After a long period of stagnancy since its original inception, Ayurveda research has caught up speed in the recent times. The research methodology in general got modernized both in terms of data capturing methods and inferential process. Thereby, we are witnessing more and more sophisticated study designs being employed and more of allopathic parameters being measured in investigations undertaken in Ayurveda. This article attempts to consolidate some of the methodological developments currently being pursued in the domain.

1. Investigation modes in Ayurveda
After a long period of stagnancy since its original inception, Ayurveda research has caught up
speed in the recent times. The research methodology in general got modernized both in terms
of data capturing methods and inferential process. Thereby, we are witnessing more and more
sophisticated study designs being employed and more of allopathic parameters being
measured in investigations undertaken in Ayurveda. This article attempts to consolidate some
of the methodological developments currently being pursued in the domain.
Statistics is traditionally defined as the science of collection, organization, analysis and
interpretation of data. This process as applied to research is part of the broader scientific
approach to knowledge discovery. Creativity, objectivity, repeatability, pattern recognition and
modelling are hallmarks of modern knowledge discovery process. Historically, the paradigm
shift mainly occurred in terms of availability of big data and computationally intensive methods
although the core principles of data collection and inference remained the same. In this
transformation, Bayesian approaches gathered some momentum over the Frequentist
methods.
As usual, the broad modes of investigations are the following:
Experimentation
Phase I trials seem to be rarely undertaken in Ayurveda as most of the formulations have an
old history. Reverse pharmacology is in order most of the times because the conventional
drug discovery approach of screening thousands of molecules and their biological targets is
time-consuming and expensive. Reverse pharmacology makes it less time-consuming and
less expensive, with lower risks. The experimental designs are kept simple in such trials and
the repeated measurements over time are analysed through generalized linear models.
Distinction between different types of trials like superiority, equivalence and non-inferiority
trials is a notable item to be looked into while designing these experiments. Sample size
computations and hypothesis testing procedures differ with these types of trials. A large
number of hypotheses gets tested due to multiple characters observed but multiplicity
corrections are not frequently carried out. The sample size is kept around 100-200 which can
at best serve as a Phase II trial. It is important to gather information on treatment compliance
in such trials to get estimates of efficacy rather than effectiveness.
Large Phase III Randomized Clinical Trials (RCTs) of 300-3000 patients are not that popular
in Ayurveda. Post marketing studies (Phase IV) also do not seem to be systematically
enforced. However, pharmacovigilance is practiced by many institutions although the safety
concerns are not very high with Ayurvedic formulations.
One dominant feature that is missing in Ayurveda trials is the use of stratification required in
Ayurveda experiments. Ayurveda by its very principles recommends biotype (Prakriti) -
specific treatments which is emerging only now in modern medicine. However, we do not see
such stratification widely practiced in many Ayurveda trials. Ayurgenomic studies are still in its
infancy and when developed fully could throw in very important information of fundamental
value.
Bayesian designs like adaptive designs are not practiced either due to deficiency in knowledge
or experts or the sample size not being over critical in Ayurveda trials. Similarly, less emphasis
is given to creation of SDTM/ADaM datasets as there is no insistence on these standards by
approving authorities. The use of crossover designs become relevant for reducing the sample
size but such designs are rarely adopted.

2. Surveys
Surveys should ordinarily form a convenient mode of investigation as it can generate
information of value quickly and are also applicable to a large population. Other than
stratification, the basic sampling methods are simple random sampling, multistage sampling
and systematic sampling. On the other hand, multiphase sampling can effectively be used for
measuring multiple characters some of which are difficult to measure and also for studying
time trends. Surveys are popular in Ayurveda and stratified multistage sampling is a very
useful option. Stratification improves precision whereas multistage sampling reduces cost. For
a change assessment, at least a two-phase sampling will work out effective.
The conventional sampling uses sampling frames which are lists of all sampling units in the
population like list of individuals, households, schools, villages or other convenient units. In
instances where such frames are not possible to be formed, area frames are utilizable. Area
sampling involves sampling from a map, an aerial photograph, or a similar area frame. It is
often the sampling method of choice when a sampling frame isn’t available. For example, a
city map can be divided into equal sized blocks, from which random samples can be
drawn. The use of area frames got momentum with the availability of Geographic Information
System (GIS) with which a huge number of characteristics can be analysed and visualized in
multiple layers, simultaneously. For instance, in a prevalence study, area sampling is an option
to relate the prevalence with any geographical features.
Sometimes, choice of a domain (subpopulation based on region or other attributes) becomes
relevant. A suitable choice of a domain coupled with small area estimation is an efficient way
of conducting surveys but the estimation methods are quite complex and not practical for small
scale surveys.
Survey data can be used to study relationship between different attributes but the major
disadvantage of using such data is the inability to attribute causation for observed correlations
unless a corresponding justification can be worked out based on technical arguments. The
relationships identified are of value and could lead to identification of many underlying effects.
A host of regression and associated techniques are available to investigate the relationships
between variables and to develop prediction models. They invariably use a training set and
thus are classified as supervised learning techniques. In contrast quite many techniques
belong to unsupervised learning which have more of descriptive value. In this respect, many
multivariate analyses like principal component analysis and clustering become useful.
Regression analysis involves certain inbuilt assumptions and care has to be taken to check
these assumptions and take remedial measures in case of violation. Model validation is also
an important step in the overall process.
Case control studies
Case control studies have been identified as a very practical means to study association
between occurrence of diseases and exposure factors. If properly executed, this approach
can be a valuable source of information. By definition, a case-control study is always
retrospective because it starts with an outcome and then traces back to investigate exposures.
When the subjects are enrolled in their respective groups, the outcome of each subject is
already known by the investigator. This, and not the fact that the investigator usually makes
use of previously collected data, is what makes case-control studies ‘retrospective’.
Although controls must be like the cases in many ways, it is possible to over-match. Over-
matching can make it difficult to find enough controls. Also, once a matching variable has been
selected, it is not possible to analyse it as a risk factor. For instance, matching for a particular

3. kind of surgery would mean including the same percentage of controls as cases who had the
same surgery. if this were done, it would not be possible to include the surgery as a potential
risk factor for the incidence of cases. Matching controls to cases will mitigate the effects
of confounders. A confounding variable is one which is associated with the exposure and is a
cause of the outcome. If exposure to toxin ‘X’ is associated with melanoma, but exposure to
toxin ‘X’ is also associated with exposure to sunlight (assuming that sunlight is a risk factor for
melanoma), then sunlight is a potential confounder of the association between toxin ‘X’ and
melanoma.
Case control studies help us identify the major exposure factors associated with
occurrence/non-occurrence of a condition. It is possible to calculate the odds ratios as well
through statistical analysis. Again, model validation is an important step usually assessed
through accuracy, sensitivity or specificity. Logistic regression has been identified as the most
useful technique to be adopted in such studies with its variants such as ordinal logistic and
multinomial logistic regression. In the case of matched samples, conditional logistic regression
needs to be applied. Many more classifiers are available to be used in such situations like
decision tree, random forest, k-nearest neighbour techniques, neural network and support
vector machines. Many of these can be used for both classification and prediction problems.
These are part of the broader data science methods usually applicable to large datasets.
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. Traditional regression methods are
not equipped to handle censoring, a special type of missing data that occurs in time-to-event
analyses when subjects do not experience the event of interest during the follow-up time.
There are four main methodological considerations in the analysis of time to event or survival
data. It is important to have a clear definition of the target event, the time origin, the time scale,
and to describe how participants will exit the study. Once these are well-defined, then the
analysis becomes more straight-forward. Typically, there is a single target event, but there are
extensions of survival analyses that allow for multiple events or repeated events. The time
origin is the point at which follow-up time starts. There are three main types of censoring, right,
left, and interval. If the events occur beyond the end of the study, then the data is right-
censored. Left-censored data occurs when the event is observed, but exact event time is
unknown. Interval-censored data occurs when the event is observed in an interval so the exact
event time is unknown. Most survival analytic methods are designed for right-censored
observations, but methods for interval and left-censored data are available.
Three different types of research questions that may be of interest for TTE data include:
What proportion of individuals will remain free of the event after a certain time, survival
function, S(t): the probability that an individual will survive beyond time t, i.e., Pr (T>t).
What proportion of individuals will have the event after a certain time, probability density
function, f(t), or the cumulative incidence function, F(t): the probability that an individual will
have a survival time less than or equal to t, i.e., Pr (T≤t).
What is the risk of the event at a particular point in time, among those who have survived until
that point, hazard function, h(t): the instantaneous potential of experiencing an event at time t,
conditional on having survived to that time; Cumulative hazard function and H(t): the integral
of the hazard function from time 0 to time t, which equals the area under the curve h(t) between
time 0 and time t.
The main assumption in analysing TTE data is that of non-informative censoring: individuals
that are censored have the same probability of experiencing a subsequent event as individuals

4. that remain in the study. Informative censoring is analogous to non-ignorable missing data,
which will bias the analysis. There is no definitive way to test whether censoring is non-
informative, though exploring patterns of censoring may indicate whether an assumption of
non-informative censoring is reasonable. If informative censoring is suspected, sensitivity
analyses, such as best-case and worst-case scenarios, can be used to try to quantify the effect
that informative censoring has on the analysis. Another assumption when analysing TTE data
is that there is sufficient follow-up time and number of events for adequate statistical power.
This needs to be considered in the study design phase, as most survival analyses are based
on cohort studies.
There are three main approaches to analysing TTE data: non-parametric, semi-parametric
and parametric approaches. The choice of which approach to use should be driven by the
research question of interest.
Non-parametric approaches do not rely on assumptions about the shape or form of
parameters in the underlying population. The most common non-parametric approach in the
literature is the Kaplan-Meier (or product limit) estimator. The main assumptions of this
method, in addition to non-informative censoring, is that there is no cohort effect on survival,
so subjects have the same survival probability regardless of when they came under study. To
test the difference between the survival curves, the log rank test or the Wilcoxon test can be
used.
As a case of semi-parametric approach, the Cox Proportional model is the most commonly
used multivariable approach for analysing survival data in medical research. It is essentially a
time-to-event regression model, which describes the relation between the event incidence, as
expressed by the hazard function, and a set of covariates. The parametric component is
comprised of the covariate vector. The covariate vector multiplies the baseline hazard by the
same amount regardless of time, so the effect of any covariate is the same at any time during
follow-up, and this is the basis for the proportional hazards assumption. There are methods to
test proportional hazards assumptions and also methods to deal when these assumptions are
violated.
Parametric approaches are more informative than non- and semi-parametric approaches. In
addition to calculating relative effect estimates, they can also be used to predict survival time,
hazard rates and mean and median survival times. They can also be used to make absolute
risk predictions over time and to plot covariate-adjusted survival curves. When the parametric
form is correctly specified, parametric models have more power than semi-parametric models.
Accelerated Failure Time (AFT) models are a class of parametric survival models that can be
linearized by taking the natural log of the survival time model. An initial step in fitting an AFT
model is determining which distribution should be specified for the survival times Ti. Under the
AFT model parameterization, the distribution chosen for Ti dictates the distribution of the error
term εi. For instance, if survival times are modelled as a Weibull distribution, the error term is
assumed to follow an extreme-value distribution. There is a large number of choices available
for the distributional form of Ti and the estimation methods also differ accordingly.
Time series analysis
Time series data occur frequently in clinical domain. 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. Such data have become more abundant these
times with the availability of wearables like smart watches and other electronic devices. 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.

5. Methods for time series analysis may be divided into two classes: frequency-domain methods
and time-domain methods. The former includes spectral analysis and wavelet analysis; the
latter includes auto-correlation and cross-correlation analysis. Additionally, time series
models help in identifying trends, seasonality and cyclical nature inherent in a series. These
models are many times useful for forecasting, i.e., predicting future values of the series.
For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a
number of cycles per unit time. For counts per unit of time, the SI unit for frequency is
hertz (Hz); 1 Hz means that an event repeats once per second. The time period (T) is the
duration of one cycle and is the reciprocal of the frequency (f): T = (1/f). The fundamental basis
of analysis in the frequency domain is the Fourier transform. Fourier showed that any periodic
waveform can be decomposed into a series of sine and cosine waves. The power
spectrum Sx(f) of a time series [xt = f(t)] describes the distribution of power into frequency
components composing that signal. According to Fourier analysis, any physical signal can be
decomposed into a number of discrete frequencies, or a spectrum of frequencies over a
continuous range. The statistical average of a certain signal or sort of signal (including noise)
as analysed in terms of its frequency content, is called its spectrum. The more commonly used
term is the power spectral density (or simply power spectrum), which applies to signals
existing over all time, or over a time period large enough (especially in relation to the duration
of a measurement) that it could as well have been over an infinite time interval.
Spectral analysis is one class of procedures which has immense potential in Ayurveda
because serial measurements at small intervals like ECG are abundantly used in Ayurveda
clinical trials. Also, diagnosis through pulse is a fundamental aspect of Ayurveda.
Meta-analysis
Researchers trying to aggregate and synthesize the literature on a particular topic are
increasingly conducting meta-analyses. Broadly speaking, a meta-analysis can be defined as
a systematic literature review supported by statistical methods where the goal is to aggregate
and contrast the findings from several related studies. Thus, meta-analysis aims to assess the
relative effectiveness of several interventions and synthesize evidence across a network of
randomized and/or non-randomized clinical trials or other relevant sources of information. For
example, we may be able to express the results from a RCT examining the effectiveness of a
medication in terms of an odds ratio, indicating how much higher/lower the odds of a particular
outcome (e.g., remission) were in the treatment compared to the control group. The set of
odds ratios from several studies examining the same medication then forms the data which is
used for further analyses. For example, we can estimate the average effectiveness of the
medication (i.e., the average odds ratio) or conduct a moderator analysis, that is, we can
examine whether the effectiveness of the medication depends on the characteristics of the
studies like average age of the participants, geographical location etc. Depending on the types
of studies and the information provided therein, a variety of different outcome measures can
be used for a meta-analysis, including the odds ratio, relative risk, risk difference, the
correlation coefficient, and the (standardized) mean difference.
Both fixed and random/mixed effects models are employed to analyse the data from meta-
analytical studies. Also, the models work both under frequentist and Bayesian framework.
Bayesian analysis will require specification of priors, i.e., information available on the status
of parameters of our model. A graphical overview of the synthesized results can be obtained
by creating a forest plot.
Network meta-analysis (NMA) extends traditional meta-analysis concept by including multiple
pairwise comparisons across a range of interventions across studies. With a network meta-
analysis, the relative effectiveness of two treatments can be estimated even if no studies
directly compare them (indirect comparisons). It provides direct evidence which comes from
studies directly randomizing treatments of interest and indirect evidence which comes from

6. studies comparing treatments of interest with a common comparator. Direct and indirect
treatment comparisons are also popularly referred to as mixed treatment comparisons (MTC).
For instance, with two independent trials with treatments H and Q against Placebo (P), it is
possible to make indirect comparisons between H and Q based on NMA. If a direct comparison
between H and Q is available, this information can then be combined with indirect comparison
to produce stronger evidence.
Researchers are also increasingly using real world evidence (RWE) for synthesizing
information from nonclinical sources with information from regular RCTs. RWE can include
non-randomized studies, electronic health records, disease registries, and claims data but are
not limited to these. Although RCTs are considered the most reliable source of information on
relative treatment effects, their strictly experimental setting and inclusion criteria may limit their
ability to predict results in real-world clinical practice. RWE is increasingly used due to its
greater potential for generalizability to clinical practice than RCT findings. However, RWE is
associated with selection bias due to the absence of randomization.
Other investigation modes
Studies in pharmacokinetics, epidemiology, ayur-genomics and biotechnology are other
investigation modes which are highly specialized. The details of these methods are reserved
for a later context.
Kadiroo Jayaraman
AyurData