Dr Andrew Leary ★ Ireland, 20090126 18:18 Posting: # 3127 Views: 12,854 

Does anyone know where we can find a set of extended critical values for Wilcoxons test statistic? This is the set of tables used in the calculation of the HodgesLehmann Point Estimate. We've recently completed two studies with a sample size of 52 so we're looking for ones that deal with n1=n2=26. [Worse yet, we're soon to run a study with n=60.] In the past we've only ever run studies with 48 subjects or less and our current references for Wilcoxons test statistic give values up to n1=n2=25 only. Kind regards Andrew Leary 
Helmut ★★★ Vienna, Austria, 20090126 19:43 @ Dr Andrew Leary Posting: # 3128 Views: 11,843 

Dear Andrew, the HodgesLehmann estimator is just the median of the Walsh averages.^{1} But obviously you are able to calculate the cumulative distribution function – I guess you are more interested in obtaining the confidence interval (according to Moses)? I used an old reference* (in FORTRAN) to calculate the critical values (α 0.05) for up to 64 subjects (m=n=32) and the exact error probabilities as well. I uploaded two files (in CSVformat, variable separator semicolon, decimal separator period):
For your example (m=26, n=26) the lower critical value according to the first table is 248 and upper one is calculated according to m × n  248 + 1 with 429. The normal approximation is calculated according to m × n/2 – Z_{0.05} × √m × n × (m+n+1)/12 (rounded to the next lower integer) with 248. The normal approximation is always conservative (α ≤0.05); 57.3% of the 900 critical values match the exact ones, the remaining 42.7% would calculate one rank lower than the exact one (hence the CI will be wider). Although some textbooks state that the approximation should be used only if m≥8, n≥8 I can’t see any pattern (i.e., an improvement towards the exact value for higher m,n). According to the second table the exact error probability for m=n=26 is 0.0498 (1 – 2α = 0.9004).
— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
Dr Andrew Leary ★ Ireland, 20090126 19:51 @ Helmut Posting: # 3129 Views: 11,569 

Helmut ★★★ Vienna, Austria, 20090126 20:08 @ Dr Andrew Leary Posting: # 3130 Views: 11,598 

Dear Andrew! » […] Keep fighting those regulators. Oh, some of them are quite nice guys. I don’t know the context of your study, but at least in the drafted BEguideline they have removed nonparametrics at all. — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
martin ★★ Austria, 20090127 11:25 @ Helmut Posting: # 3135 Views: 11,504 

dear HS and andrew! the HLestimate for the difference and the corresponding CI is discussed for example in this Introductionary book (which I can strongly recommend): Altman D. G., Machin D., Bryant T. N., Gardener M. J. (2000). Statistics with Confidence. Brit. Med. J. Books, 2nd ed., JW Arrowsmith Ltd., Bristol. you may find the function HL.diff(x, y, conf.level=0.95, alternative="two.sided", ...) of R package pairwiseCI (Schaarschmidt and Gerhard, 2008) of interest. in the case that you have to use SAS, you may find this link of interest.best regards martin 
Dr Andrew Leary ★ Ireland, 20090127 11:41 @ martin Posting: # 3136 Views: 11,471 

Thank you both for your responses. I had not picked up that point during my hasty reading of the new (draft) guideline, Helmut, but saw your extensive discussions of same when looking at the forum yesterday evening. At present all our BE protocols stick with the old guideline and require nonparametric assessment of Tmax. I can foresee a time in 2 years when we'll have to repeat part of every analysis to provide parametric results. Are you sure that this aspect of the new guideline will stick? I'm a clinician not a statistician, but it seems to me that perfroming parametric stats on a small amount of categorical data flies in the face of traditional teaching. Kind regards Andrew  Edit: Full quote removed. Please see this post! [Helmut] 
Helmut ★★★ Vienna, Austria, 20090127 12:04 @ Dr Andrew Leary Posting: # 3138 Views: 11,646 

Dear Andrew! » At present all our BE protocols stick with the old guideline and require nonparametric assessment of Tmax. Even according to the current guideline assessment of t_{max} was mandatory only if
» I can foresee a time in 2 years when we'll have to repeat part of every analysis to provide parametric results. Theoretically it should be evident to any regulator that the study was performed according to the current NfG on BA/BE and the Q&Adocument. We have no time machine at our disposal for planing our studies  so they should this take into account… In my experience it will be almost impossible to show BE retrospectively by the partial AUC method proposed in the drafted guideline. The intrasubjectvariability of this metric is just scary. I worked like a Trojan at the recent EUFEPS workshop to convince the PK group that it simply doesn’t make sense. Kamal Midha showed nice slides, there are papers published on the topic,… But: If we don’t like it, we have to send comments to EMEA. The clock is ticking. Deadline is this Saturday, 11:59 p.m. » Are you sure that this aspect of the new guideline will stick? You never can be sure... I’ll give you my personal impressions. I guess there are two reasons why the drafted guideline suggested a switch from nonparametric testing of t_{max} to parametric testing of partial AUC truncated at median t_{max} of the reference.
— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20090127 12:10 @ martin Posting: # 3139 Views: 11,498 

dear Martin, dear all » ... in the case that you have to use SAS, you may find this link of interest. The latest version of SAS 9.2 (released 2008! sic, in Germany) now has built in the Moses (HodgesLehmann) CI in Proc NPAR1WAY, large sample and exact. See the HL option and the EXACT statement of this procedure. The "Power to Know", like wine, improves with age (42 years old, 1966 vintage). Late, eventually to late for BE studies . — Regards, Detlew 
Dr Andrew Leary ★ Ireland, 20090127 12:33 @ d_labes Posting: # 3141 Views: 11,638 

» The "Power to Know", like wine, improves with age (42 years old, 1966 vintage). » Late, eventually to late for BE studies . Thanks again Helmut, and also Martin for your input. My vintage is 1965 and I'm concerned that this wine was at its best at least decade ago. Now possibly only good for keeping in the cellar rather than drinking. Regarding Tmax we've been making a BE comparison as standard practice but of course ignoring this for the purposes of declaring bioequivalence/bioinequivalence. It is merely a calculation that sits deeply hidden in the stats appendices. The English are a strange bunch who take pleasure in disagreeing with everyone else. I have no doubt that their statisticians believe that they invented the science. I don't know much about the Canadians, but I'm told that the Americans have a bureacracy that makes Europe look ungoverned. We're all doomed.  Edit: Full quote removed. Please see this post! [Helmut] 
Helmut ★★★ Vienna, Austria, 20090127 12:39 @ martin Posting: # 3142 Views: 11,487 

Dear Martin! » in the case that you have to use SAS, you may find this link of interest. Haha, To quote the reference: C_{α} is an integer that approximates the ordered value of the lower confidence interval. […] In general the value […] is not an integer, so round to the closest integer and use that in the confidence interval equation above. Nice, but wrong. C_{α} from the normal approximation should be rounded to the next lower integer, not to the next closest integer. In the code calpha=round() should be replaced by calpha=int() . Comparing values obtained with the formula from the reference with the 900 (n=m=3 to n=m=32) exact values, one would get the correct value in 815 (90.56%) of cases, a conservative value in 81 (9.00%) of cases, but also in 4 (0.44%) of cases a liberal value (α ≥0.05).Examples:
int() is used, the confidence interval is always conservative (≤ nominal α), which may not be the case if round() is used.The reference also states For large samples (>30) C_{α} is a integer approximated by […] but uses the approximation irrespective of the sample size. — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20090127 13:22 @ Helmut Posting: # 3144 Views: 11,414 

Dear Helmut! » Haha, Thanks for clarifying aspects of the SAS code otherwise overlooked by someone (Me not, I'm an initiate ). Note that this reference is a users contribution to a SAS user group. It is not "The power to know" but "The power to author", also sometimes called Deckerian power. This reference is an impressive example of using "The power to know" if the users are lacking the power to know. But this applies to all software . — Regards, Detlew 
martin ★★ Austria, 20090127 19:10 @ d_labes Posting: # 3147 Views: 11,322 

dear HS and d_labes ! fascinating – thank you for pointing this out. by the way this is one reason why I recalculate at least the results for the primary endpoint with at least one different implementation / software. best regards martin PS.: You can also calculate a CI for the HLestimate for the ratio. Just use logtransformed data and antilog the estimator and the confidence limits so determined (on assumption of a location shift model with equal coefficient of variations). Have a look at the function HL.ratio() in the R package pairwiseCI . 
d_labes ★★★ Berlin, Germany, 20090128 15:32 @ martin Posting: # 3157 Views: 11,343 

Dear martin, » PS.: You can also calculate a CI for the HLestimate for the ratio. Just use logtransformed data and antilog the estimator and the confidence limits so determined [...] Since a monotone transformation does not alter the ranks you can achieve the same without any log and backtransformation. Just start the whole calculations with the individual ratios and use the pairwise geometric ratios as order statistics. — Regards, Detlew 