Bioequivalence and Bioavailability Forum

Dear Shri,

please see here.

Hi Shri,

❝ the data is like given below where a, b, c, d are treatment given to subjects and the 0=cure, 1=mild, 2=modrate, 3=sevior

Without being a stats shark I think this might be a candidate for the Friedman test. It seems illogical to me if a n x k contingency table is applicable here since (as far as I understand) the data are not counts but gradings.

EM.

dear shri !

The most important things regarding selection of a statistical tests is to

1. define the null and the alternative hypothesis
   
2. define your type I error
   
3. define an adequate measure for the treatment effect(s) as confidence intervals are much more informative than plain p-values

and not looking for a test suitable for a given spreadsheet

hope this helps

Martin

PS.: on the assumption that your null hypothesis is no treatment effect on your variable (which have to be defined exactly such as median score, proportions per score, etc. ) you may have the following alternatives

• treatment arms are different
  
• pairwise comparisons of treatments which results in a multiplicity problem
  
• in case of a natural order of your treatment (e.g. dose levels) you may interested in the alternative of an increase/decrase as dose increase
  
• you may have a dose-finding problem; ie. selection of the lowest / highest dose which differs from your control treatment which can be formulated as a sequence of hypothesis testing problems
  
• etc. etc.

there is also the other way round in the case that you want to show non-inferiority or equivalence between two or more treatment arms (e.g. identification of the maximum safe dose).

as you can see it is very important that you are able to define your null and your alternative hypothesis.

Dear Shri,

I presume this is a 4-period crossover study with four treatments, right?

Response is ordinal since your values are ordered categories.

You are interested in the differences (or equivalence?) between the treatments a, b, c and d, right?

I myself hadn't any such complicated, not an every-day-analysis to do in my career, thanks God . It's therefore out of my feasibility to point you to the right statistical method.

But I have some tips for you (but only if my presumptions are fulfilled):

• Treat your ordered categories (ranks) as metric (of course they are not ) and use them in the ordinary evaluation via parametric ANOVA. This is what Helmut has suggested in this thread regarding non-parametric evaluation of tmax. This will give a rough "feeling" for treatment differences.
  
  
• Read Chapter 6 "Analysis of Categorical Data" in
  Byron Jones, Michael G. Kenward
  "Design and Analysis of Cross-Over Trials"
  CHAPMAN & HALL/CRC
  Boca Raton, London New York Washington, D.C. (2003)
  Second Edition
  
  Read the paper
  Ezzet, F. and Whitehead, J.
  "A random effects model for ordinal response from a cross-over trial"
  Statistics in Medicine 10, 901-907 (1991)
  I'm not totally aware but it seems the keyword is "Logistic regression".
  
  And last but not least with the keywords from the subject line of this post.
  
  
• Consult a statistician of your very confidence who has "The power to know" with such a data analysis and outsource this analysis .
  

Hope this helps.