A brief introduction to Advanced Statistical Manual for Ayurveda Research

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Balance
Calmness
Serenity
Introducing
Advanced Statistical Manual
for Ayurveda Research
Kadiroo Jayaraman
Praveen Venugopal
AyurData

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The basic manual
covered the syllabus
specified for M.D.
students on Medical
Statistics, by the Central
Council of Indian
Medicine.
Earlier Release

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In the advanced manual, we
have covered more
advanced statistical
applications including that in
data science.
The mode of presentation is
that the concept is
introduced first, followed by
illustration and the use in a
real context.
Some mathematics will be
involved but well explained
in the text.
Current Release

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TOPICS COVERED
1.Analysis of Repeated Measures
2.Multiple Linear Regression
3.Superiority, Bioequivalence and Non-inferiority trials
4.Logistic Regression
5.Decision Trees
6.Random Forest
7.Support Vector Machines
8.Naïve Bayes Classifier
9.Neural Networks
10.K-Nearest Neighbour Technique
11.Principal Component Analysis
12.Cluster Analysis
13.Stratified Multistage Sampling
14.Analysis of Time Series Data
15.Analysis of Time-to-event Data

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Logistic Regression
Logistic model (or logit model) is used to model the probability of events
realized in two classes such as alive/dead or healthy/sick etc. The
dependent variable in this case would take values of 1 or 0. The
theoretical form of the model is,
Logistic models are especially suited for case-control studies and are
useful in understanding the predisposing factors leading to a diseased
condition.
The fitting of the logistic model including the derivation of ROC curve and
optimal cut-off points and measuring the goodness of fit are illustrated
using real data from Ayurveda.

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Decision Trees
Decision tree is a type of supervised learning algorithm (having a pre-
defined target variable) that is mostly used in classification problems.
In this technique, we split the population or sample into two or more
homogeneous sets (or sub-populations) based on the most significant
splitter/differentiator in input variables.
One popular measure used for spitting is the information gain. This is
equivalent to selecting a particular node with maximum reduction in
entropy as measured by Shannon’s index (H).
where s is the number of groups at a node and 𝑝𝑖 indicate the proportion
of individuals in the ith group.

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Decision Trees
Decision tree for exposure factors of Coronary Artery Disease

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Random Forest
Random forest is an ensemble technique in which the idea is to generate
multiple models on a training dataset and then simply combine (average)
their output rules or their hypotheses to generate a stronger model which
performs very well.
For instance, in the case of fitting a decision tree, we consider fitting
several decision trees and taking the average decision tree. It consists of a
resampling plan that considers not only subsamples but also a subset of
features in each sample generated.
This way, it gives out a model with considerably better efficiency in
prediction or classification.
The use of random forest is illustrated in the context of some real data in
Ayurveda.

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Support Vector Machines
Given a set of training examples, each marked as belonging to one or the
other of two categories, a support vector machine (SVM) training algorithm
builds a model that assigns new examples to one category or the other. In
theory, SVM is a discriminative classifier formally defined by a separating
hyperplane.
It is useful for even for non-linear separation of the data points.

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Naïve Bayes Classifier
Naive Bayes is a common technique used in the field of medical science
and is especially used for cancer detection.
The foundation of naive Bayes algorithm is the Baye’s theorem which
states that
P(B/A) = P(B) * P(A/B) / P(A)
For the case multiple variables, we evaluate the posterior probability as,
𝑃(𝑌/𝑋1, … , 𝑋 𝑛)𝛼 𝑃(𝑌) ς𝑖=1
𝑛
𝑃(𝑋𝑖/𝑌)
For classification, we may use the following equation:
𝑌 = 𝑎𝑟𝑔𝑢𝑚𝑎𝑥 𝑦 𝑃(𝑌) ෑ
𝑖=1
𝑛
𝑃(𝑋𝑖/𝑌)

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Neural Networks
A neural network is a series of algorithms that endeavours to recognize
underlying relationships in a set of data through a process that mimics the
way the human brain operates.
A neural network is akin to the human brain’s neural network. The basic
computational unit of the brain is a neuron. A ‘neuron’ in a neural network
is a mathematical function that collects and classifies information
according to a specific architecture.

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Neural Networks
A neural network could involve both forward and backward propagation.
After a series of iterations, the algorithm arrives at a decision on
identification or classification.
The use of neural networks in classification is illustrated using example
from Ayurveda.

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K-Nearest Neighbour Technique (K-NN)
K-NN is a simple algorithm that stores all available cases and classifies
new cases based on a similarity measure (e.g., distance functions). K-NN
can be used for both classification and predictive problems.
A case is classified by a majority vote of its neighbours meaning the case
being assigned to the most common class amongst its K nearest
neighbours measured by a distance function. Some of the distance
measures applicable for continuous variables are the following.

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