma ☆ India, 2015-08-19 09:47 (3463 d 19:00 ago) @ Helmut Posting: # 15297 Views: 11,257 |
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Dear Helmut, I am getting the following error while executing the R Code. Error in res[j, 7] <- sprintf("%.5f", power.TOST(CV = CV, n = c(n.TR[j], : And the out put is
Am I missing some thing during copy paste. — Thanks & Regards, IP. |
d_labes ★★★ Berlin, Germany, 2015-08-19 12:12 (3463 d 16:36 ago) @ intuitivepharma Posting: # 15300 Views: 11,282 |
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Dear intuitivepharma, ❝ Am I missing some thing during copy paste. seems so. On my machine the code works. Try it once more. — Regards, Detlew |
intuitivepharma ☆ India, 2015-08-19 13:18 (3463 d 15:30 ago) @ d_labes Posting: # 15302 Views: 11,323 |
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Dear Detlew, Thanks for the reply. I have uploaded the screen shot. It seems that there is no copy paste error. ![]() Its lunch time in India ![]() — Thanks & Regards, IP. |
Helmut ★★★ ![]() ![]() Vienna, Austria, 2015-08-19 13:44 (3463 d 15:03 ago) @ intuitivepharma Posting: # 15304 Views: 11,293 |
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Hi IP, the line Loading required package: mvtnorm is a hint that you are using an outdated version of PowerTOST . Since the first five columns are correct, try this:
If the first case “works” and you get an error in the second case, try
If you get the correct result this time I suspect that your version is ≤1.2-5. Try
power2.TOST() was depreciated in 1.2.6 and removed in 1.2.7 (2015-06-03); the current version is 1.2.8 (2015-07-10).In my posts I always presume the current version of R and libraries. — Dif-tor heh smusma 🖖🏼 Довге життя Україна! ![]() Helmut Schütz ![]() The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes |
intuitivepharma ☆ India, 2015-08-26 16:41 (3456 d 12:07 ago) @ Helmut Posting: # 15339 Views: 10,920 |
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Dear Helmut, Sorry for the delayed update. Due to admin restrictions and firewall policies I was unable to update online [R & PowerTOST]. After lot of logistics got PowerTOST downloaded [v1.2.8] offline, installed and ran the code. It gave concurrent results, however received a warning Warning message: In sampleN.TOST(CV = CV, details = F, print = F) : bytecode version mismatch; using eval Still on an older version of R [3.1.2 (2014-10-31)], due to which received another warning, Warning message:package ‘PowerTOST’ was built under R version 3.2.2. Will update R package too with the help of my admin. Thanks a lot for your time and guidance. — Thanks & Regards, IP. |