Factorial Designing for Pharmaceutical Product and Process Development

Vinod K.R.* and Sandhya S.

Nalanda College of Pharmacy, Nalgonda– 508001, Anshra Pradesh, India.

ABSTRACT:

The conventional experimental designs are not adequately contributing robustness of the experiment. Quality by design is an essential tool for time and cost effectiveness. Common design is factorial design. Factorial designing is more flexible and gives more knowledge about process and product and several software are also available. This manuscript gives the reader an in depth information of factorial experimental design, its theoretical background and how to implement this statistical tool in the real practical research.

KEYWORDS: total quality management, quality by design, interaction, factorial design

INTRODUCTION:

History of applications of statistics in research

In the recorded history of human civilization, never before was there so much of scientific and technological advancements and innovations, all over the world. These days quality and quantity has equal significance when comes to the production. Thus standard operation procedures (SOP), in process quality control (IPQC) and Total quality management (TQM) came into existence. The concept behind all these developments are to reduce the errors and save time, energy and cost. Reliable predictions based on scientific speculations achieve greater credibility and robustness of a product as well as process. In conventional experimental approach, QA is assured by physical testing and inspection, specifications are based on history of batch, focus only on reproducibility, discourages changes thus freezing the process, specifications depends on batch history. QbD thus have an upper hand in the reliability of data and is more flexible. Thus design of experiments (DOE) became a useful tool for determining specific factors affecting defect levels in a product. DOE is based on a historical background which goes back to 1920s, when Prof. Ronald Fisher, a British statistician developed ground breaking applications in discoveries. This method now became universal software tool for engineers and researchers.

K2 Corporation, Washington, noticed a radical growth in production expenditure upto 30%. DOE found out the reason and solution. The findings slashed down from 250 to 2.5 labor hours. In another report John Deere Engine works, Waterloo, Lowa, by implementing DOE, saved $ 500, 000/ anum. Types of statistical designing are factorial designs, sequential simplex techniques, response surface methodology, D- optimal techniques and I-optimal techniques. Out of these, the former one is the most applicable in pharmacy.

But before discussing the concept of factorial design, we need to personalize, some common terminologies which is stated and elaborated as below.

Optimization-Perfect, effective or functional of a method/ process/ product. Thus it is the determination of the experimental conditions resulting in its optimal performance.

Objective- Used to indicate either the property of interest (criteria) or the goal of an optimization experiment.

Variables- Development of a product/ process involves several influential factors, at various % of influence. Variations are independent, dependent, quantitative and qualitative variables. Independent variable are under direct control of the investigator ( drug concentration, polymer composition etc. ) Dependent variable are the response of the finished product ( tablet/ microsphere ) based on the influence of dependent variables eg. Drug release profile etc. Quantitative variables are those can take up numerical values. Eg. Temperature, pressure, concentration. Qualitative variables include type of carrier/ polymer etc. The dependence can be linear or non linear as shown in figure no. 1.

Fig 1. Difference between linear and non linear interaction

Response- Objective variable that is calculated, which measures the relationship between the change in level of each of the factors and the change in response.

Factor- A factor is an assigned variable. Quantitative factor has a numerical value (1%,2%), qualitative factors include batch of materials, excipients, treatment, diet, labs, analysts etc. Single factor design fits into one way ANOVA.

Levels- levels of a factor are values or designations assigned to the factor. Descriptions of factor and levels is given in table no. 1.

Effect- Is the change in response by a varying level of a particular factor.

Table 1. Description of factor and level

Factor	Level
concentration	mg, μg
temperature	25º,70º
Drug treatment	Drug, placebo

Design space- Is the established range of process parameters that has been demonstrated to provide QA. Working within the design space is not generally considered as a change of the approved ranges for process parameters and formulation attributes. Movement out of space is considered as a change and would normally initiate a regulatory post approval change process^{1, 2}.

Factorial experimental design:^{3, 4}

The implementing QbD utilizes the design space so that reliable and consistent information is achieved with minimum number of experiments.

Merits of factorial designing:

1. Quality incorporated into product as well as process, is based on scientific understanding.

2. Specifications will be based on performance of the product.

3. Focus on robustness, understanding and controlling.

4. Process is flexible within the design space.

5. Submission of the report will be explained by the product and process knowledge.

Number of variables influences the results of a research product and process development. Variables are called as “factors” in factorial design. Some factors never been considered or it might have discovered during the process. Byrne and Taguchi classified factors that can be important for the outcome of an experiment into controllable (noise)and non noise factors. Noise factors are further described into difficult, impossible and expensive to control. Researchers mainly use controllable factors. Thus random factors and co-variants are seldom used. ANOVA and multiple regression analysis are based on factorial approaches. Softwares are available to support the calculations^{5, 6}.

Factorial design (FD) is also known as experimental designs for the first degree models, are the most common technique. The simplest way to set up a design of experiments (DOE) is to take 2 or more variables (n) and test at different levels. In a full factorial approach all factors are combined with each other on all levels and the number of experiments becomes f ⁿ where f is the factor and n is the level. 3² full factorial design involves nine experiments, 4² involves 16 and 5² involves 25. if the level becomes 3 then the number of experiments becomes 3³, 4³ and 5³. Naturally the number of experiments becomes more and exceeds manageable levels. Therefore the levels considered are usually 2 to minimize the number of experiments. If each factor has the same number of levels, the design is said to be symmetric eg. 2², 3³ etc. If the number of level differs from the factor the design is called asymmetric, eg. 2³, 3² etc. But if it is essential to conduct the design for all required experiments, one can consider fractional factorial design (FFD). Here the experiments are cut short systematically. FFD is a fraction (1/ x ^p) of the complete FD, were p is degree of fractionation. The total number of experiments for FFD is given by f ^n-p. Each experimentation is called as “trial” or “run”. Standard symbols, data interpretation,experimental design representation and interaction are mentioned in table no. 2, 3, figure no. 2 and 3 respectively.

Table 2. Standard symbols for particular ratio of drug: excipients

Formulation	Standard symbols	Effect (%drug release)
Low drug- low excipient	1	10 %
Low drug- high excipient	a	10%
High drug- low excipients	b	20%
High drug- high excipient	ab	30%

Note : low and high value refers to low and high concentration presented for the drug and excipients.

Interaction = [ab-b]- [a-(1)] / 2 = 5%

Table 3.

Experiment	f1	f2	f3	Interpretation
1	-1	-1	-1	Zero level interaction
2	-1	+1	-1	Main factor effect f2
3	+1	-1	-1	Main factor effect f1
4	-1	-1	+1	Main factor effect f3
5	+1	+1	+1	Interaction between f1, f2,f3.

Fig 2: 2² design (4 experiments can be conducted )and 2³ design (8 experiments can be carried out). Low (-1) and high (+1) levels are combined together.

Fig 3: A) no interaction, B) disordinal interaction, C) ordinal interaction

[E – effect, L1 and L2- levels of 1^st and 2^nd factor]

Central composite design (CCD):

Central composit design (CCD) is a special advanced form of full factorial design first described by Box et al. Instead of square and cube, 2² and 2³ are represented by circular or spherical respectively (fig 4). In addition to 2ⁿ full factorial design a centroid experiment (axial points) and a set of experiments (star points) are also involved. To achieve circular or spherical domains, the star points are situated in a definite distance from the centroid along the axis from the centre point.

Fig 4: central composit designs for 2² and 2³

Fractional factorial design is opposite to Taguchi model. To avoid the above problems fractional factorial designs were introduced. Here large multi fractional studies should be divided into blocks. Within each block experiments were undertaken randomly. Blocks must be performed one at a time. Correction in the factorial design can be made between the blocks. Advantage of such study is that first block may reveal all information required. Some free soft ware down loads are also available regarding factorial designing⁷

Demonstration of factorial designing:⁸

Adetogun GE et al. has reported the implementation of factorial designing, in his experiment. To study the type of gum as a binding agent (B), its concentraton (C) and relative density (D) of the tablet on tensile strength (TS), brittle fracture index (BFI), dsintegraton time (DT) and crushing strength-friability/ disintegraton time ration (CSFR/ DT) of paracetamol tablets, experiments were performed in a factorial design, formulations statistics. Here each of high variables were utilized as “high level” ( subscript H)and “low level” ( subscript L). Number of experiments were 2³ ie, 8. Thus the combinations were:

B_LC_LD_L, B_LC_LD_H, B_LC_HD_L, B_LC_HD_H

B_HC_HD_H, B_HC_HD_L, B_HC_LD_H, B_HC_LD_L

B_L : represents formulation with binding agents Delonix regia seed gum + tragacanth or acacia gum + tragacanth.

B_H : represents formulation with binding agents tragacanth + acacia gum or delonix regia seed gum + acacia gum.

C_H and C_L represents high (5% w/w) and low concentration (2% w/w) of gum binding agent respectively.

D_L and D_H represents tablet relative density of 0.80 and 0.90 respectively.

By grouping the results from the combinations into a number of sets, it was possible to assess the effects that each of the three variables (B, C, D) had on the mechanical/ disintegration properties of the tablets and determine whether the variables were interacting independently of each other.

The effects of increasing B, from its low to high level, on the mechanical/ disintegration parameters were found by summing up all “high” levels of B and subtracting the sum of “low” levels of B.

¼ {(B_HC_HD_H + B_HC_HD_L + B_HC_LD_H + B_HC_LD_L) – ( B_LC_LD_L + B_LC_LD_H + B_LD_HD_L + B_LC_HD_H) }

The same procedure was used for C and D. Then the results of combinations n which they appear “high” and “low” levels were summed up and the sum of the combinations was subtracted to obtain the interaction coefficient. Eg. For B and C:

¼ {(B_LC_LD_L + B_LC_LD_H + B_LC_HD_L + B_LC_HD_H) – ( B_HC_HD_H + B_HC_HD_L + B_HD_LD_H + B_HC_LD_L) }

A zero result indicates no interaction, but if the interaction coefficient differs from zero, then the two variables concerned were interacting with each other. The more the coefficient differs from zero, the higher the interaction. The results were subjected to the analysis of variations (ANOVA) at a 5 % probability level.

Demerits of factorial designing:

1. Insignificant variables may not be able to detect on time.

2. Not possible to separate the aliased effects from each other.

3. Later if the result indicates undesired effects and then all the experiments undertaken at that level are of no use.

4. At worse the full experimental plan has to be redesigned and repeated.

5. May not be economic and consumes more time.

ACKNOWLEDGMENT:

The authors are highly indebted to the Principal and Management of Nalanda College of Pharmacy in providing all the library facilities to carry out the reviews.

REFERENCES:

1. Fridrun Podczeck, Aims and objectives of experimental design and optimization in formulation and process development, in: Larry Augsburger L, Stephen Hoag W. Pharmaceutical dosage forms: tablets 3^rd ed. (2), Informa Health Care, New york, 2008.

2. Sanford Bolton, Charles Bon. Pharmaceutical Statistics. Practical and Clinical applications, 4^th ed. (135), Mark Dekker, NY, 2005.

3. Singh B, Ahuja N. Book revew on Pharmaceutcal experimental design, Int J Pharm., 248, 195- 247, 2000.

4. Design Space and PAT- Q8ICH. Draft guidance on pharmaceutical development by Kovalycsik, Wyeth research vaccines RandD. Quality operatons.

5. http://wareseeker.com/free-factorial-design/, as on 24/12/2010.

6. http://www.brothersoft.com/downloads/factorial-design.html, as on 24/12/2010.

7. Krupakar BR. Design of experiments for pharmaceutical formulation development, Pharmainfo.net, 6 (4), 2008.

8. Adetogun GE, Alebiowu G. Evaluation of the qualitative effects of variables on a paracetamol tablet formulation prepared with gum as binding agent, J pharm. Res. 8 (4), 176-180, 2009.

Received on 07.04.2011

Accepted on 30.04.2011

© A&V Publication all right reserved

Research Journal of Pharmaceutical Dosage Forms and Technology. 3(5): Sept.-Oct. 2011, 199-202