Department of PharmacologyL. M. College of Pharmacy, Ahmedabad-09

Department of PharmacologyL. M. College of Pharmacy, Ahmedabad-09

CONTENTSINTRODUCTIONSPECIFIC DESIGN UNDER CROSSOVERADVANTAGES / DISADVANTAGES ANOVA FOR CROSSOVER

BIOEQUIVALENCE STUDYTEST FOR CARRYOVER EFFECT

INTRODUCTIONThe 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 B or B A first week second week first week second week

Where A and B are the two treatment

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 period- 2

Drug Placebo

patient order-1

Placebo Drug

order-2

placebo

Specific design under crossover are:

Two treatment two period crossover designTwo treatment four period crossover design

(switchover design) Latin square Design Graeco Latin square Design Balance incomplete block Design (BIBD)

Two treatment two period crossover designIn 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

No.Period 1 Period 2

1 A B

2 A B

3 B Wash out period A

4 A B

5 B A

6 B 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@ Subject NO 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

@ = 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 designMore 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.

B

A

Carryover effect

• 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 d.f SS MS P

Subject

period

Treatment

Error

Total

*p < 0.05.

Data for the Bioequivalence comparing drug A and drug B

AUC ∑si

subject order A B

1 AB 290 210 500

2 BA 201 163 364

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

∑ x 2513 2006

290

163

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

∑ 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

Calculation for ANOVA :

Total degrees of freedom = Total number of observations - 1

= 24-1

= 23Degree 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

period MS

F= Error MS = 12.6

Treatment MS

F= Error MS =10.0

To test the different among the treatment & among the product F ratio is formed :

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 = 38940

d.f 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% levelIf the carryover effect is not significant proceed with the usual

analysisIf 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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