Part 4 of the Advanced Statistical Manual for Ayurveda Research

1. CONFIDENTIAL © 2019 AyurData
Balance
Calmness
Serenity
Introducing
Advanced Statistical Manual
for Ayurveda Research
Kadiroo Jayaraman
Praveen Venugopal
AyurData

2. © 2019 AyurData /CONFIDENTIAL 2
The basic manual
covered the syllabus
specified for M.D.
students on Medical
Statistics, by the Central
Council of Indian
Medicine.
Earlier Release

3. © 2019 AyurData /CONFIDENTIAL 3
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

4. © 2019 AyurData /CONFIDENTIAL 4
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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Stratified Multistage Sampling
This is one of the most popular sampling schemes in large scale surveys.
In Ayurveda, this sampling design can be used effectively in prevalence
studies and other types status surveys.
The basic idea is to group the population into homogeneous units based
on geographical proximity or based on other characteristics and then
implement a multistage sampling within each stratum.
A two stage sampling will take a sample of larger clusters of sampling
units (primary stage units) and then get a subsample of smaller cluster of
units (second stage units) with each selected first stage units.
Stratified subsampling can provide greater precision than a simple random
sample of the same size. Multistage sampling works the other way that
variance gets inflated by subsampling but saves time and effort.

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Analysis of Time Series Data
A time series is a sequence of observations recorded at a succession of time
intervals. It could be an output from an ECG or EEG, serial recording of pulse rate or
recordings of gait or tremor through digital devises from patients suffering from
Parkinson’s disease.
The peculiarity with time series data is that of correlation between successive
measurements (autocorrelation) which calls for special methods of analysis.
Quite often, the object of interest is to recognize the pattern of movements or
fluctuations over time and compare such patterns across different experimental
settings.
Methods for time series analysis may be divided into two classes: time-
domain methods and frequency-domain methods.
Time-domain methods splits the series into trend, cyclical, seasonal and random
components. Frequency-domain methods identifies mainly cyclical patterns through
spectral analysis, after making the series stationary.

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Analysis of Time Series Data
The power spectrum obtained through spectral analysis of heart rate shows
concentration at a frequency of about 0.015 Hz equivalent to a cycle duration of
64 seconds. This pattern is commonly observed in the context of congestive heart
failure, where circulatory delays interfere with regulation of carbon dioxide and
oxygen in the blood, leading to slow oscillations of heart rate.

8. © 2019 AyurData /CONFIDENTIAL 8
Analysis of Time-to-event Data
Time-to-event (TTE) data is unique because the outcome of interest is not only
whether or not an event occurred, but also ‘when’ that event occurred such as in
survival studies.
The major objects of interest are:
• S(t) = 1 – F(t): The survival function and the cumulative probability density
function.
• h(t)=f(t)/S(t): The instantaneous hazard equals the unconditional probability of
experiencing the event at time t, scaled by the fraction alive at time t.
• H(t) = -log[S(t)] The cumulative hazard function equals the negative log of the
survival function.
• S(t) = e –H(t) The survival function equals the exponentiated negative cumulative
hazard function.
One challenge specific to survival analysis is that only some individuals will have
experienced the event by the end of the study, and therefore survival times will be
unknown for a subset of the study group.
One of

9. © 2019 AyurData /CONFIDENTIAL 9
Analysis of Time-to-event Data
Special estimation methods and models are available to deal with such data.
Kaplan-Meier Estimator
Cox proportional hazards model
Accelerated Failure Time (AFT) models
The advanced manual discusses all the above methods
Survival curves for the two treatment groups

10. © 2019 AyurData /CONFIDENTIAL 10
Recommendations
In order to bring Ayurveda research in line with the mainstream scientific
research, there is a need to incorporate modern methods in research.
Ours was a humble attempt in this regard to bring to light some of the
more popular analytical methods in the Ayurveda context.
Our recommendation is to understand and utilize these techniques in your
research activities and bring Ayurveda to the forefront.
We are willing to conduct a training workshop on these methods for the
benefit of the researchers in Ayurveda.
Kindle edition of the book is available in amazon (link available in the
AyurData Facebook page):
https://www.facebook.com/pg/AyurData/posts/?ref=page_internal

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THANK YOU
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AyurData Team
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