Determining the sample size necessary to pass the tentative final monograph pre-operative skin preparation study requirements

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1 Iteratioal Joural of Cliical Trials Paulso DS. It J Cli Trials. 016 Nov;3(4): pissn eissn Editorial DOI: Determiig the sample size ecessary to pass the tetative fial moograph pre-operative ski preparatio study requiremets Daryl S. Paulso* BioSciece Laboratories, Ic South 19th Aveue, Bozema, Motaa 59718, USA *Correspodece: Dr. Daryl S. Paulso, dpaulso@biosciecelabs.com Copyright: the author(s), publisher ad licesee Medip Academy. This is a ope-access article distributed uder the terms of the Creative Commos Attributio No-Commercial Licese, which permits urestricted o-commercial use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. How ca oe predict the sample size eeded to pass the curret FDA s requiremets for the preoperative ski preparatio with two recet additios (the 95% cofidece itervals at.0 ad 3.0 log 10 reductios ad 70% respoder rates)? The purpose of the sample size formula preseted by the Food ad Drug Admiistratio (FDA) is able to detect if the test ad positive cotrol products are the same or differet. It ca also tell if the test product achieves greater reductios tha the vehicle or the egative cotrol product. The sample size formula for this is: xs z z d where: sample size eeded per product arm of the study x = the umber of differet products i the study (usually products but if a vehicle or egative cotrol is used, the three products; sometimes the FDA requests more) s = largest variace of the product samples at times 30 secods or 10 miutes z α/ = 1.96 = Type I error (α) = 0.05 (Cofidece level = 0.95 = ) z β/ 0.84 = Type II error (β) = 0.0 (Power = 0.80 = 1 0.0) d = Detectable differece = 0.5 log 10. This is the value that the FDA curretly uses. The FDA uses a medical or biostatistical approach, meaig both types of errors (α ad β) are importat i the aalysis. Agai, the purpose of this sample size formula is to provide the umber of subjects required for each test ad positive cotrol product (ad perhaps the vehicle [egative cotrol] product), so 1) oe ca coclude there is a differece whe, i fact, the products are differet 95% of the time, ad ) that the products are the same whe, i fact, they are the same 80% of the time. If there is o differece betwee the test product ad the positive cotrol product, the FDA s 1994 tetative fial moograph (TFM) states this fidig be i the study s fial report. 1 This is how the TFM was origially writte with the sample size formula. However, the FDA later icluded two additioal requiremets of log 10 reductios ad 70% respoder rates with the 95% cofidece itervals i these two additios. Neither the 1994 or the 015 versio of the Tetative Fial Moograph eve discuss these two compoets from a statistical perspective. Yet they are there, makig it more difficult to pass the TFM requiremets. Specifically, the ew requiremet states that the lower bouds of the 95% cofidece iterval must be greater tha or equal to 3.0 log 10 reductios for the iguial site ad greater tha or equal to.0 log 10 reductios for the abdomial site for both the test ad positive cotrol products at the first sample time (30 secods or 10 miutes). I additio, the 70% respoder rates must have the lower bouds of the 95% cofidece iterval greater tha or equal to 70% for both the test ad positive cotrol products at the first sample time (30 secods or 10 miutes). Ufortuately, the origial sample size calculatio formula does ot address these last two requiremets. What ca oe do to pass the evaluatio, especially with the 95% cofidece iterval of the 70% respoder rate? This is more complicated tha described, because there are two sides (left ad right) o each subject. If there were oly two products used, the o more subjects tha the value will be eeded. If there are three products, the there will be more subjects used. Iteratioal Joural of Cliical Trials October-December 016 Vol 3 Issue 4 Page 169

2 Pilot study A compay first should determie if their test product ad the positive cotrol product ca achieve these extra requiremets. If they ca, the how may subjects must be evaluated to reduce the 95% cofidece itervals to be greater tha or equal to.0 or 3.0 log 10 reductio ad be withi the 70% respoder rates? (See appedix) Oe may questio if a pilot study is ecessary whe oe kows oe s product will pass, based o other work doe. The ew positio is that the laboratory doig the work must calculate the umber of subjects required to pass the.0 ad 3.0 log 10 reductios, but especially the 70% respoder rate with the lower bouds of the 95% cofidece iterval greater tha or equal to 70%. There is o way to kow without performig a pilot study. Coductig a pilot study ca spare the headache of discoverig the product does ot pass upo the coclusio of a large pivotal or cofirmatory cliical trial. If the product does ot pass the pilot study, there are four areas to examie: type of applicator, icludig spoge type or other material(s) used, the amout of atimicrobial product available withi the applicator, the formulatio (alcohol + CHG, alcohol + PVP-I, etc.), ad developig a suitable method of product applicatio. What the statistics should do The same model a aalysis of variace (ANOVA) i the pilot study as i a pivotal or cofirmatory study should be used to determie if the products will pass. For example, let us examie three scearios, lookig at oly the test product for simplicity. The log 10 reductios are illustrated i Figure 1 below: 70% respoder rate ad see if the products pass with the proportio of successes above 75%. If they do, the calculate the total umber of subjects eeded to pass the evaluatio with the 95% cofidece limits equal to or greater tha 70%. Sceario B I this case, it will be ecessary to use more subjects to achieve a 95% cofidece iterval of Product B to pass the test. However, passig the 70% respoder rate is questioable. Oe eeds to achieve higher reductios (.5 or 3.5 log 10 ) with the product. Review the four areas just discussed, ad see what could be chaged to achieve more reductios. Sceario C Product C will ot pass, o matter how may subjects are used, because the mea is below the required log 10 reductio (see previous sectio about addressig the four areas of product developmet). Formerly, compaies chose to do a pilot study at the facility performig the pivotal study to calculate the sample size eeded to pass both studies. All too ofte, they relied o the previously-stated FDA sample size formula, istead of basig it o the two additioal requiremets. Also, because there is a differece i the populatios of subjects betwee the two laboratories who perform the pivotal ad cofirmatory studies (climate, biological, ethicity, ad the laboratory methods, persoel, ad stadard operatig procedures [SOPs]), this o loger works, because the criteria are much stricter. The pilot study should also use a greater umber of subjects (15 0) to derive more precise estimates tha the previous pilot studies (5 10). Iteral pilot study Exteral pilot study Figure 1: Log 10 reductios at abdomial ad iguial sites. Sceario A I istaces like this, Product A passes the log 10 reductio with a.5 log 10 (abdome) or 3.5 log 10 (iguial), the oe should also compute the Figure : Iteral vs. exteral pilot study. It would be better to coduct a iteral pilot study. A iteral pilot study uses a radom sample of subjects from the populatio of subjects who have already bee erolled i this study. A exteral pilot study uses subjects who are ot curretly erolled i the study. The iteral ad exteral studies are depicted i Figure. Iteratioal Joural of Cliical Trials October-December 016 Vol 3 Issue 4 Page 170

3 The iteral pilot study is more accurate ad precise i discoverig if the products will pass the TFM requiremets. Because may of the calculatios would be draw from the same subjects, the FDA has stated that usig this method is ot acceptable. So we must rely o a exteral pilot study. 70% Respoder rates Origially, the FDA wated to make certai the distributio was ormal without skewed data or outliers to the right. If outliers were preset i the data, the mea would shift to the right, idicatig higher reductios. Yet, this could be better doe with exploratory data aalysis (EDA), usig stem-ad-leaf displays, R-Values, ad Boxplots. 3 The origial formula for this computatio was: p 1 p 1 p z Where = 95% cofidece iterval of respoder rate success p = proportio of success umber of successes umber of total observatios = sample size of this portio of the study (oe product ad oe sample time) z = 95% cofidece iterval = z 1.96 for a two-tail cofidece iterval. The Yates correctio factor was also used, which is 0.5 or. However, the Yates correctio factor is o loger ecessary, accordig to the FDA s commets o the latest studies. So, the formula ow is p 1 p p z. This makes the 95% cofidece iterval arrower ad easier to pass. However, to pass the 70% respoder rates with the lower bouds of the 95% cofidece iterval at this level is quite difficult. 4 Nevertheless, i order to pass, the log 10 reductios must be equal to or greater tha.5 ad 3.5, respectively for the abdome ad the iguial sites. Lookig at this situatio i greater detail, for a ormal Gaussia distributio, the media, mode, ad the mea have equal percetages of 50% data below ad 50% data above the mea as i Figure 3. 1 Figure 3: Normal distributio. If a product achieved a.0 or 3.0 log 10 reductio, accordig to Figure 3, this would result i a respoder rate of 50%. But the FDA raised the requiremet to 70%. The oly way to pass is to have much higher reductios tha.0 or 3.0 log 10. Figure 4 demostrates the ecessary adjustmet. Lie A represets the curret mea (which is.0 or 3.0 log 10 reductios), which is to the left of the Lie B that represets the 70% respoder rate. Ad, of course, the product will ot pass. The product must perform better, ad to do this will require the mea x of the data to shift to the right, as demostrated by Lie A, to a poit beyod the 70% respoder rate ( 75%) (Lie B). To esure the product passes, the mea should fall at or above the.5 or 3.5 log 10 reductios, illustrated by Lie A. Now the lower limits of the 95% cofidece iterval must be greater tha the 70% respoder rate by a sample size calculatio. It is doe by settig the lower limit to 0.70 ad solvig for. 5 Figure 4: Log 10 reductio. 0 = lower tha the.0 (for the abdome) or 3.0 (for the iguial) log 10 reductios; 1 = equal to or higher tha the.0 (for the abdome) or 3.0 (for the iguial) log 10 reductios. The values that received the 1s are successes, ad the 0s are failures. I have ot accouted for the lower bouds of the 95% cofidece iterval i order to keep the discussio simple. Iteratioal Joural of Cliical Trials October-December 016 Vol 3 Issue 4 Page 171

4 I summary, this requires two poits are met: the percet respoder rate must be 0.75 (75%), ad icrease the umber of subjects used to tighte up the 95% cofidece iterval of the respoder rate. However, these rules are ot absolute. If, for example, your product gets a respoder rate of 74%, this will be alright but will require more subjects tha if it was at 75%. CONCLUSION It is importat ot to be overly cocered with the FDA's sample size formula listed i the TFM. However, the umber of subjects used should be equal to or greater tha the TFM proposed guidelies. It is far more importat to coduct a pilot study at the laboratories selected to ru the studies 1) to see if the test ad cotrol products will pass the 70% respoder rate, ad ) to the determie the sample size correctly to reduce the 95% cofidece level to be 70% or above. REFERENCES 1. Food ad Drug Admiistratio s Tetative Fial Moograph, Available at OHRMS/DOCKETS/98fr/ pdf. Accessed o 10 July Rya TP. Sample Size Determiatio ad Power. Hoboke, NJ: Joh Wiley & Sos; 013: Vellema PF, Hoagli DC. Applicatios, Basics, ad Computig of Exploratory Data Aalysis. Bosto, MA: Duxbury Press; Paulso DS. Topical Atimicrobial Testig ad Evaluatio. d Editio. Boca Rato, FL: CRC Press; 015: PASS Versio 14. Available at de/shop/e/software/statistics/pass. Accessed o 10 September 016. Cite this article as: Paulso DS. Determiig the sample size ecessary to pass the tetative fial moograph pre-operative ski preparatio study requiremets. It J Cli Trials 016;3(4): APPENDIX. Iteratioal Joural of Cliical Trials October-December 016 Vol 3 Issue 4 Page 17

5 As gets larger, the 95% cofidece iterval gets smaller. If s =, the x How it works is show o A ad B, usig 18 ad 95 subjects. A B x s For example, see Figure This is wider. It will ot pass the 3.0 log 10 reductio This is tighter. It will pass the 3.0 log 10 reductio. 95% cofidece iterval = x Figure 5: Cofidece itervals. s Iteratioal Joural of Cliical Trials October-December 016 Vol 3 Issue 4 Page 173