���M.S.S. in Health Economics�HE 604: Public Health and Epidemiology (PHE)�Sampling Techniques��

Dr. Aninda Nishat Moitry

MBBS, MPH, MSc, FRSPH

05 March 2023

Overview of presentation

• Basic concepts of sampling
• Non-probability sampling
• Probability sampling
• Sampling in randomized trials

Basic concepts of statistical�inference

• To answer a research question about a specific population, we, ideally should get information on the entire population
• Using a sample to make inferences about a population is the most vital aspect of epidemiologic research
• Inference are based on the process of taking a single random sample of a specific size from a population and using this sample to make judgments about the population as a whole
• These judgments are made in terms of means, variances or other summarizing statistics
• Summarizing numbers for the population are called parameters and are represented by Greek letters such as:

μ = mean,

σ= standard deviation and

s = regression coefficient

Population

• All members of a group for which information is desired or sought
• Defined unambiguously in relation to other characteristics such as time, geographic or other boundaries or characteristics
• Living being such as humans, animals, plants and microorganism or non living documents, times, events and places

Census

• Information collected from every member of a population
• Gives us complete and unbiased results
• Costly, time consuming and often hard to maintain the quality
• May not be feasible at times

Sample

• Part of a population from which information is obtained in order to derive an estimate of the population parameter
• One or more sample unit are selected to get a sample

Some definitions

• Target Population:
• Population to which the results will be generalized
• Sampling Unit:
• Smallest unit from which sample can be selected
• Sampling frame (SF):

- List of sampling units from which sample is drawn

• Sampling scheme:

- Method of selecting sampling units from SF

Population, Sampling frame, and�Sample

The rationale

• Why we do sample:
• Don’t have enough resource
• Not feasible to study all of a population
• To ensure optimum quality
• What we do
• We estimate parameter from statistics
• Statistics
• Numerical characteristics of a sample

Types of Sampling

• Non-probability samples
• Probability samples

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�Non-Probability Sampling�

• Any sampling method where some elements of population have no chance of selection
• Non‐probability sampling saves time, money and other resources but lacks external validity and information credibility
• Characteristics:
• Probability of being chosen is unknown
• Cheaper- but unable to generalise
• Potential for bias

Non Probability Sampling

Non Probability Sampling

• Purposive sampling:
• Respondents who would serve the purpose are selected as sample
• Selection of the sample is heavily dependent on the judgment of the interviews
• May not have fixed sample size nor any sampling design and it is the researcher who would select the sample considering whether the sample would serve the study
• Used during developing questionnaires, pilot studies and qualitative research such as case studies, key informant interview etc.

Non Probability Sampling (Contd.)

• Convenient sample:
• Find some people easy to find
• Snowball sample:
• Fine a few people relevant for your topic
• Ask them to refer you more
• Snowball sampling works well to study ‘hard to find’ populations and to explore sensitive issues such as
• Impact of male homosexuality on AIDS, impact of gambling or drug addiction in a conservative society
• Quota sampling
• Determine the population with some characteristics
• Create quota based on those characteristics
• Select people for each quota

What is Probability Sampling?

• Sampling:
• The act of taking a sample a process of selecting what/who will participate in a study
• You want this sample to be representative of the population as a whole so that your results are generalizable
• There is a known probability of every sample being selected

What is Probability Sampling? (Contd.)

• Random sampling: Each subject has a known probability of being selected
• Simple random sampling
• Systematic sampling
• Two-stage/multistage sampling (cluster sampling)
• Stratified sampling
• Allows application of statistical sampling theory to results to:
• Generalize
• Test hypotheses

Simple Random Sampling

• The most basic sampling design
• Randomization based on a single sequence of assignments
• Basic method are:
• Flipping a coin
• Throwing a dice
• Random number table or
• Computer-generated random numbers
• Applicable when population is small, homogeneous & readily available
• Needs a complete list of target population
• Assign a number to each of the units in a population and then use a random number generator
• Each element thus has an equal probability of selection

Challenges of SRS

• Can be problematic in relatively small sample size clinical trials resulting in an unequal number of participants among groups
• Minority subgroups of interest in population may not be present in sample in sufficient numbers for study

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Stratified Sampling

• This method addresses the need to control and balance the influence of covariates
• First, specific covariates are identified by the researcher
• Second, a separate block for each combination of covariates is generated
• Then, participants are assigned to the appropriate block of covariates
• Then, simple randomization is used within each block to assign participants to one of the groups
• When population is heterogeneous, break up the population into homogenous non overlapping groups (strata) before sampling
• Two primary reasons for using a stratified sampling design:
• To potentially improve representativeness, in terms of the stratifying variables, by gaining greater control over the composition of the sample
• To ensure that particular groups within a population are adequately represented in the sample

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Example of Stratified Sampling

Challenges of Stratified Sampling

• Sampling frame of entire population has to be prepared separately for each stratum
• When examining multiple criteria, stratifying variables may be related to some, but not to others, further complicating the design, and potentially reducing the utility of the strata
• In case of designs with a large number of strata, or those with a specified minimum sample size per group), stratified sampling can potentially require a larger sample than would other methods

Systematic Sampling

• Sampling fraction: Ratio between sample size and population size
• Every Kth unit is selected for inclusion in the sample
• Empirically identical to simple random sampling
• Used when probability sampling techniques are not applicable (no precise sampling frame)
• Involves a random start and then proceeds with the selection of every kth element onwards. k=(population size/sample size)
• The starting point is not automatically the first in the list, but instead randomly chosen from within the first to the kth element in the list
• A simple example would be to select every 10th name from the telephone directory (an 'every 10th' sample, also referred to as 'sampling with a skip of 10')

Cluster sampling

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• Also known as group randomised trials or community randomised trials
• Most appropriate design to assess the community-level impact of an intervention
• Clusters of people or intact social units, rather than individuals are randomised
• Primary Sampling Units– the clusters
• Secondary Sampling Units- individuals/ households
• Outcomes can be measured both at individuals or community level within those clusters
• Creating a “buffer zone "is important

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Cluster sampling: A visual example

Types of cluster sampling

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• One-stage cluster sample:
• List all the clusters in the population
• Select the clusters usually (with simple random sampling)
• All elements in the sampled clusters are selected for the survey
• Two-stage cluster sample:
• List all the clusters in the population
• First, select the clusters, usually by simple random sampling
• A subset of the elements in the selected clusters are then sampled in the second-stage (with simple random sampling or systematic random sampling)
• Multi stage cluster
• A more complicated form of cluster sampling in which larger clusters are further subdivided into smaller clusters
• A total population of interest is first divided into “clusters”
• Then, those divide these first-stage clusters are further divided into second-stage cluster using a second element
• Thus, it creates a more representative sample of the population

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Pros and Cons of Cluster Sampling

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• Advantages:
• Generating sampling frame for clusters is economical
• Less time for listing and implementation
• Also suitable for survey of institutions
• Disadvantages:
• May not reflect the diversity of the community
• Provides less information per observation than an SRS of the same size
• Standard errors of the estimates are high
• Standard approaches to sample size estimation and analysis no longer apply

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Randomization in Experimental Studies

Block Randomization

• The researcher divide the sample into relatively homogeneous subgroups or blocks
• Then, the experimental design is implemented within each block
• The key idea is that the variability within each block is less than the variability of the entire sample
• Although balance in sample size may be achieved with this method, groups may be generated that are rarely comparable in terms of certain covariates

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Covariate Adaptive Randomization

• A new participant is sequentially assigned to a particular treatment group by taking into account
• The specific covariates
• Previous assignments of participants
• Here the method of “minimization” is used by assessing the imbalance of sample size among several covariates
• This style allows the researcher to make a case-by-case decision on group assignment

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Thank You