The document discusses statistical modeling in the pharmaceutical industry. It notes that statistical modeling is one approach used to address challenges related to cost, time, and quality in drug discovery and development. The goals of statistical models include understanding the mechanisms by which data is generated and extracting information from data. Statistical modeling aims to translate known properties and hypotheses into mathematical representations. This allows for simplified descriptions of experiments and mechanisms. The identification of appropriate models requires thorough investigation. Descriptive models aim to describe data structures while mechanistic models seek to understand underlying phenomena. Statistical modeling has advantages of reducing costs and time while improving success rates.

1. Statistical modeling

2. • The new major challenge that the pharmaceutical industry is facing in
the discovery and development of new drugs is to reduce costs and
time needed from discovery to market, while at the same time raising
standards of quality.
• If the pharmaceutical industry cannot find a solution to reduce both
costs and time , then its whole business model will be jeopardized.
• The market will hardly be able , even in the near future , to afford
excessively expensive drugs, regardless of their quality .

3. • The development of models in the pharmaceutical industry is
certainly one of the significant breakthroughs proposed to face the
challenges of cost , speed , and quality , somewhat imitating what
happens in the aeronautics industry.
• The concept, however , is that of adapting just another new
technology , known as modelling

4. • The purpose of the model is essentially for that of translating the known
properties as well as some new hypotheses into a mathematical
representation.
• In this way, a model is a simplifying representation of the data- generating
mechanism under investigation.
• The identification of an appropriate model is required
• It is not easy and may require thorough investigation.

5. • Model is a simplified description of an experiment or real life mechanism
• Refers to visualization
• Developing mathematical expression
• Modelling is an attempt to explain the output into mathematical
relationship or graphical expression
• Models explain the experiment, results and behaviour
• Models should be developed in preclinical stages

6. • Statistically modeling: IN PHARMACEUTICAL RESEARCH AND
DEVELOPMENT
• What is Statistics?
• Statistics is a scientific study of numerical data based on natural
phenomena.
• It is also the science of collecting, organizing, interpreting and
reporting data.
• A statistical model is a class of mathematical models, which includes
certain assumptions concerning the generation of some sample data
from a large population

7. Pharmaceutical statistics:
• Pharmaceutical statistics is the application of statistics to matters
concerning the pharmaceutical industry.
• This can be from issues of design of experiments, to analysis of drug
trials, to issue of commercialization of a medicine.
• Evaluate the activity of a drug; e.g., effect of caffeine on attention, to
compare the analgesic effect of plant extract and NSAID.

8. • To explore whether the changes produced by the drug are due to the
action of drug or by chance.
• To compare the action of two or more different drugs or different
dosages of the same drug are studied using statistical methods.
• To find an association between disease and risk factors such as
Coronary artery disease and smoking.

9. • Objectives of statistical models:
• Understand the mechanisms from which the data is generated
• To extract the information from data and response values
• To select appropriate parameters (responses/point estimates )for a
given input.
• Improving the models will help understanding the experiment on
successive drugs
• improving the model’s ability will help to represent reality.
• To identify the most likely sub family of models (likely parameters) with
satisfactory confidence regions

10. Advantages of statistical modelling
• to reduce cost and time and improve quality
• Short time of discovery
• Rate of success becomes high
• Disadvantages:
• Modelling is not easy thorough investigation was required
• It requires specific software for analyzing the data and proposing the
decisions

11. • New Technologies Vs Statistical modelling
• Newer Technologies are also dramatically evolving , opening doors to
opportunities never seen before.
• Micro array technologies, virtual models
• The standard way to discover new drugs is essentially by trial and error .
• The “new technologies “ approach has given rise to new hope in that it
has permitted many more attempts per unit time , increasing
proportionally , however , also the number of errors .

12. • Limitations of newer technologies
• Method is expensive
• Success rate is not guranteed
• Require time for understanding and mastering the technology
• Time for development is not shortened
• So, better to go for statistical modeling

13. • Statistical modelling-Analysis
• According to breiman , there are two cultures in the use of statistical modelling to
reach conclusions from data.
• Data modeling culture:
• data are generated by a given stochastic (probability/randomness) data model.
• It predicts the responses for the given input variables
• Algorithmic modeling culture: uses algorithmic models and treats the data
mechanistically as unknown.
• Used to understand the nature of interaction (mechanism) between two types of
variables

14. • Statistics thinks of the data as being generated by a black box into
which a vector of input variables x (independent variable) enter and
out of which a vector of response variables y (dependent variable)
exits.

15. In the pharmaceutical industry, however, in-depth use of models for efficient
optimization and continuous learning is not generally made.
pharmacokinetics/pharmacodynamics (PK/PD), models are built to
characterize the kinetics and action of new compounds or platforms of
compounds, knowledge crucial for designing new experiments and optimizing
drug dosage.
in medicinal chemistry with QSAR-related models. These can all be defined as
mechanistic models, and they are useful. But in these models, the stochastic
noise inherent in the data, the variability that makes biology so much more
different from the physical sciences, is not as a general rule appropriately
taken into account

16. • The purpose of the model is essentially for that of translating the
known properties about the black box as well as some new
hypotheses into a mathematical representation.
• In this way , a model is a simplifying representation of the data –
generating mechanism under investigation.
• The identification of an appropriate model is often not easy and may
require thorough investigation.

17. • Two of the main goals of performing statistical investigations are to be
able to predict,
• what the responses are going to be future input variables
• To Extract some information about how nature is associating the
response variables to the input variables.
• A third possible goal might be
• To understand the foundations of the mechanisms from which the
data are generated or going to be generated.

18. • Descriptive VS Mechanical modeling
• If the purpose is just to provide a reasonable description of the data in
some appropriate way without any attempt at understanding the
underlying phenomenon, that is, the data-generating mechanism, then the
family of models is selected based on its adequacy to represent the data
structure.
• The net result in this case is only a descriptive model of the phenomenon.

19. • These models are very useful for discriminating between alternative
hypotheses but are totally useless for capturing the fundamental
characteristics of a mechanism.
• In this instance, the order of the model is chosen based on its
competence to describe the data arrangement.
• This type of model is very useful for discriminating between
alternating hypothesis but are useless for capturing the fundamental
characteristics of a mechanism.

20. • Mechanistic modeling:
• Whenever the interest lies in the understanding of the mechanisms of
action, it is critical to be able to count on a strong collaboration
between scientists, specialists in the field, and statisticians or
mathematicians.
• The former must provide updated, rich, and reliable information
about the problem.
• Whereas the latter are trained for translating scientific information in
mathematical models.

23. • Purpose of the module :
• To translate the known properties about as well as some new
hypothesis into a mathematical representation.
• The family of models is selected depends on the main purpose of the
exercise.
• If the purpose is just to provide a reasonable description of the data
without any attempt at understanding the underlying phenomenon,
that is, the data-generating mechanism.
• Then the family of models is selected based on its adequacy to
represent the data structure.

24. • Animal tumour: growth data are used for the representation of the
different concepts encountered during the development of a model
and its after-identification use.
• The data represent the tumor growth in rats over a period of 80 days.
• We are interested in modeling the growth of experimental tumors
subcutaneously implanted in rats to be able to differentiate between
treatment regimens

25. • Two groups of rats have received different treatments, placebo and a
new drug at a fixed dose.
• So in addition to the construction of an appropriate model for
representing the tumor growth, there is an interest in the statistical
significance of the effect of treatment .
• The raw data for one subject who received placebo are represented
as open circles. For the considered subject, the tumor volume grows
from nearly 0 to about 3000 cubic millimeter.

26. • Example: A first evaluation of the data can be done by running non-
parametric statistical estimation techniques like, for example, the
Nadaraya–Watson kernel regression estimate.
• These techniques have the advantage of being relatively cost-free in
terms of assumptions, but they do not provide any possibility of
interpreting the outcome and are not at all reliable when
extrapolating.
• The fact that these techniques do not require a lot of assumptions
makes them relatively close to what algorithm-oriented people try to
do.

27. • The special characteristics of the growth curves are that the exhibited
growth profile generally is a nonlinear function of time with an
asymptote;
• That random variability associated to the data is likely to increase
with size, so that the dispersion is not constant;
• And finally, that successive responses are measured on the same
subject so that they will generally not be independent .
• Note that different individuals may have different tumor growth rates,
either inherently or because of environmental effects or treatment.

29. • Example 2: The growth rate of a living organism or tissue can often be
characterized by two competing processes.
• The net increase is then given by the difference between anabolism
and catabolism, between the synthesis of new body matter and its
loss.
• Catabolism is often assumed to be proportional to the quantity
chosen to characterize the size of the living being, namely, weight or
volume, where as anabolism is assumed to have an allometric
relationship to the same quantity.