CLINICAL PHARMACOLOGY AND PHARMACODYNAMICS
Clinical pharmacology:
Definition:
Clinical pharmacology is the science of drugs and their clinical
use. It has a broad scope, in the discovery of new target
molecules, to the effects of drug usage in whole populations.
The main objective is to promote the safety of prescription,
maximize the drug effects and minimize the side effects.
It is important that there be association with pharmacists
skilled in areas of drug information, medication safety and other
aspects of pharmacy practice related to clinical pharmacology.
Clinical pharmacology has a wide variety of branches which
includes
a. Pharmacodynamics.
b. Pharmacokinetics.
c. Drug development.
d. Drug interactions.
e. Adverse drug reactions.
f. Toxicology.
A. Pharmacodynamics:
Definition:
The study of how a drug acts on a living organism, including the
pharmacologic response and the duration and magnitude of response
observed relative to the concentration of the drug at an active
site in the organism.
These branches include the clinical studies. These clinical
studies can be studied under various regulatory guidelines which
include,
CLINICAL STUDY DESIGN DOCUMENTATION, PRESENTATION AND
INTERPRETATION AS PER REGULATORY GUIDELINES OF EUROPEAN COMMUNITY
:
Pharmaceutical companies spend billions of dollars every year on
carrying out clinical study by conducting clinical studies for
their potential products. These studies are funded by charities,
government research councils and other bodies. A set of official
guidelines has been issued in Europe that cover many aspects of
clinical trials. Any incorrect procedures lead to refusal to grant
the relevant marketing approval.
a. The most important of these guidelines is following of
Guidance on Good Clinical Practice (GCP).
b. It also sets out the basic requirements on
1. The protection of trial subjects.
2. The design of procedures to be used in the trial.
3. The recording and reporting of results.
4. The documentation that is required, and the monitoring and
audit of the trial to ensure that these requirements are being
met.
Since 1990, there has also been an international process, known
as the International Conference on Harmonization of Technical
Requirements for Registration of Pharmaceuticals for Human Use
(ICH), which involves representatives of the regulatory authorities
and industry associations of Europe, Japan and the US.
The objective of the ICH is to harmonize pharmaceutical
regulatory requirements on an
International basis to minimize the possibility that tests and
trials on new medicinal products have to be repeated for the
purposes of obtaining regulatory approval in different
Countries.
In broad terms, the European law states that, where an applicant
wishes to obtain marketing approval for a new medicinal product the
pharmaceutical companies must follow the follow the key points they
include,
All clinical trials should be carried out in accordance with the
Declaration of Helsinki (world medical association) the freely
given informed consent of each trial subject should be obtained and
documented.
The clinical trials should not begin before the authorization of
ethical committee.
All aspects of conduct of the trial should be documented in
pre-established, written procedures (e.g. written protocols) and
documentation and records of the trial should be archived for
specified minimum periods of time.
The clinical study design, should include the following
points:
A description of the type/design of trial to be conducted(e.g.
double-blind, placebo-controlled, parallel design) and a schematic
diagram of trial design, procedures and stages.
A description of the measures taken to minimize/avoid bias,
including: Randomization.
A description of the trial treatment(s) and the dosage and
dosage regimen of the investigational product(s). Also include a
description of the dosage form, packaging, and labeling of the
investigational product(s).
The expected duration of subject participation, and a
description of the sequence and duration of all trial periods,
including follow-up, if any.
A description of the "stopping rules" or "discontinuation
criteria" for individual subjects, parts of trial and entire
trial.
All records, in any form (including, but not limited to,
written, electronic, magnetic, and optical records, and scans,
x-rays, and electrocardiograms) that describe or record the
methods, conduct, and/or results of a trial, the factors affecting
a trial, and the actions taken.
The act by a regulatory authority (ies) of conducting an
official review of documents, facilities, records, and any other
resources that are deemed by the authority(ies) to be related to
the clinical trial should be deemed appropriate by the regulatory
authority(ies).
CLINICAL STUDY DESIGN DOCUMENTATION, PRESENTATION AND
INTERPRETATION AS PER REGULATORY GUIDELINES OF UNITED STATES
AUTHORITIES:
The U.S. Food and Drug Administration is a scientific,
regulatory, and public health agency that oversees items accounting
for 25 cents of every dollar spent by consumers.
Clinical Trial Design: Authorities conduct CLINICAL STUDY DESIGN
based on scientifically designed protocols, which balance potential
risk to the research participant with the possible benefit to the
participant and to society.
1. The study design usually performed in normal health
subjects.
2. For the study of the drug analytical methods should be
validated for accuracy, precision, and sensitivity.
3. Different methods yield different results so a standard
method should be employed in the total course of study.
4. The design should be authorized by the FDA authorities for
further release in to the market.
Clinical interpretation is important in evaluation of the
results of the clinical study.
A small difference between drug product and standard,
significantly produce a very big difference in therapeutic response
during the clinical interpretation of the data.
Presentation of data:
1. According to US FDA data should be presented in graphical
form and talker forms. ANOVA is needed to determine statistical
significance between the standard and the drug designed in the
pharmacological parameters.
2. Enough care should be taken for the storage of data until it
is presented
3. The guidelines taken for the study and the approvals given by
the FDA agencies should also be included with the presentation of
the final data.
4. Further the drug is finally released in to the market for the
usage if the FDA satisfies with the presented data.
CLINICAL STUDY DESIGN DOCUMENTATION, PRESENTATION AND
INTERPRETATION OF REGULATORY GUIDELINES IN INDIA:
India has become hub for clinical trials among South Asian
countries due to abundant availability of large and diverse
patient's pool, faster enrollment of patients, availability of
trained investigators, plenty of super specialty hospitals with
excellent infrastructure and increasingly accommodating regulatory
environment.
It is estimated that nearly 20% of all global clinical trials
will be conducted in India by 2010.
In volume terms, it is the worlds fourth largest market in unit
sales, but ranks 13th in value terms with an annual revenue of
approximately US$ 5 billion.
The world has identified India as an emerging hub for
collaborative and outsourced research and development (R&D) and
went on to observe that Indian pharma companies had topped drug
filings with the US FDA for 2003, with a total of 126 DMFs(DRUG
FILINGS), accounting for 20% of all drugs coming into the US
market, higher than Spain, Italy, Israel, and China.
For a drug to do the clinical studies, it should be registered
in Clinical Trials Registry-India (CTRI).
In order to make clinical data available on online clinical
registry has been initiated by Indian Council of Medical Research.
(ICMR).
The 2 goals of this ICMR is the transparency and accountability
of clinical research.
In India study design was approved by Indian council of medical
research (ICMR); and ethical guidelines was provided by the
institutional ethics committee (IECs).
This study design should be according to the regulatory
guidelines framed by the ICMR and drug controller of India.
The study design should be presented to the drug controller of
India for the approval of the investigational new drug.
Interpretation of the clinical studies should be done and it
should be according to the guidelines mentioned by ICMR
committee.
The interpretation should provide the adverse effects, and any
toxic reactions that are seen with the drugs that are
developed.
Drug registration is done only after the submission of the
interpretation data ,and the drug was finally released in to the
market.
ICH-GCP compliance for the study design:
Drugs Controller General of India (DCI) has the prominent role
in overseeing clinical trial in India along with Ethics
committee.
The DCGIs office depends on external experts and other
government agencies for advice.
Additional permissions are required for the export of blood
samples to foreign central laboratories.
The Indian Council of Medical Research (ICMR) guidelines for
clinical trials insist on the setting up of ethics committees at
the institutional levels.
The IEC (Indian Ethical Committee) responsibility is to
scrutinize and approve the clinical trial before the study begins
and also to conduct periodic reviews of the progress of the
trial.
The implementation of the GATT(General Agreement on Tariff and
Trade) has opened a new opportunities for India to concentrate on
the clinical trial market.
In January 2005, India adopted a new rule that will allow
pharmaceutical companies to begin phase II and Phase III trials
concurrently with trials of the same phase conducted abroad,
thereby reducing clinical development time.
With the latest amendment (20th January 2005) to the Schedule Y
of Drugs and Cosmetic Act 1945, the reporting of adverse events
from clinical trials has become clearer and unambiguous.
Good clinical practice represents the requirements for
protection of participantsin clinical trials.
It also provides the detailed requirements for investigators and
sponsors with regard to planning execution, documentation,
analysis, and reporting of studies.
The above steps are taken in order to ensure the quality and
logical consistency of data findings and conclusions.
Purpose of ICH (international conference on harmonization) : to
ensure the safety and efficacy, and most efficient, and cost
effective drugs to be produced in India.
Principles of ICH:
According to ICH clinical trials should be conducted ethically
with declaration of ICMR regulatory guidelines.
The main principles include:
1. Rights, safety, & well being of subjects are
important.
2. Study must be scientifically designed.
3. Investigators must be qualified.
4. Records must be maintained for accurate reporting,
interpretation, and verification.
5. Clinical trials must meet the Good Manufacturing
Practices
CLINICAL TRIALS
Clinical Research Industry has billions of dollars every year on
carrying out clinical trials for their potential products, The main
survival point of the pharmaceutical industry is innovation and for
introducing grown around the world at an unbelievable rate in the
past few years. Now a days Pharmaceutical companies spend new drugs
in the market, the companies have to conduct clinical trials as per
ICH GCP guidelines as well as guidelines of the country where trial
is planned.
Definition: As per Drugs and Cosmetics Rules, 1945,"Clinical
trial" means a systematic study of new drug(s) in human subject(s)
to generate data for discovering and / or verifying the clinical,
pharmacological (including pharmacodynamic and pharmacokinetic) and
/or adverse effects with the objective of determining safety and /
or efficacy of the new drug."
Clinical trials are designed to help us find out how to give a
new treatment safely and effectively to people.
A clinical trial is a tool for testing a drug, device, or
technique.
Clinical trials are necessary to evaluate the medicines before
they enter in to market.
These clinical trial studies were extensively done in animals
and in humans to find out the efficacy and safety of the drug
product which is to be marketed.
The following phases are involved in the clinical trials which
includes:
1. Phase -I.
2. Phase -II.
3. Phase -III.
4. Phase -IV.
Phase -I: clinical trials test a new biomedical intervention in
a small group of people (e.g., 20-100) for the first time to
evaluate safety (e.g., to determine a safe dosage range and to
identify side effects).
These clinical trials are developed after the investigational
new drug application is submitted.
Main purpose: The main purpose of this phase is to determine
drug toxicity profile and to assess tolerability.
In most of the cases children and pregnant women and serious
primary diseases(eg: cardiac, hepatic, renal, hematological
disorders) are excluded in this phase.
In general patients receiving contaminant drug therapy should be
excluded (eg: malignancy therapy).
Individuals with mild but stable illness may also be included in
this phase.
In general out patients are not be utilized as initial
recipients of investigational new drug in this phase.
Hospital employees and volunteers may be in some cases may be
utilized as intial recipients in this phase, since they can be
under the supervision of clinical investigator.
Generally healthy human volunteers are selected for this phase
studies.
The initial dose of drug is usually low i,e one tenth of the
highest no-effect dose observed during the animal studies.
The phase-I clinical trials are designed to determine the:
1. Human pharmacology of the drug.
2. Structural activity relationship.
3. Side effects associated with increasing doses.
Qualification & investigators:
Phase -1 clinical studies are performed by investigators skilled
in initial evaluation of a variety of compounds for safety and
pharmacological effect.
Where the patients with a specific disease are being studied the
investigator should be expert in treating that disease.
Procedure for carrying out of phase-I clinical trials:
The procedure involved in this phase is physical examination
followed by laboratory screening tests should be performed to
screen out individual with medical abnormalities. These tests
include
1. Urine analysis.
2. Platelet estimation.
3. Bun (serum creatinine).
4. Liver functional studies.
5. Post prandial blood sugar
6. E.C.G and other drug related tests.
Prior to administration of new drugs the subjects or patients
shall not been allowed to take the OTC drugs.
Single dose studies of phase-I:
a. The phase -I studies are desirable to begin with small group
eg: 5 on a drug or 5 on a placebo for a period of 5-7 days to
observe the adverse effects and will move to the larger groups.
b. The subjects should be seen at least once daily.
c. Practical examination will be performed during and post
therapy and all laboratory examinations should be repeated at least
once in week.
d. The duration of drug study will be dependent up on the nature
of the drug.
e. Blood levels should be tested with single and multiple
doses.
f. The subjects ability to tolerate the drug & any un
pleasant effects of drug are observed and recorded.
g. Capsules without any excipients will be used for
Investigational drug studies for the case of orally administration
of drugs.
h. Phase -1 study are useful in selecting different analogues of
the lead compound.
If the studies demonstrate sufficient merit and if the order of
drug toxicity is low, phase-2, a study begins.
Phase -II studies:
Subjects patients selected for early phase 2 studies should
ordinarily be free from hematologic hepatic, renal, and cardiac and
other serious diseases.
Carried out relatively in small group of targeted patients.
Phase -2 studies involve controlled clinical studies to evaluate
the effectiveness of drug ,this phase involves the study of side
effects and toxicity symptoms that were not shown during animal
clinical trials.
Qualifications of investigators:
Only clinical experts in the disease being treated are used as
investigators in phase -2.
Procedure:
Dose response studies are performed to determine the optimum
dosage regimen for treating the disease.
During the phase, additional data are collected on the drugs
pharmacokinetic studies were undertaken to determine dose response
and dosage ranging called phase -2a studies.
Each patient is monitored for the appearance for the drug effect
while the dose is carefully increased to determine the minimum
effective dose.
Then the dose is extended beyond the minimally effective dose to
the level at which a patient reveals extremely undesirable toxic or
adverse effect.
The greater the range between the dose of drug determine
minimally effective and that which causes severe side effects the
greater is the drugs safe margin, called as phase-2b studies.
If the clinical results of phase -2 indicate the safe margin for
the new drugs, these studies can be ended with the approval of
FDA.
Patients should ordinarily be seen by the investigators at least
for 2-4 weeks.
Specialized safety and pharmacological lab tests are
performed.
When the investigational drug is altered significantly in
months, to accommodate blood analysis studies should be
performed.
Routine safety tests to be done at frequent intervals, if these
tests are satisfactory then phase -3 studies were carried out.
Phase -III studies:
These are better known trials of safety and efficacy.
Include several 100-1000 patients in controlled and uncontrolled
trials.
Objective:
The objective is to determine the usefulness of drug in an
expanded patient base.
This phase includes further toxicological studies that occurring
the patients during the course of study.
Procedure:
Large scale, multi center clinical studies are performed with
the final dosage from developed in phase-2.
Many additional clinicians having patients with the condition
for drugs intended use or recruited to participate in this
trial.
Several dosage strength of proposed drug may be evaluated during
this stage using formulations intended to be proposed in new drug
application and in marketing.
Sufficient information on drugs safety & effectiveness is
expected to be gathered during phase -3 to evaluate the overall
benefit risk relationship of the drug and file a complete
information of the drug.
These studies are done to determine safety and efficacy of the
drug product in large population with disease or condition for
which the drug was developed.
Finally these studies concentrate on the new toxic effects that
occurred in large group of population which were not evident in
previous phases of clinical studies.
After the phase -3 studies the New Drug Application was
submitted.
Submission of New Drug Application (NDA):
An NDA is submitted to FDA for review and approval after
completion of clinical trials that show to the satisfaction of
medical community that the drug product is effective in all
parameters is reasonably safe as demonstrated by animal and human
studies.
For example : of 20 drugs entering clinical testing 13-14 will
successfully complete phase-1 trials and go on phase -2, about 9
will complete phase -2, and go to phase -3,and only one or two will
clear phase -3 and on average per year only about 20 drugs will
ultimately be approved for marketing
S.NO
NUMBER OF PATIENTS
LENGTH
PURPOSE
% OF DRUG SUCESSFULLY COMPLEETING
Phase -1
20-100
Several months
Mainly safety
67
Phase -2
Up to 100
Several months to 2 years
Some term safety & mainly efficacy
45
Phase -3
100-1000
1-4 years
Safety effectiveness and dosage
5-10
Phase IV:
After the NDA is submitted and before approval to market the
product is obtained approval from FDA, manufacturing scale up
activities occur.
Scale up is the increase in the batch size from the clinical
batch, the submission batch or both, up to the full scale
production batch size using finished market production.
The drug formulation may be modified slightly as a result of
data obtained during the manufacture scale up and validation
process.
US-FDA approved drugs during recent years;
YEAR
TOTAL DRUS APPROVED
2001
24
2002
17
2003
21
2004
31
2005
03
2006
10
2007
19
2008
12
E.g. Some of the US-FDA drugs approved drugs for HIV and its
complications;
APPROVED DRUG
TREATMENT FOR CONDITION
Alitertinoin
Cutaneous lesions in aids patients related to kaposis
sarcoma
Atazanavir
HIV-1
Dronabinol
For stimulation of apetite and to prevent loss of weight in AIDS
patients
Immunoglobulins
Infection prophylaxis in pediatric patients effected with
HIV.
Interferon ALFA-2a
AIDS related kaposis sarcoma.
Interferon ALFA-2a
AIDS related kaposis sarcoma.
Paclitaxel
AIDS related kaposis sarcoma.
After the FDA grants market approval of the drug, the product
development may continue.
The drug product may be improved as a result of market demands,
supply, and regulatory factors.
Some time the approved drugs are banned due to the unwanted side
effects.
e.g. Analgin (for blood disorder), Rofecoxib (cardio vascular
disease).
In such banned cases these use should be discouraged.
DRUG
INDICATION
CAUSE FOR BAN
Analgin
Analgesic
Bone marrow depression
Cisapride
Acidity, constipation ,GERD
Irregular heart beats
Furazolidine
Anti-diarrhoeal
Carcinogenic
Nimesulide
Pain killer, fever
Hepatotoxic
Piperazine
Anthelmenthic
Causes nerve damage
Nitro furantoin
Anti-bacterial cream
carcinogenic
DESIGN DOCUMENTATION OF CLINICAL DATA:
Factors such as age, sex disease state, food habits, Time of
sample to be administered are to be considered in study design
documentation.
The design includes:
1. Experimental design.
2. Study population.
3. Sample size and dropouts.
1. EXPERIMENTAL DESIGN:
This design includes the following sub divisions;
a. Replicated cross over design.
b. Non-replicated design.
A. Replicated cross over design.
This design is recommended when an individual bioequivalence is
used to allow the estimation of in various measurements following
the four period, two-sequence and two-formulation method.
For this design lots of T & R (test and reference),
formulations should be used for repeated administrations which
should be separated by proper wash out period.
The Three period design can be tabulated as follows
PERIOD
1
2
3
SEQUENCE
1
T
R
T
2
R
T
R
A greater number of subjects are tested in this type of design
to obtain the efficacy of the new drug.
B. Non-replicated design:
A conventional study design such as the standard two formulation
, two-period, two-sequence cross over design used for
bio-equivalence comparision.
Here an average number of populations are used.
2. STUDY POPULATION: Unless otherwise indicated by a specific
guidance recruited for in-vivo bio equivalence studies should be 18
years, or elder and capable of giving informed consent.
An attempt should be made to enter an heterogeneous a study
population as possible, with a reasonable balance of males and
females, young and elderly and subjects of different racial
groups.
Restrictions to entry in to studies should be based solely on
safety considerations.
In some studies, it may be useful to recruit patients for whom
the drug product is intended.
In this situation sponsors/applicants should attempt to enter
the patients whose disease process is stable for the duration of
the study.
IND (investigational new drug) may be required for some studies
to ensure safety of patients.
3. SAMPLE SIZE AND DROP-OUTS:
A minimum number of 12 subjects should be included in any
study.
Number of subjects for this studies are based on either the
population or individual bio-equivalence approach should be
estimated by stimulation, because analytical methods/approaches for
estimation are not available
Sponsors should provide a sufficient number of subjects in the
study, to allow for drop-outs, because replacement of subjects
during the study could help in the statistical model and
analysis.
Sponsors who wish to replace the drop-outs during the study
should be done according to the protocol.
Additional subjects will not be allowed to enter in to the
study, as it will affect the analysis of the total study
design.
PRESENTATION OF CLINICAL DATA:
The obtained data from the clinical study can be presented in
the following manner;
The drug concentration in biological fluid determined at each
sampling time should be furnished on the original scales for
participating in the study.
The derived pharmacokinetic measures should also be furnished on
the original scale.
The mean, standard deviation, and co-efficient of variance for
each variable should be calculated and tabulated in the final
report
In addition to the arithmetic mean and standard deviation (or
co-efficient of variance) for TEST AND REFERENCE products; and
geometric means should also be included.
The measures taken for the test subjects should be displayed in
parallel with the data obtained in their study.
The ratio of individual geometric mean of the test product to
the individual geometric mean of reference product should be
tabulated side by side for each subject.
The presentation of the clinical data should be done according
to the regulatory agencies concerned
INTERPREATION OF CLINICAL DATA:
OBJECTIVES:
To explain differences in approaches to safety data and efficacy
data.
To demonstrate that adequate attention needs to be given to the
assessment, analysis, and reporting of adverse events to permit
valid assessment of potential risks of intervention.
To highlight the distinctions between rare, serious adverse
events and common, non-serious adverse events
To define terms commonly used in the description of adverse
events.
To explain methods by which causality for adverse events can be
assessed.
The interpreted data should be stored in online services, and it
should be available during audits that were conducted by the
regulatory agencies.
The interpretation of clinical data must also includes the total
study details that was conducted, which includes the adverse
reaction of drugs, and toxicological studies e.tc.
STATISTICAL ANALYSIS OF CLINICAL DATA
The experimental results of clinical studies can be analyzed in
many ways; one of the simplest method of analysis of clinical data
is by statistical analysis method.
STATISTICAL ANALYSIS:
Statistical Analyses to be used must be clearly identified and
should form basis of the statistical model for the clinical
Study.
Before 1970s clinical data was determined based only on the
values of cmax values for the generic product; which should be
within + or 20% of those reference products.
During recent years FDA requires the confidence limits to the
mean data , using an analysis known as the two/one sided test
procedure.
The test formulation was considered to be bio equivalent to the
reference only if
AUCtest Cmax of test
By this procedure if the test and the reference products are not
bio-equivalent they will differ by 20-25% in both AUC and in Cmax
results.
The generic manufacturer should carry out the tests at least to
90% confidence for providing the values regarding the mean
responses of the products that should be within limits of
0.8-1.5.
Since these tests are carried out at 0.05 level of significance
these can be reliable.
In some cases the value or range (20-25%) can be given up to
30%. E.g. Anti-psychotics.
Any subsequent deviation(s) should be described and justified in
the Final Report.
Results of the statistical analyses should be presented in a
manner that is likely to facilitate the interpretation of their
clinical data.
FACTORIAL DESIGNS:
Factorial designs are used in experiments where the effects of
different factors or conditions on experimental results are to be
elucidated.
Some practical examples where factorial designs are used are;
experiments to determine the effect of pressure and lubricant on
the hardness of table formulation, to determine the effect of
disintegrant and lubricant concentration on tablet dissolution.
Factorial designs are the choice for the simultaneous
determination of several factors and their interactions.
Definitions:
1.FACTOR:
A factor is an assigned variable such as concentration,
temperature, lubricating agent, drug treatment or diet.
The choice of factors to be included in experiment depends up on
experimental objectives.
A factor may be qualitative or quantitative.
Quantitative factor has numerical value assigned to it, e.g the
factor concentration may be given the values 1%,2%,3% and examples
of qualitative factors are treatment, diet, batches of materials,
tablet diluents.
Qualitative factors are assigned names rather than numbers.
LEVELS:
The levels of a factor are the values or designations assigned
to the factor.
Examples of levels 300 and 500 for the factor temperature, 0.1
molar and 0.3 molar for the factor concentration, drug and placebo
for the factor drug treatment.
The trials that comprise factorial experiments consists of all
combinations of all levels of all factors. As an example two factor
experiment would be appropriate for the investigation of effects of
drug concentration on the tablet. If both factors were at two
levels four runs would be required as follows:
SYMBOL
FORMULATION
1
Low drug and low lubricant concentration
a
Low drug and high lubricant concentration
b
high drug and low lubricant concentration
ab
high drug and high lubricant concentration
Here low and high refers to the factor concentration
Advantages of factorial designs:
In the absence of interaction, factorial designs have maximum
efficacy in estimating the drug effects.
If interaction exists factorial designs are necessary to reveal
and identify the interactions.
Since factor effects are measured over varying levels of other
factors, conclusions apply to a wide range of conditions.
Maximum use is made of the data since all main effects and
interactions are calculated from all of the data.
Factorial designs are orthogonal, all estimated effects and
interactions are independent of effects of others.
For example the result obtained is only due to main effect of
interest and is not influenced by any other factors.
A simple factorial design helps in revealing the difference in
action of drugs which are tested in different locations. For e.g.
if the tests performed on the patients of Newyork and the patients
of los angels give different results, factorial design will reveal
the causes for the differences such as climatic conditions, body
nature e.t.c.
Thus the factorial designs are useful in the estimation of
different factors or conditions on experiment result.
and
< 1.2
0.8