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Department of Pharmacology
L. M. College of Pharmacy, Ahmedabad-09
CONTENTS
 INTRODUCTION
 SPECIFIC DESIGN UNDER CROSSOVER
 ADVANTAGES / DISADVANTAGES
 ANOVA FOR CROSSOVER
BIOEQUIVALENCE STUDY
 TEST FOR CARRYOVER EFFECT
INTRODUCTION
 The crossover design(changeover design) is a
very popular & often desirable design in clinical
experiment.
 comparative bioavailability or bioequivalence
studies, in which two or more formulation of same
drugs are compared
 Each patient acts his or her own control
 In this design typically two treatment are compared, with
each patient or subject taking each treatment in turn.
 The treatment are taken on two occasion often called
visits, period, or legs.
 The order of treatment is randomized that is –
“Either A is followed by B or B is followed by A ”
A
first week
B
second week
or
B
first week
Where A and B are the two treatment
A
second week
 Each patient receive both the treatments
( drug & placebo)
 Comparison is “within” patient not “between” the
patients
 The smaller the within or intrasubject variability
relative to between or intersubject variability the
more efficient will be crossover design.
Crossover Trial
period- 1
Drug
patient
period- 2
placeb
o
Placebo
order-1
Drug
Placebo
order-2
Specific design under crossover are:
 Two treatment two period crossover design
 Two treatment four period crossover design
(switchover design)
 Latin square Design
 Graeco Latin square Design
 Balance incomplete block Design (BIBD)
Two treatment two period crossover design
 In a study involving two treatment in which each subject
receive both the treatment.
 Even number of subject are selected. half of them are assigned
to first treatment(A), rest half to other treatment(B) in the first
period
 After washout period planned the subject received treatment A
or B in first period are treated with treatment B or A
respectively in second period.
 This design is very often used in bio-eqivalence studies &
comparison of two antihypertensive agent
Two treatment two period crossover design:
Subject
Period 1
Period 2
No.
1
A
B
2
A
B
3
B
4
A
B
5
B
A
6
B
A
Wash out period
A
@ = include wash out period after each treatment period
Two treatment four period crossover design (switchover design)
 Like in previous design the patient are randomly assigned to
two treatment and thereafter two treatments are given
alternatively for more than two period.
 Switchover design are used in disease that are associated with
periodic conditions.
 In females some diseases are associated with menstrual cycles.
 These menstrual cycle may be ovulatory or non-ovulatory if
any study is restricted to only two cycle it is likely that one or
both menstrual cycle in some female are non-ovulatory. So in
order to have exposure to ovulatory as well as non-ovulatory
cycle. more than two period are included in study design.
Two treatment four period crossover design (switchover design)
period@
1
2
3
4
1
A
B
A
B
2
B
A
B
A
3
B
A
B
A
4
A
B
A
B
5
A
B
A
B
Subject NO
@ = include wash out period after each treatment period
Latin square design
 In a study where three or more treatments are involved with
a condition that each subject is required to be exposed to all
treatments in different sequence.
 In this design with three treatments, total number of subjects
(generally in multiples of three)is randomly assigned to three
treatment group in period one.
 The treatment in 2nd & 3rd period is given in cyclic order
(namely A to B,B to C or C to A)
 Such design are used in bioequivalence and agriculture
experiment.
Latin square Design
Subject NO
period 1@
period 2@
period3
1
A
B
C
2
C
A
B
3
B
C
A
4
B
C
A
5
A
B
C
6
C
A
B
@ = include wash out period after each treatment period
Graeco Latin square design
 This design is used when effect of treatment and factor are
required to be studied simultaneously in cases where number
of treatment and number of factor is exactly the same.
 In this design subjects are assigned to different combination of
treatment and factor in period1
 Where A,B and C are treatment and x,y and z are factor and
combination's available are treatment A with factor x (Ax),B
with factor y (By) and C with factor z (Cz)
 This design is mostly used in agricultural experiments and
some times to identify drug-drug or drug-food interaction.
Graeco Latin square Design
Subject NO
period 1@
period 2@
period3
1
Ax
By
Cz
2
Cz
Ax
By
3
By
Cz
Ax
4
By
Cz
Ax
5
Ax
By
Cz
6
Cz
Ax
By
@ = include wash out period after each treatment period
Balance incomplete block Design (BIBD)
 in bio-equivalence(BE) studies simple three – treatment, three
period crossover design can actually be used.
 BE studies, carried out with this design will need withdrawal of
blood sample in each period. thus over the three periods, total
volume of blood sample withdrawal from each subject exceed
ethically permitted upper limit posing ethical issues.
 So study carried out using statistically valid design – four treatment
& two periods – BIBD
 As per this design if there are four treatment A,B,C and D, six
possible pair of treatments can be formed namely ,AB, AC, AD,
BC,BD and CD. Subject are first assigned randomly to six pairs
treatment, then remaining subjects are assigned randomly to exactly
opposite pairs.
Next six subject will be assigned to exactly opposite combination
Balance incomplete block Design (BIBD)
Subject NO
period 1@
period 2@
1
A
B
2
C
D
3
B
C
4
A
D
5
A
C
6
B
D
@ = include wash out period after each treatment period
Advantage of Crossover design v/s parallel design
 Increase precision relative to parallel group design
 More economical: one-half number of patient or subject have been
recruited to obtain same number of observation as in parallel design.
 Cross-over design in term of cost depend on the economy of the
patient recruitment, cost of experimental observations as well as
relative within-patient /between patient variation.
 The smaller the within patient variation relative to between patient
variation .the more efficient will be crossover design.
 Cross-over design may actually Save the time because fewer patient
are needed to obtain equal power compared to the parallel design.
Disadvantage of Crossover design v/s parallel design
 Take longer to complete than a parallel study because of extra testing
period .
 Missing data pose a more serious problem than in parallel design.
 If an observation is lost in one of the legs of two period crossover the
statistical analysis is more difficult and the design loses some
efficiency.
 The most serious problem with use of crossover design is one
common to all Latin square design is differential carryover or
residual effect.
 Carryover effect occurs when the response on second period(legs) is
depend on the response in the first period
 Differential carryover effect where the short interval between
administration of dosage forms X and Y is not sufficient to rid the
body of drug when formulation X is given first. This results in an
apparent larger blood level for formulation Y when it is given
subsequent to formulation X.
 carryover effects are not as obvious. These effects can be caused by
such uncontrolled factors as psychological or physiological states of
the patients, or by external factors such as the weather, clinical
setting, assay techniques, and so on.
A
Carryover effect
B
• Sufficient long washout period
ensure that carryover of blood
concentration of drug is absent.
Analysis of variance Table for the crossover Bioequivalence study
(AUC)
source
Subject
period
Treatment
Error
Total
*p < 0.05.
d.f
SS
MS
P
Data for the Bioequivalence comparing drug A and drug B
AUC
∑si
subject
order
A
B
1
AB
290
210
500
2
BA
201
163
163
364
3
AB
187
116
303
4
AB
168
77
245
5
BA
200
220
420
6
BA
151
133
284
7
AB
294
140
434
8
BA
97
190
287
9
BA
228
168
396
10
AB
250
161
411
11
AB
293
240
533
12
BA
154
188
342
Mean
209.4
167.2
2513
2006
∑
x
 The AUC data in Table is the data for the first period are obtained by noting
the order of administration. Subject 1 took product A during the first period
(290) subject 2 took B during the first period (163); and so on.
 Therefore, the first period observations are
290 ,163 ,187, 168, 220, 133 ,294 ,190 ,168, 250, 293 ,188
(sum = 2544)
∑p1 = 2544
 The second period observations are
210, 201,116 ,77, 200 ,151, 140 ,97 ,228 ,161,240 ,154
(sum =1975 )
∑p2 = 1975
The period sum of square can be calculated as follow:
•Where ∑x1 and ∑x2 are sums of all observations in the first and
second period
• N is the number of subject
•C.T. is the correction term
Calculation for ANOVA :
 ∑ xt is the some of all observation :
2513+2006 = 4519
 ∑xA is the some of observation for product A = 2513
 ∑xB is the some of observation for product B = 2006
 ∑ P1 is sum of all observation
for period 1 =2544

∑P2 is sum of all observation for period 2 = 1975

∑x2T is the some of squared observation = 929321
 Total degrees of freedom = Total number of observations - 1
= 24-1
= 23
 Degree of freedom for subject = Total no. of subject - 1
= 12 – 1
= 11
 Degree of freedom for period = Total no. of period - 1
=2–1
= 1
 Degree of freedom for treatment = Total no. of treatment - 1
=2–1
= 1
 Degree of freedom for Error = Total d.f – subject d.f – period
d.f – treatment d.f
= 23- 11- 1-1
= 10
Calculate the mean square (MS)
It is obtained by dividing each sum of squares
with corresponding degrees of freedom
General equation: MS= SS/df
To test the different among the treatment & among the product
F ratio is formed :
F=
period MS
Error MS
= 12.6
F=
Treatment MS
Error MS
=10.0
Test for carryover (sequence) effect:
 Compute some of squares due to carryover effect by
comparing the results for group I to group II
 Group I and Group II which differ in order of treatment
group I ( treatment A first, B second) and group II (treatment
B first , A second)
 It can be demonstrated that in absence of sequence effects the
average result for group I is expected be the equal to the
average result for group II.
Data for bioequivalence study comparing Drug A and Drug B
The sum of squares is calculated as :
The sequence some of squares is
The proper error term to test the sequence effect is within
group Means square represented by some of squares between
subject within group
sum of squares =
Where (C.T )I and (C.T)II are correction term for group I and
group II,
within group some of square is == =
 the within group some of square has 10 degree of freedom
i. e. 5 from each group.
The mean square is : sum of square
d.f
38940
10
=
3894
Test the sequence effect = sequence some of square
within group mean square
= 4620.375
3894
= 1.19
=
 The effect is not significant at 5% level
 If the carryover effect is not significant proceed with the usual
analysis
 If the carryover effect is significant ,the usual analysis is not
valid.
 The recommended analysis use only first period result deleting
the data contaminated by carryover.( second period result)
using only the first period data so the analysis is appropriate
for one way analysis of variance.
References: Pharmaceutical Statistics, practical and clinical
application, forth edition by S. Bolton & C. Bon
 Basic principle of clinical research and methodology
edition by sk gupta
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