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 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

patient period-

1

period-

2

Drug o order-1 Placebo Placebo Drug 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 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) Subject NO 1

period @

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 2 nd & 3 rd 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.

Subject NO 1 2 3 4 5 6

Latin square Design

period 1@ period 2@ period3 A C B B A C B A C A B C C A B C B A @ = 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.

Subject NO 1 2 3 4 5 6

Graeco Latin square Design

period 1@ period 2@ period3 Ax Cz By By Ax Cz Cz By Ax By Ax Cz Ax By Cz 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 2 3 4 5 6 A B C D B C A D A C 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.

  The smaller the within patient variation relative to between patient variation .the more efficient will be crossover 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.

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 d.f

SS MS P

Subject period Treatment Error Total *p < 0.05.

Data for the Bioequivalence comparing drug A and drug B

subject 1 2 3 4 5 6 7 8 9 10 11 12 order AB BA AB AB BA BA AB BA BA AB AB BA Mean ∑ x A 201 187 168 200 151 294 97 228 250 293 154 209.4

2513

AUC

B 210 116 77 220 133 140 190 168 161 240 188 167.2

2006

∑ s i

287 396 411 533 342 500 364 303 245 420 284 434

 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) ∑p 1 = 2544 The second period observations are 210, 201,116 ,77, 200 ,151, 140 ,97 ,228 ,161,240 ,154 (sum =1975 ) ∑p 2 = 1975

The period sum of square can be calculated as follow: • Where ∑ x 1 and ∑ x 2 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 :  ∑ x t is the some of all observation : 2513+2006 = 4519  ∑ x A is the some of observation for product A = 2513   ∑ P 1 is sum of all observation for period 1 =2544  ∑ P2 is sum of all observation for period 2 = 1975  ∑ x B is the some of observation for product B = 2006 ∑x 2 T 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 : period MS F= Error MS = 12.6 Treatment MS F= 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 group II, and (C.T) II are correction term for group I and 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% 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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