- Vishnu Datta.M

Bioavailability1

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

Bioeqivalence*

“The absence of a significant difference in the rate and extent to which theactive 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

Various study designs employed2 areCompletely Randomized DesignRandomized block DesignsRepeated Measures, Cross-over and Carry-over DesignLatin Square DesignsPaired Comparative DesignParallel DesignFactorial Design Cluster Design

Completely Randomized Design

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

Completely Randomized Design

Completely Randomized Design

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.

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.

Randomized block Design

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.

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.

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.

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.

Randomized block Design

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 = 32 = 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) .

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.

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

Randomized block Design

Repeated measures Cross-over & carry over Design

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.

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.

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.

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.

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).

Latin Square Design

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.

A B C DB C D AC D A BD A B C

 

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.

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

 

Latin Square Designs Selected Latin Squares

3 x 3 4 x 4A B C A B C D A B C D A B C D A B C DB C A B A D C B C D A B D A C B A D CC A B C D B A C D A B C A D B C D A B

D C A B D A B C D C B A D C B A 

5 x 5 6 x 6A B C D E A B C D E FB A E C D B F D C A EC D A E B C D E F B AD E B A C D A F E C BE C D B A E C A B F D

F E B A D C

A Latin Square

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.

Latin Square Design

Pros +++++•Minimizes the inter subject variability in plasma drug levels

•Minimizes the carry over effectsintra subject

•Variations due to time effect

•Treatments can be studied from a small-scale experiment

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

Incomplete Block Designs

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.

Repeated Measures Designs

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)

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.

March 31, 2007 Jerzy Wojdylo, Latin Squares, Cubes and Hypercubes

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Orthogonal LS – NYT 4/26/1959

March 31, 2007 Jerzy Wojdylo, Latin Squares, Cubes and Hypercubes

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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 nZ+, with exception of n = 2 and n = 6.

Data strawb; input row column irrig $ weight @@; datalines;1 1 drip 51 1 2 over 119 1 3 none 602 1 none 98 2 2 drip 43 2 3 over 313 1 over 99 3 2 none 87 3 3 drip 49; run;proc glm; class row column irrig; model weight = row column irrig; title 'Strawberry Irrigation Latin Square Exp'; run;

Latin Square in SAS

Sum of Source DF Squares Mean Square F Value Pr > F Model 6 5840.000000 973.333333 1.20 0.5205 Error 2 1621.555556 810.777778 Corrected Total 8 7461.555556

R-Square Coeff Var Root MSE weight Mean 0.782679 40.23037 28.47416 70.77778

Source DF Type I SS Mean Square F Value Pr > F row 2 817.555556 408.777778 0.50 0.6648 column 2 2616.222222 1308.111111 1.61 0.3826 irrig 2 2406.222222 1203.111111 1.48 0.4026

Source DF Type III SS Mean Square F Value Pr > F row 2 817.555556 408.777778 0.50 0.6648 column 2 2616.222222 1308.111111 1.61 0.3826 irrig 2 2406.222222 1203.111111 1.48 0.4026

March 31, 2007 Jerzy Wojdylo, Latin Squares, Cubes and Hypercubes

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Completion Problems

• The ugly (?)a. k. a. sudoku

99 66 33 44 66 77 22 11 88

88 77 44 11 33 22 99 66 55

66 11 22 88 99 55 44 77 33

22 33 66 77 88 99 55 99 11

11 99 88 22 55 33 77 44 66

77 44 55 66 11 44 33 88 22

55 88 77 33 44 11 66 22 99

33 22 11 99 77 66 88 55 44

44 66 99 55 22 88 11 33 77

~In case you blinked and missed something~

1. Bioavailability and bioequivalence (chapter-11)Biopharmaceutics And Pharmacokinetics A Treatise – D.M Brahmankar, Sunil B. Jaiswal Pg.no 315.

2. Zintzaras E, Bouka P. National Drug Organization, Athens, Greece.Bioequivalence studies: biometrical concepts of alternative designs and pooled analysis.Eur J Drug Metab Pharmacokinet. 1999 Jul-Sep;24(3):225-32.

3. Stufken, J. (1996). "Optimal Crossover Designs". In Ghosh, S. and Rao, C. R.. Design and Analysis of Experiments. Handbook of Statistics. 13. North-Holland. pp. 63–90. ISBN 0-444-82061-2.

4. http://www2.semo.edu/jwojdylo/research.htm5. http://www.math.pitt.edu/~egw1/6. Completely Randomized Designs Adapted from Experimental

Designs, 2nd ed., (1957) by Cochran and Cox, John Wiley & Sons, Inc.

~In case you blinked and missed something~

• Bailey, R.A. (2008). "6 Row-Column designs and 9 More about Latin squares". Design of Comparative Experiments. Cambridge University Press. ISBN 978-0-521-68357-9. MR 2422352. Pre-publication chapters are available on-line.

• Dénes, J.; Keedwell, A. D. (1974). Latin squares and their applications. New York-London: Academic Press. pp. 547. ISBN 0-12-209350-X. MR 351850.

• Dénes, J. H.; Keedwell, A. D. (1991). Latin squares: New developments in the theory and applications. Annals of Discrete Mathematics. 46. Amsterdam: Academic Press. pp. xiv+454. ISBN 0-444-88899-3. MR 1096296.

• Hinkelmann, Klaus; Kempthorne, Oscar (2008). Design and Analysis of Experiments. I , II (Second ed.). Wiley. ISBN 978-0-470-38551-7. MR 2363107.

– Hinkelmann, Klaus; Kempthorne, Oscar (2008). Design and Analysis of Experiments, Volume I: Introduction to Experimental Design (Second ed.). Wiley.ISBN 978-0-471-72756-9. MR 2363107.

– Hinkelmann, Klaus; Kempthorne, Oscar (2005). Design and Analysis of Experiments, Volume 2: Advanced Experimental Design (First ed.). Wiley. ISBN 978-0-471-55177-5. MR 2129060.

• Knuth, Donald (2011). Volume 4A: Combinatorial Algorithms, Part 1. The Art of Computer Programming (First ed.). Reading, Massachusetts: Addison-Wesley. pp. xv+883pp. ISBN 0-201-03804-8.

• Laywine, Charles F.; Mullen, Gary L. (1998). Discrete mathematics using Latin squares. Wiley-Interscience Series in Discrete Mathematics and Optimization. New York: John Wiley & Sons, Inc.. pp. xviii+305. ISBN 0-471-24064-8. MR 1644242.

• Shah, Kirti R.; Sinha, Bikas K. (1989). "4 Row-Column Designs". Theory of Optimal Designs. Lecture Notes in Statistics. 54. Springer-Verlag. pp. 66–84. ISBN 0-387-96991-8. MR 1016151.

• Shah, K. R.; Sinha, Bikas K. (1996). "Row-column designs". In S. Ghosh and C. R. Rao. Design and analysis of experiments. Handbook of Statistics. 13. Amsterdam: North-Holland Publishing Co.. pp. 903–937. ISBN 0-444-82061-2. MR 1492586.

• Raghavarao, Damaraju (1988). Constructions and Combinatorial Problems in Design of Experiments (corrected reprint of the 1971 Wiley ed.). New York: Dover. ISBN 0-486-65685-3. MR 1102899.

• Street, Anne Penfold and Street, Deborah J. (1987). Combinatorics of Experimental Design. New York: Oxford University Press. pp. 400+xiv pp.. ISBN 0-19-853256-3, 0-19-853255-5. MR 908490.

• J. H. van Lint, R. M. Wilson: A Course in Combinatorics. Cambridge University Press 1992,ISBN 0-521-42260-4, p. 157

!!All the very best!!