This document discusses various study designs used in bioequivalence studies, including completely randomized designs, randomized block designs, repeated measures cross-over designs, Latin square designs, and incomplete block designs. It provides definitions and examples of each design. For each design, it outlines the methodology, pros, and cons. It also provides examples to illustrate Latin square designs and randomized block designs.

1. - Vishnu Datta.M

2. Bioavailability1
Defined as the rate and extent (amount)
of absorption of unchanged drug from its dosage form

3. Bioeqivalence*
“The absence of a significant difference in the rate and extent to which the
active ingredient or active moiety in pharmaceutical equivalents
or pharmaceutical alternatives becomes available at the site of drug
action when administered at the same molar dose under similar conditions
in an appropriately designed study.”
*CDER U.S. Food & Drug Administration

5. Various study designs employed2 are
Completely Randomized Design
Randomized block Designs
Repeated Measures, Cross-over and Carry-over
Design
Latin Square Designs
Paired Comparative Design
Parallel Design
Factorial Design
Cluster Design

7. Completely Randomized Design

8. Completely Randomized Design
• Random
http://www.thefreedictionary.com/random
1. Having no specific pattern, purpose, or objective: random
movements. See Synonyms at chance.
2. Mathematics & Statistics Of or relating to a type of circumstance or
event that is described by a probability distribution.
3. Lacking any definite plan or prearranged order; haphazard
Coming to>>>Completely Randomized Design

9. Completely Randomized Design

10. Completely Randomized Design

11. Completely Randomized Design
• In this design all treatments are randomly allocated
among all experimental subjects.
• METHOD OF RANDOMISATION:
Label all subjects with same number of digits.
Randomly select non repeating numbers from these
labels.
Subject them for the first treatment and then repeat
for all other treatments.

12. Completely Randomized Design
Pros +++++
Easy to construct.
Can accommodate any number of treatments
and subjects.
Simple to analyze even though the sample sizes
might not be same for each treatment.
Cons - - - - - - - Can be applied to only those situations in which
there are relatively few treatments.
All subjects must be as homogenous as possible.

13. Randomized block Design

14. Randomized block Design
• First subjects are sorted into homogenous
groups, called blocks and the treatments are
then assigned at random within the blocks.
• METHOD OF RANDOMISATION:
• Subjects having similar background
characteristics are formed as blocks
• Randomization for different blocks are done
independent of each other.

15. Randomized block Design
Pros +++++
Can accommodate any number of replications.
Different treatments need not have equal sample size.
Statistical analysis is relatively simple.
The design is easy to construct.
Cons - - - - - - - Missing observations with in a block require more
complex analysis.
Degree of freedom of experimental error are not as
large as with a completely randomized design.

16. Randomized block Design
• Suppose a researcher is interested in how
several treatments affect a continuous response
variable (Y).
• The treatments may be the levels of a single
factor or they may be the combinations of levels
of several factors.
• Suppose we have available to us a total of N =
nt experimental units to which we are going to
apply the different treatments.

17. Randomized block Design
The Randomized block Design randomly divides the
experimental units into t groups of size n and
randomly assigns a treatment to each group.
•Randomized block Designs divides the group of experimental
units into ‘n’ homogeneous groups of size ‘t’.
•These homogeneous groups are called blocks.
•The treatments are then randomly assigned to the
experimental units in each block - one treatment to
a unit in each block.

18. Example
• Suppose we are interested in how weight gain
(Y) in rats is affected by Source of protein (Beef,
Cereal, and Pork) and by Level of Protein (High
or Low).
• There are a total of t = 3×2 = 6 treatment
combinations of the two factors (Beef -High
Protein, Cereal-High Protein, Pork-High Protein,
Beef -Low Protein, Cereal-Low Protein, and
Pork-Low Protein) .

19. Randomized block Design
• Suppose we have available to us a total of N =
60 experimental rats to which we are going to
apply the different diets based on the t = 6
treatment combinations.
• Prior to the experimentation the rats were
divided into n = 10 homogeneous groups of size
6.

20. Randomized block Design
• The grouping was based on factors that
had previously been ignored (Example Initial weight size, appetite size etc.)
• Within each of the 10 blocks a rat is
randomly assigned a treatment
combination (diet).
• The weight gain after a fixed period is
measured for each of the test animals and
is tabulated

21. Randomized block Design

22. Repeated measures Cross-over & carry over Design

23. Repeated measures Cross-over & carry over Design
• This is essentially a randomized block design in
which the same subject serves as a block .
• Since we take repeated measures on each
subject we get the design name ‘Repeated measured Design’.
• The administration of two or more treatments
one after the other in a specified or random
order to the same group of patients is called a
Cross-over Design or Change over design.

24. Repeated measures Cross-over & carry over Design
• A crossover clinical trial is a repeated measures
design in which each patient is randomly
assigned to a sequence of treatments, including
at least two treatments (of which one "treatment"
may be a standard treatment or a placebo).
• Nearly all crossover designs have "balance",
which means that all subjects should receive the
same number of treatments and that all subjects
participate for the same number of periods. In
most crossover trials, in fact, each subject
receives all treatments.

25. Repeated measures Cross-over & carry over Design
• Glitches
• >>distortion from the accuracy due to
residual effects from the preceding
treatment usually called Carryover effects
• To prevent this allow for a washout period
during most of the drug is eliminated from
the body 10 elimination half-lives.

26. Repeated measures Cross-over & carry over Design
• Method of randoMization
• Complete randomization is used to randomize the order of
treatments for each subject.
Pros +++++
• Provide good precision for comparing treatments because all
sources of variability bet subjects are excluded from the
experimental error.
• It is economic on subjects this is particularly important only
when few subjects can be utilized for the experiments.
• When the interest is in the effects of a treatment over time it is
usually desirable to observe the same subject at different
points of time than observing different subjects at specified
point of time.

27. Repeated measures Cross-over & carry over Design
Cons - - - - - - - •There may be order-effect which is connected
with position in the treatment order
•There may be carry over effect
•Order effects: that are associated with the passage of
time include practice effect (improvement in
performance due to repeated practice with a task) and
fatigue effect (decline in performance as the research
participant becomes tired or bored while performing a
sequence of tasks) (Cozby, 2009).

28. Latin Square Design

29. Latin Square Design
• A Latin square is a square array of objects
(letters A, B, C, …) such that each object
appears once and only once in each row and
each column. Example - 4 x 4 Latin Square.
ABCD
BCDA
CDAB
DABC

30. Latin Square Design
• In experimental design, a Latin square is an n ×
n array filled with n different symbols, each
occurring exactly once in each row and
exactly once in each column.

31. In a Latin square You have three factors:
• Treatments (t) (letters A, B, C, …)
• Rows (t)
• Columns (t)
The number of treatments = the number of rows = the number
of columns = t.
The row-column treatments are represented by cells in a t x t
array.
The treatments are assigned to row-column combinations
using a Latin-square arrangement

32. Latin Square Designs
Selected Latin Squares
3x3
4x4
ABC ABCD
BCA BADC
CAB CDBA
DCAB
5x5
ABCDE
BAECD
CDAEB
DEBAC
ECDBA
ABCD
BCDA
CDAB
DABC
6x6
ABCDEF
BFDCAE
CDEFBA
DAFECB
ECABFD
FEBADC
ABCD
BDAC
CADB
DCBA
ABCD
BADC
CDAB
DCBA

33. A Latin Square

34. Latin Square Design
• It is completely randomised design, randomised block design
and repeated measures design are experiments where the
person remains on the treatment from starting till the end of
the experiment are called continuous trial.
• A latin square design is a two-factor design with one
observation in each cell.
• Subject and treatment
• Such a design is useful compared to earlier when three or
more treatments are compared carry over effects are
balanced.
• Randomised, balanced, cRoss-oveR latin squaRe
designs aRe commonly used foR bioequivalence
studies.

35. Latin Square Design
Pros +++++
•Minimizes the inter subject variability in
plasma drug levels
•Minimizes the carry over effects
intra subject
•Variations due to time effect
•Treatments can be studied from a smallscale experiment

36. Latin Square Design
Cons - - - - - - - -
•Use of Latin Square will lead to a very small number of
degrees of freedom
•Randomization required is somewhat complex than
earlier designs considered
•Study takes a long time as appropriate washout
period is required which will be long if drug has long
half life
•When the number of formulations to be tested is
more>>>the study becomes difficult and also the
subject dropouts are high

37. Incomplete Block Designs

38. Incomplete Block Designs
• In the incomplete block design, each block only
gets a subset of the treatments.
• You might imagine a simple story in which you
had seven automobile tire brands that you wanted
to compare and your blocks were cars. Well, on
each car you can only put four tires! There's no
way you can do it differently—a car only has four
wheels. So, we have at most four treatments in
each block. If we really have seven treatments
then we would have to use an incomplete block
design.
• An incomplete block design is one in which not all
the treatments occur in every block.

39. Repeated Measures Designs

40. Repeated Measures Designs
We have experimental units that
• may be grouped according to one or
several factors (the grouping factors)
Then on each experimental unit we have
• not a single measurement but a group of
measurements (the repeated measures)
• The repeated measures may be taken at
combinations of levels of one or several
factors (The repeated measures factors)

41. Example
In the following study the experimenter
was interested in how the level of a certain
enzyme changed in cardiac patients after
open heart surgery.
The enzyme was measured
• immediately after surgery (Day 0),
• one day (Day 1),
• two days (Day 2) and
• one week (Day 7) after surgery
for n = 15 cardiac surgical patients.

47. Orthogonal LS – NYT 4/26/1959
March 31, 2007
Jerzy Wojdylo, Latin Squares,
Cubes and Hypercubes
47

48. Orthogonal LS – History 1960
• 1960 R.C. Bose, S.S. Shrikhande, E.T.
Parker, Further Results on the
Construction of Mutually Orthogonal Latin
Squares and the Falsity of Euler's
Conjecture, Canadian Journal of
Mathematics, vol. 12 (1960), pp. 189-203.
• There exists a pair of orthogonal LS for all
n∈Z+, with exception of n = 2 and n = 6.
March 31, 2007
Jerzy Wojdylo, Latin Squares,
Cubes and Hypercubes
48

49. Data strawb;
Sum of
input row column irrig $ weight @@;
Source
DF
Squares
Mean Square
F Value
datalines;
Pr
1 1 drip > F 1 2 over 119 1 3 none
51
60
Model 98 2 2 drip
6
5840.000000
973.333333 Square in
1.20
2 1 none
43 2 3 over
31
Latin
0.5205 3 2 none
3 1 over
99
87 3 3 drip
49
Error
2
1621.555556
810.777778 SAS
; run;
8
7461.555556
proc Corrected Total
glm;
class row column irrig;
R-Square
Root MSE
weight Mean
model weight = row column irrig; Coeff Var
0.782679
40.23037
70.77778
title 'Strawberry Irrigation Latin Square Exp'; 28.47416
run;
Source
Pr > F
row
0.6648
column
0.3826
irrig
0.4026
DF
Type I SS
Mean Square
F Value
2
817.555556
408.777778
0.50
2
2616.222222
1308.111111
1.61
2
2406.222222
1203.111111
1.48
Source
Pr > F
row
0.6648
column
0.3826
irrig
0.4026
DF
Type III SS
Mean Square
F Value
2
817.555556
408.777778
0.50
2
2616.222222
1308.111111
1.61
2
2406.222222
1203.111111
1.48

50. Completion Problems
9
• The ugly (?)
8
a. k. a. sudoku
6
2
1
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March 31, 2007
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Jerzy Wojdylo, Latin Squares, Cubes
and Hypercubes
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52. ~In case you blinked and missed something~
•
•
•
•
•
•
•
•
•
•
•
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53. !!All the very best!!