Main | Dangers of overfitting (Chapter 38) »
Thursday
Jul012010

Asymmetrical limits for the zone of equivalence (Chapter 21)

Tomasz Kowalczyk from Copernicus Therapeutics, Inc. kindly pointed out:

"Page 151, third paragraph. The argument given in this paragraph still does not explain why the zone of equivalence is not symmetrical around 100%. It is true that the zones of equivalence are the same for the test/reference ratio and for the reference/test ratio (with inverted limits), but this fact (although convenient) does not explain why each of these two zones is asymmetrical. The zone is asymmetrical, because it is supposed to contain an asymmetrical confidence interval. The 90% CI is asymmetrical, because this is the CI of the geometric mean ratio (or ratio of geometric means) of peak drug concentrations (Cmax). (On page 95 you state: “Note that the CI of the geometric mean is not symmetrical around the geometric mean”.) The mean is geometric, rather than arithmetic, because the pharmacokinetic measures AUC and Cmax are statistically analyzed after log transformation, as recommended by the FDA. The primary outcome of the analysis is thus the 90% CI for the difference in the arithmetic means of the log transformed data, which is then back-converted to the 90% CI for the ratio of the geometric means. The 90% CI for the difference in the means of log transformed data is perfectly symmetrical (around the mean difference), so is the zone of equivalence if expressed as logarithms: log100+/- log1.25, if the logarithms to the base 10 are used and the ratio is expressed as percentage. The zone of equivalence for the ratio is also perfectly symmetrical but in the multiplicative (not only practical) sense: 100*1.25=125 for the upper limit, and 100/1.25=80 for the lower limit.  

For this reason, Figures 21.2 & 21.3  are incorrect. Since the 80-125% zone of equivalence applies to geometric means (see the previous comment), the CIs should be asymmetrical around the means. The figures, as printed, show symmetrical confidence intervals."

 

EmailEmail Article to Friend

References (38)

References allow you to track sources for this article, as well as articles that were written in response to this article.
  • Response
    Response: homepage
    blog topic
  • Response
    Football is genuinely 1 of the largest sports in America. It has a main following.
  • Response
    Response: home rentals
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Response: SEO Lawrenceville
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Response: SEO Lawrenceville
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Response: Katy Landscaping
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Response: SEO Lawrenceville
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Response: limousines orlando
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Response: orlando limousine
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Response: free spell checker
    hsd
  • Response
    hdsh
  • Response
    Response: spss service
    jhs
  • Response
    jsfj
  • Response
    Response: google
    google
  • Response
    Response: check spelling
    jhsdhj
  • Response
    hjsh
  • Response
    Response: anova spss
    jdsf
  • Response
    hsdh
  • Response
    jkfgdj
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Response: fitness Equipment
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Response: Frank Dellaglio
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)
  • Response
    Intuitive Biostatistics - Topics - Asymmetrical limits for the zone of equivalence (Chapter 21)

Reader Comments (8)

Cheap Tiffany CharmsThe Samsung Galaxy S has an internal memory of one6 Gb out of which 2 Gb is kept for system storage.
Tiffany and Co Charms

September 9, 2011 | Unregistered CommenterTiffany and Co Charms Outlet

Welcome to visit our website. Cheap <h1>monster beats</h1> are known as Beats By Dr Dre, All products are promotional with <h1>discount monster beats</h1> at present, we have a professional quality inspection technician, so do not worry about the quanlity. If you place a order sucessfully in our online store, then we will send the <h1>beats by dr dre</h1> with fast delivery, free shipping. Wearing the <h1>dre beats</h1> and cheap <h1>beats by dre us</h1>, you can enjoy the wonderful music.

November 22, 2011 | Unregistered Commenterdiscount monster beats

The particular content is very helpful with regard to new bloggers and provides an excellent starting place to start with. May talk about your posting on my subsequent post. Many thanks.
31 day fat loss cure
diet solution program
SEO Company India
muscle x edge
diet solution program
how to enlarge your penis
What is Vimax
Vimax
vimax
african mango

November 25, 2011 | Unregistered Commenterroderickmerr1229

Now this kind of particulars are very well worth looking for, straight answers for site visitors together with something to suit your needs as will definitely show the conventional in the author.
motocross gear
dirt bikes for sale
motocross gear
motocross gear
yamaha motocross dealers
suzuki motocross dealers
used motocross bikes for sale
motocross gear
motocross pants
motocross helmets

November 26, 2011 | Unregistered Commenterroderickmerr1229

christmas decorationschristmas decorations
christmas ornamentschristmas ornaments
christmas lightschristmas lights
christmas treechristmas tree
ugly christmas sweaterugly christmas sweater
artificial christmas treeartificial christmas tree
business christmas cardsbusiness christmas cards
bulk christmas ornamentsbulk christmas ornaments
buble christmasbuble christmas
busch christmas stocking kitsbusch christmas stocking kits
busch gardedns christmasbusch gardedns christmas
bulk christmas lightsbulk christmas lights
burlap christmas stockingsburlap christmas stockings
bulk christmas giftsbulk christmas gifts
bulk christmas cardsbulk christmas cards
buble christmas albumbuble christmas album
vintage christmas tableclothvintage christmas tablecloth
vintage christmas treevintage christmas tree
vintage christmas tree toppervintage christmas tree topper
vintage christmas tree skirtvintage christmas tree skirt
vintage christmas tree pinvintage christmas tree pin
vintage christmas tree ornamentsvintage christmas tree ornaments
vintage christmas tagsvintage christmas tags
vintage christmas tree lightsvintage christmas tree lights
vintage christmas towelvintage christmas towel
outdoor christmas decorationsoutdoor christmas decorations
vintage christmas decorationsvintage christmas decorations
christmas dresschristmas dress
christmas disheschristmas dishes
girls christmas dressgirls christmas dress
christmas dvdchristmas dvd
christmas decorchristmas decor
christmas dinnerwarechristmas dinnerware
light outdoor christmas decorationslight outdoor christmas decorations
christmas movieschristmas movies
christmas movies in Movies & TVchristmas movies in Movies & TV
christmas movies in Musicchristmas movies in Music
christmas musicchristmas music
christmas movies on dvdchristmas movies on dvd
christmas music 2011christmas music 2011
vintage christmas tree ornamentsvintage christmas tree ornaments
vintage christmas tagsvintage christmas tags
vintage christmas tree lightsvintage christmas tree lights
vintage christmas towelvintage christmas towel
outdoor christmas decorationsoutdoor christmas decorations
vintage christmas decorationsvintage christmas decorations
christmas dresschristmas dress
christmas disheschristmas dishes
christmas crackerschristmas crackers
christmas cdchristmas cd
cheap christmas cardscheap christmas cards

December 21, 2011 | Unregistered Commenterdesigner handbags outlet

1<h1>Louis Vuitton Bags</h1>
<h1>Coach Outlet Store Online</h1>
<h1>Coach Purses Outlet</h1>
<h1>Coach Online Outlet Store</h1>
<h1>Coach Factory Outlet Store Online</h1>
<h1>Coach Factory Store Online</h1>
<h1>Cheap Louis Vuitton Bags</h1>
<h1>Coach Factory Outlet Online</h1>
<h1>Coach Outlet Store</h1>
<h1>Louis Vuitton Outlet</h1>
<h1>Coach Purse</h1>
<h1>Authentic Louis Vuitton Handbags</h1>
<h1>Coach Outlet</h1>
<h1>Chanel Bags</h1>
<h1>Louis Vuitton Bags</h1>
<h1>Louis Vuitton Outlet</h1>
<h1>Louis Vuitton Bag</h1>
<h1>Coach Factory Outlet Online</h1>
<h1>Louis Vuitton</h1>
<h1>Coach Factory Outlet Store</h1>
<h1>Coach Factory Outlet</h1>
<h1>Coach Outlet Online Store</h1>
<h1>Coach Purse Outlet</h1>
<h1>Louis Vuitton Bags</h1>
<h1>Louis Vuitton Bags</h1>
<h1>Coach Factory Outlet Store</h1>
<h1>Coach Outlets</h1>
<h1>Coach Outlet Online</h1>
<h1>Coach Outlet Stores Online</h1>
<h1>Louis Vuitton USA</h1>
<h1>Coach Outlet</h1>
<h1>Coach Factory Online</h1>
<h1>www.louisvuitton.com</h1>
<h1>Coach Outlet Online</h1>
<h1>Coach Outlet Bags</h1>
<h1>Coach Purse Outlet Online</h1>
<h1>Louis Vuitton</h1>
<h1>Coach Outlet Online</h1>
<h1>Coach Purses Outlet</h1>
<h1>Coach Bags</h1>
<h1>Coach Online Store</h1>
<h1>Coach Handbags Outlet</h1>
<h1>Chanel Outlet Store</h1>
<h1>Cheap Louis Vuitton</h1>
<h1>Chanel Outlet</h1>
<h1>Louis Vuitton Sunglasses</h1>
<h1>Coach Outlet Online</h1>
<h1>LV Bags</h1>
<h1>Coach Outlet Store Online</h1>
<h1>Coco Chanel Bags</h1>
<h1>Chanel Handbags</h1>
<h1>Coach Outlet</h1>
<h1>Louis Vuitton Outlet</h1>
<h1>Coach Purses</h1>
<h1>Coach Handbags Outlet</h1>
<h1>Coach Factory Outlet Online</h1>
<h1>Louis Vuitton Outlet</h1>
<h1>Chanel Outlet Store Online</h1>
<h1>Coach Outlet Online</h1>
<h1>Coach Handbags</h1>
<h1>Coach Outlet</h1>
<h1>Burberry Outlet</h1>
<h1>Burberry Scarf</h1>
<h1>Coach Outlet Store Online</h1>
<h1>Louis Vuitton</h1>
<h1>Louis Vuitton Outlet</h1>
<h1>Coach Bag</h1>
<h1>Coach Outlet</h1>
<h1>Coach Factory Outlet Store</h1>
<h1>Coach Factory</h1>
<h1>Coach Purses Outlet Online</h1>
<h1>Louis Vuitton Bags</h1>
<h1>Coach Factory Store</h1>
<h1>Louis Vuitton</h1>
<h1>Coach Online Outlet Store</h1>
<h1>Louis Vuitton Bags</h1>
<h1>Louis Vuitton Outlet</h1>
<h1>Coach Outlet Store Online</h1>
<h1>Coach Factory Store</h1>
<h1>www.louisvuitton.com</h1>
<h1>Coach Handbags Factory Outlet</h1>
<h1>Coach Online Factory Store</h1>
<h1>Coach Factory Store Online</h1>
<h1>Coach Outlet Online</h1>
<h1>Coach Factory Handbag Outlet Store</h1>
<h1>Coach Outlet Stores</h1>
<h1>Coach Factory Outlet</h1>
<h1>Coach Factory Outlet Online</h1>
<h1>Coach Store Online</h1>
<h1>Coach Factory Outlet Online</h1>
<h1>Coach Factory Store Online</h1>
<h1>Coach Factory Outlet</h1>
<h1>Coach Outlet</h1>
<h1>Louis Vuitton Handbags</h1>
<h1>Coach Handbag Outlet</h1>
<h1>Louis Vuitton</h1>
<h1>Cheap Coach Bags</h1>
<h1>Coach Outlet Store Online</h1>
<h1>Chanel Bags</h1>
<h1>Louis Vuitton Handbags</h1>
<h1>www.louisvuitton.com</h1>
<h1>Coach Factory Online</h1>
<h1>Louis Vuitton Purses</h1>
<h1>Coach Factory Outlet Online</h1>
<h1>Chanel Outlet Online</h1>
<h1>Coach Outlets</h1>
<h1>Louis Vuitton Handbags</h1>
<h1>Coach Factory Online</h1>
<h1>Coach Outlet Store Online</h1>
<h1>Coach Outlet Store Online</h1>
<h1>Coach Outlet Online</h1>
<h1>Coach Factory Outlet</h1>
<h1>Louis Vuitton Purses</h1>
<h1>Coach Factory Outlet Online</h1>
<h1>Chanel Bags</h1>
<h1>Coach Store Online</h1>
<h1>Coach Factory</h1>
<h1>Coach Bags</h1>
<h1>Coach Factory Outlet Online</h1>
<h1>Louis Vuitton Handbags</h1>
<h1>Coach Outlet Store</h1>
<h1>Coach Outlet Store</h1>
<h1>Louis Vuitton</h1>
<h1>Louis Vuitton Purses</h1>
<h1>Coach Outlet Purses</h1>
<h1>Coach Online Outlet Store</h1>
<h1>Coach Factory Outlet</h1>
<h1>Coach Bags Outlet</h1>
<h1>Coach Outlet Stores Online</h1>
<h1>Louis Vuitton Handbags</h1>
<h1>Coach Factory Online Sale</h1>
<h1>Coach Store Online</h1>
<h1>Coach Handbags</h1>
<h1>Coach Outlet Handbags</h1>
<h1>Coach Purse Outlet</h1>
<h1>Louis Vuitton Outlet Online</h1>
<h1>Coach Outlet Online Store</h1>
<h1>Coach Factory Outlet</h1>
<h1>Coco Chanel Handbags</h1>
<h1>Burberry Outlet</h1>
<h1>Coach Online Factory Store</h1>
<h1>Louis Vuitton</h1>
<h1>Coach Outlet Store Online</h1>

December 28, 2011 | Unregistered CommenterCoach Outlet Online

Nice article....I appreciate you...
this page contains nice information....
Craftsman Kitchen Cabinets

February 10, 2012 | Unregistered CommenterCraftsman Kitchen Cabinets

PostPost a New Comment

Enter your information below to add a new comment.

My response is on my own website »
Author Email (optional):
Author URL (optional):
Post:
 
All HTML will be escaped. Hyperlinks will be created for URLs automatically.