1. The document discusses sampling techniques and sample size calculations for quantitative and qualitative data. It provides formulas to calculate sample size based on population parameters, desired confidence level, and allowable error. 2. Meta-analysis is defined as the statistical analysis of results from multiple studies to integrate findings. Conducting meta-analysis allows for more precise and generalizable treatment estimates compared to single studies. 3. Both advantages and limitations of meta-analysis are discussed. While it provides powerful tools to synthesize evidence, limitations include heterogeneity between studies, publication bias, and potential for poor methodology.

1. Presenter:
Saurabh Bhardwaj MD,
Cardiology Trainee,
National Heart Institute,
New Delhi

2.  Sample is a representative of the population to which the results will be eventually generalized.
 It is not possible to include each member (sampling unit) of the population in an experimental study or
enquiry or examine all the millions of people.
 Difficulties faced- uniformity and correctness may vary, cost, time consuming and laborious. Solution-
use an appropriate sampling technique.
 The two main objectives of sampling are:
 1. Estimation of population parameters (mean, proportion, etc.) from the sample statistics.
 2.To test the hypothesis about the population from which the sample or samples are drawn.
 There are two main characteristics of a representative sample:
 1. Precision which implies the size of the sample
 2. Unbiased character
 The sample should be sufficiently large to provide statistical stability or reliability.

3. For Qualitative data
 If the SD (σ) in a population is known from the past experience, the size of sample can be
determined by the following formulae with the desired allowable error (E).
 At 5% risk the true estimate will lie beyond the allowable error (variation).
 Hence, the first step is to decide how large an error due to sampling defects can be
tolerated or allowed in the estimates. Such allowable error has to be stated by the
investigator.
 The second step is to express the allowable error in terms of confidence limits. Suppose E is
the allowable error in the sample mean and we are willing to take a 5% chance that the
error will exceed E. so=
Example
 Mean pulse rate of a population is believed to be 70 per minute with a standard deviation of
8 beats. Calculate the minimum size of the sample to verify this, if allowable error E = ±1
beat at 5% risk.
 If E is less, n will be more, i.e. larger the sample size, lesser will be the error.

4.  Assumption usually made is that the allowable error does not exceed 10% or 20% of the
positive character.
 The size can be calculated by the following formula with a desired allowable error (E) at 5%
risk that the true estimate will not exceed allowable error by 10% or 20% or ‘p’
 𝒏 = 𝟒𝒑𝒒/𝑬2
 Where ‘p’ is the positive character, q = 1 – p and E = allowable error, 10% or 20% of ‘p’.
Example
 Incidence rate in the last influenza epidemic was found to be 50 per thousand (5%) of the
population exposed. What should be the size of sample to find incidence rate in the current
epidemic if allowable error is 0.005 and 0.01?
 If E = 0.005
 𝑛 = 4 ∗ 0.05 ∗ 0.95/(0.005)2 =7600
 If E = 0.01
 𝑛 = 4 ∗ 0.05 ∗ 0.95/ 0.01 2 = 1900
 So larger the permissible error, the smaller will be the size of sample required for both
types of data.

5.  The first definition of metaanalysis was given by Gene Glass [1976] as
“the statistical analysis of a large collection of results from individual studies for the purpose
of integrating the findings”.
 Huque [1988] defined the term as
“A statistical analysis that combines or integrates the results of several independent
clinical trials considered by the analyst to be combinable”
 Offer the advantage of applying objective statistical criteria, including addressing the
variability between studies (heterogeneity) and thus can easily be done with the ready to
use software regardless of the number of studies that need to be synthesized.
 Steps while conducting meta-analysis
 1. Formulating a research question
 2.Writing the protocol and registering it in public domain.
 3. Identification of the studies using a clear and comprehensive search strategy.
 4. Selecting the right studies to be included [based on the protocol]
 5. Data abstraction
 6. Quality Assessment of included studies
 7. Statistical analysis [including generating the Forest plot]

7. In general, meta-analysis will allow the researcher:
1. To produce a more precise estimate of the effect of a particular treatment than it is
possible using only a single study.
2. To produce a treatment effect estimate that has more “generalizability” arising from the
combination of different studies and theories. Deduction from theory, building a meta-
analysis model, will provide a useful insight to risk assessors and modelers), as it is
obtained from studies that use different populations and factors.
3. To define coding variables or moderators that contain specific information of the
individual studies such as population type (male, female, strata, etc), data collection
procedures, research designs and other basic study characteristics. These coding variables
may make it possible to explain the differences among results from individual studies.
4. To assess the presence of heterogeneity and explore the robustness of the main findings
using sensitivity analysis.

8.  A single number cannot summarize an entire area of research as each study is different
from the other
 Publication bias. Negative studies are less likely to be published.
 When studies are combined, it is like mixing apples and oranges [as every study
fundamentally differs from another].
 Key studies may be ignored.
 A meta -analysis may show a completely different result that a large Randomized
Controlled Trial [RCT].
 The researcher may perform the meta-analysis poorly

9.  Meta -analyses are extremely important in today’s world of Evidence Based Medicine as they
have the ability to use powerful statistical tools and software to combine studies with identical
research questions [those that have similar designs, selection criteria and patient populations].
 Their utility lies in the fact that individually, these studies may be small and underpowered to pick
up treatment differences, but when combined in a metaanalysis; answer a well-formulated
question to guide Evidence based clinical practice.
 Key challenges-
 adequacy of the literature search and the subsequent data abstraction.
 how similar [or dissimilar] are the studies that have been put together and thus looking at
heterogeneity.
 choice of the model used.
 quality of the studies and the presence [or lack thereof] of publication bias.
 Both researchers carrying out the metaanalysis and readers who evaluate and use them should
bear all of the above in mind as decision making in clinical practice is influenced by them.

10. "Our main business of life is not to see what lies dimly at a distance,
but to do what lies clearly at hand."
-Thomas Carlyle