Sampling Techniques Dr Shaik Shaffi Ahamed Ph D

Sampling Techniques Dr. Shaik Shaffi Ahamed Ph. D. , Assistant Professor Department of Family & Community Medicine College of Medicine King Saud University

Why should we take sample? , Can’t we study the whole ? It is possible depends on objective -to know how many live in a country --age and sex categories --changing pattern of age structure --when plan for country CENSUS --death in a hospital record all the death It is not possible -to test the life of bulbs – burn bulbs till it lost its life -count of RBW in blood – draw all the blood & count -Count the stars in the sky It is not necessary - estimate Hb% in blood – a drop of blood is enough – blood in any part of the body will provide same

Populations and Sampling Reasons for using samples There are many good reasons for studying a sample instead of an entire population: • Samples can be studied more quickly than populations. Speed can be important if a physician needs to determine something quickly, such as a vaccine or treatment for a new disease. • A study of a sample is less expensive than a study of an entire population because a smaller number of items or subjects are examined. This consideration is especially important in the design of large studies that require a long follow-up. • A study of the entire populations is impossible in most situations. • Sample results are often more accurate than results based on a population.

Sampling in Epidemiology • Why Sample? – Unable to study all members of a population – Reduce bias – Save time and money – Measurements may be better in sample than in entire population – Feasibility

Sampling is the process or technique of selecting a sample of appropriate characteristics and adequate size.

Terminology Study Population • A population may be defined as an aggregate of all things / units possessing a common trait or characteristic. • The whole collection of units (“the universe”).

Terminology – Cont. Target (Study) Population • The population that possesses a characteristic (parameter) which we wish to estimate or concerning which, we wish to draw conclusion. • The population you expect the eventual results of the research to apply (target of inference). • It may be real or hypothetical.

Terminology – Cont. Sample • A selected subset of the study population. • Chosen by some process (e. g. sampling) with the objective of investigating particular characteristic (parameter) of the study population. Sampling • Process of obtaining a sample from the target population.

Terminology – Cont. Sampling Frame • This is the complete list of sampling units in the target population to be subjected to the sampling procedure. • Completeness and accuracy of this list is essential for the success of the study. Sampling Units These are the individual units / entities that make up the frame just as elements are entities that make up the population.

Terminology – Cont. Study Participants • Subjects that are actually participating in the study. • Subset of study population that were contactable and consented / agreed to participate.

Study Participants - Cont. Study participants may still be not representative of the target population even with random sampling because of: – Sampling frame is out of date. – Failure to recruit eligible subjects. – Non consent or non response. – Drop Out / Withdrawal.

Terminology – Cont. Sampling Error This arises out of random sampling and is the discrepancies between sample values and the population value. Sampling Variation • Due to infinite variations among individuals and their surrounding conditions. • Produce differences among samples from the population and is due to chance.

Repeat the same study, under exactly similar conditions, we will not necessarily get identical results. • Example: In a clinical trail of 200 patients we find that the efficacy of a particular drug is 75% If we repeat the study using the same drug in another group of similar 200 patients we will not get the same efficacy of 75%. It could be 78% or 71%. “Different results from different trails though all of them conducted under the same conditions”

Example: If two drugs have the same efficacy then the difference between the cure rates of these two drugs should be zero. But in practice we may not get a difference of zero. If we find the difference is small say 2%, 3%, or 5%, we may accept the hypothesis that the two drugs are equally effective. On the other hand, if we find the difference to be large say 25%, we would infer that the difference is very large and conclude that the drugs are not

Example: If we testing the claim of pharmaceutical company that the efficacy of a particular drug is 80%. We may accept the company’s claim if we observe the efficacy in the trail to be 78%, 81%, 83% or 77%. But if the efficacy in trail happens to be 50%, we would have good cause to feel that true efficacy cannot be 80%. And the chance of such happening must be very

• THEREFORE “WHILE TAKING DECISIONS BASED ON EXPERIMENTAL DATA WE MUST GIVE SOME ALLOWANCE FOR SAMPLING VARIATION “. “VARIATION BETWEEN ONE SAMPLE AND ANOTHER SAMPLE IS KNOWN AS SAMPLING VARIATION”.

Decisions Required for selecting sample 1. Specify what is the target population. This is entirely determined by the research objective. 2. Specify what is the study population. (e. g. who are eligible for inclusion in the study) 3. Select a sampling design for obtaining a sample for study. 4. Strategy to ensure high response or participation rate, otherwise inference must take account of non-responses. Decisions will have considerable impact on study validity (soundness of conclusion or inference made).

Study populations and sampling summarized schematically Target population: real or hypothetical Select based on judgment and accessibility Study Population Probability sampling Sample Consent or respond Participants in study

How to sample ? In general 2 requirements 1. Sampling frame must be available, otherwise construct one or use special sampling techniques. Frame construction may not be easy. 2. Choose an appropriate sampling method to draw a sample from the frame.

The Sampling Design Fig. 11. 1 Process Define the Population Determine the Sampling Frame Select Sampling Technique(s) Determine the Sample Size Execute the Sampling Process

Classification of Sampling Fig. 11. 2 Techniques Sampling Techniques Nonprobability Sampling Techniques Convenience Sampling Judgmental Sampling Simple Random Sampling Systematic Sampling Probability Sampling Techniques Quota Sampling Stratified Sampling Snowball Sampling Cluster Sampling Other Sampling Techniques

Simple Random Sampling • A sample may be defined as random if every sampling unit in the study population has an equal chance of being selected. • Selection of SRS may be done by: – Drawing the number or name from a hat or box. – Using a Random Number Table. – Using a computer to generate the numbers.

SRS Methods • Lottery Method • Random Number Table method

Example • A Tattslotto draw is a good example of simple random sampling. A sample of 6 numbers is randomly generated from a population of 45, with each number having an equal chance of being selected.

Tables of random numbers are used after numbers have been assigned to numbers of the study population. Use random number table to select subject. Start anywhere. Continue selecting until the desired sample is reached

Random Number table 1 2 3 4 5 49486 93775 88744 80091 92732 94860 36746 04571 13150 65383 10169 95685 47585 53247 60900 12018 45351 15671 23026 55344 45611 71585 61487 87434 07498 89137 30984 18842 69619 53872 94541 12057 30771 19598 96069 89920 28843 87599 30181 26839 32472 32796 15255 39636 90819

How to select a simple random sample 1. 2. 3. • Define the population Determine the desired sample size List all members of the population or the potential subjects For example: – 4 th grade boys who have demonstrated problem behaviors – Lets select 10

Potential Subject Pool 1. Robert 2. Ralph 3. John 4. Andy 5. Joel 6. Thomas 7. Cooper 8. Maurice 9. Terry 10. Carl 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Ken Wilmer Alan Kevin James Henry Don Walt Doug George 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. Steve Larry Rick Bruce Clyde Sam Kent Travis Woody Brian

So our selected subjects are numbers 10, 22, 24, 15, 6, 1, 25, 11, 13, & 16. 1. Robert 2. Ralph 3. John 4. Andy 5. Joel 6. Thomas 7. Cooper 8. Maurice 9. Terry 10. Carl 11. Ken 12. Wilmer 13. Alan 14. Kevin 15. James 16. Henry 17. Don 18. Walt 19. Doug 20. George 21. Steve 22. Larry 23. Rick 24. Bruce 25. Clyde 26. Sam 27. Kent 28. Travis 29. Woody 30. Brian

• Simple random sampling – Estimate hemoglobin levels in patients with sickle cell anemia 1. 2. 3. 4. 5. 6. Determine sample size Obtain a list of all patients with sickle cell anemia in a hospital or clinic Patient is the sampling unit Use Lottery method/ a table of random numbers to select units from the sampling frame Measure hemoglobin in all patients Calculate mean and standard deviation of sample

• Simple random sampling – Advantages » Simple process and easy to understand » Easy calculation of means and variance – Disadvantages » Not most efficient method, that is, not the most precise estimate for the cost » Requires knowledge of the complete sampling frame » Cannot always be certain that there is an equal chance of selection » Non respondents or refusals

Sampling in Epidemiology • Systematic sampling – The sampling units are spaced regularly throughout the sampling frame, e. g. , every 3 rd unit would be selected – May be used as either probability sample or not » Not a probability sample unless the starting point is randomly selected » Non-random sample if the starting point is determined by some other mechanism than chance

Systematic Sampling • The sample is chosen by selecting a random starting point and then picking every i th element in succession from the sampling frame. • The sampling interval, i, is determined by dividing the population size N by the sample size n and rounding to the nearest integer. For example, there are 100, 000 elements in the population and a sample of 1, 000 is desired. In this case the sampling interval, i, is 100. A random number between 1 and 100 is selected. If, for example, this number is 23, the sample consists of elements 23, 123, 223, 323, 423, 523, and so on.

Example • If a systematic sample of 500 students were to be carried out in a university with an enrolled population of 10, 000, the sampling interval would be: • I = N/n = 10, 000/500 =20 • All students would be assigned sequential numbers. The starting point would be chosen by selecting a random number between 1 and 20. If this number was 9, then the 9 th student on the list of students would be selected along with every following 20 th student. The sample of students would be those corresponding to student numbers 9, 29, 49, 69, . . . . 9929, 9949, 9969 and 9989.

Systematic Sampling • Decide on sample size: n • Divide population of N individuals into groups of k individuals: k = N/n • Randomly select one individual from the 1 st group. • Select every k-th individual thereafter. N = 64 n=8 k=8 First Group

• Systematic sampling – Advantages » Sampling frame does not need to be defined in advance » Easier to implement in the field » If there are unrecognized trends in the sample frame, systematic sample ensure coverage of the spectrum of units – Disadvantages » Variance cannot be estimated unless assumptions are made

Stratified Sampling • A two-step process in which the population is partitioned into subpopulations, or strata. • The strata should be mutually exclusive and collectively exhaustive in that every population element should be assigned to one and only one stratum and no population elements should be omitted. • Next, elements are selected from each stratum by a random procedure, usually SRS. • A major objective of stratified sampling is to increase precision without increasing cost.

• Stratified random sample –The sampling frame comprises groups, or strata, with certain characteristics –A sample of units are selected from each group or stratum

Sampling in Epidemiology • Stratified random sample – Assess dietary intake in adolescents 1. 2. 3. 4. 5. Define three age groups: 11 -13, 14 -16, 17 -19 Stratify age groups by sex Obtain list of children in this age range from schools Randomly select children from each of the 6 strata until sample size is obtained Measure dietary intake

Stratified Random selection for drug trail in hypertension Mild Moderate Severe

• Stratified random sample – Advantages » Assures that certain subgroups are represented in a sample » Allows investigator to estimate parameters in different strata » More precise estimates of the parameters because strata are more homogeneous, e. g. , smaller variance within strata » Strata of interest can be sampled most intensively, e. g. , groups with greatest variance » Administrative advantages – Disadvantages » Loss of precision if small number of units is sampled from strata

Cluster Sampling • The population is first divided into mutually exclusively groups of elements called clusters. • Ideally, each cluster is a representative small-scale version of the population (i. e. heterogeneous group). • A simple random sample of the clusters is then taken. • All elements within each sampled (chosen) cluster form the sample. • Elements within a cluster should be as heterogeneous as possible, but clusters themselves should be as homogeneous as possible. Ideally, each cluster should be a small-scale representation of the population.

• Cluster sampling – Estimate the prevalence of dental caries in school children 1. 2. 3. 4. Among the schools in the catchments area, list all of the classrooms in each school Take a simple random sample of classrooms, or cluster of children Examine all children in a cluster for dental caries Estimate prevalence of caries within clusters than combine in overall estimate, with variance

• Cluster sampling – Advantages » The entire sampling frame need not be enumerated in advance, just the clusters once identified » More economical in terms of resources than simple random sampling – Disadvantages » Loss of precision, i. e. , wider variance, but can be accounted for with larger number of clusters

Multistage Sampling • Similar to cluster sampling except that there are two sampling events, instead of one – Primary units are randomly selected – Individual units within primary units randomly selected for measurement

Multi–Stage Sampling • This sampling method is actually a combination of the basic sampling methods carried out in stages. • Aim of subdividing the population into progressively smaller units by random sampling at each stage.

Sampling in Epidemiology • Multistage sampling – Estimate the prevalence of dental caries in school children 1. Among the schools in the catchments area, list all of the classrooms in each school 2. Take a simple random sample of classrooms, or cluster of children 3. Enumerate the children in each classroom 4. Take a simple random sample of children within the classroom 5. Examine all children in a cluster for dental caries 6. Estimate prevalence of caries within clusters than combine in overall estimate, with variance

Classification of Sampling Fig. 11. 2 Techniques Sampling Techniques Nonprobability Sampling Techniques Convenience Sampling Judgmental Sampling Simple Random Sampling Systematic Sampling Probability Sampling Techniques Quota Sampling Stratified Sampling Snowball Sampling Cluster Sampling Other Sampling Techniques

Sampling Methods Non-probability samples

Convenience Sampling Convenience sampling attempts to obtain a sample of convenient elements. Often, respondents are selected because they happen to be in the right place at the right time. – use of students, and members of social organizations – mall intercept interviews without qualifying the respondents – department stores using charge account lists – “people on the street” interviews

• Convenience sample – Case series of patients with a particular condition at a certain hospital –“Normal” graduate students walking down the hall are asked to donate blood for a study – Children with febrile seizures reporting to an emergency room Investigator decides who is enrolled in a study

Judgmental Sampling Judgmental sampling is a form of convenience sampling in which the population elements are selected based on the judgment of the researcher. – It involves hand-picking from the accessible population those individuals judged most appropriate for the study.

QUOTA SAMPLING

Quota Sampling Quota sampling may be viewed as two-stage restricted judgmental sampling. – The first stage consists of developing control categories, or quotas, of population elements. – In the second stage, sample elements are selected based on convenience or judgment. Control Characteristic Sex Male Female Population composition Sample composition Percentage Number 48 52 ____ 100 480 520 ____ 1000

QUOTA SAMPLING

Snowball Sampling In snowball sampling, an initial group of respondents is selected, usually at random. – After being interviewed, these respondents are asked to identify others who belong to the target population of interest. – Subsequent respondents are selected based on the referrals.

Consecutive sample • Consecutive sample – A case series of consecutive patients with a condition of interest – Consecutive series means ALL patients with the condition within hospital or clinic, not just the patients the investigators happen to know about

• Consecutive sample – Outcome of 1000 consecutive patients presenting to the emergency room with chest pain – Natural history of all 125 patients with HIVassociated TB during 5 year period Explicit efforts must be made to identify and recruit ALL persons with the condition of interest

Sampling Methods Non-probability samples • • Depends on expert’s opinion, Probabilities of selection not considered. Advantages: include convenience, speed, and lower cost. Disadvantages; – Lack of accuracy, – lack of results generalizability.

Random sampling: every combination of a given size has an equal chance of being chosen. Availability sampling: selecting on the basis of convenience. Cluster sampling: dividing the population into clusters, typically on the basis of geography, and taking a sample of the clusters. Multi-stage sampling: sampling subunits within sampled units. Quota sampling: selecting fixed numbers of units in each of a number of categories. Snowball sampling: asking individuals studied to provide references to others. Stratified sampling: dividing the population into groups on the basis of some characteristic and then sampling each group. Systematic sampling: choosing every nth item from a list, beginning at a random point.

Strengths and Weaknesses of Basic Sampling Techniques Table 11. 3 Technique Strengths Weaknesses Nonprobability Sampling Convenience sampling Least expensive, least time-consuming, most convenient Low cost, convenient, not time-consuming Sample can be controlled for certain characteristics Can estimate rare characteristics Selection bias, sample not representative, not recommended for descriptive or causal research Does not allow generalization, subjective Selection bias, no assurance of representativeness Time-consuming Easily understood, results projectable Difficult to construct sampling frame, expensive, lower precision, no assurance of representativeness. Can decrease representativeness Judgmental sampling Quota sampling Snowball sampling Probability sampling Simple random sampling (SRS) Systematic sampling Stratified sampling Cluster sampling Can increase representativeness, easier to implement than SRS, sampling frame not necessary Include all important subpopulations, precision Easy to implement, cost effective Difficult to select relevant stratification variables, not feasible to stratify on many variables, expensive Imprecise, difficult to compute and interpret results

Random. . . • Random Selection vs. Random Assignment – Random Selection = every member of the population has an equal chance of being selected for the sample. – Random Assignment = every member of the sample (however chosen) has an equal chance of being placed in the experimental group or the control group. » Random assignment allows for individual differences among test participants to be averaged out.

Subject Selection (Random Selection) Choosing which potential subjects will actually participate in the study

Subject Assignment (Random Assignment) Deciding which group or condition each subject will be part of Group A Group B

Population: 200 8 th Graders 40 High IQ students 120 Avg. IQ students 40 Low IQ students 30 students 15 students 15 students Group A Group B

Randomization (Random assignment to two treatments) • Randomization tends to produce study groups comparable with respect to known and unknown risk factors, • removes investigator bias in the allocation of participants • and guarantees that statistical tests will have valid significance levels • Trialist’s most powerful weapon against bias

Randomization (Cont) • Simple randomization: Toss a Coin – AAABBAAAAABABABBAAAAB AA… • Random permuted blocks (Block Randomization) – AABB-ABBA-BBAA-BAABABAB-AABB-…

Block Randomization • Each block contains all conditions of the experiment in a randomized order. E, C, C, E C, E, C, E Experimental Group N = 6 E, E, C, C Control Group N = 6

Prevalence and risk factors of HIV 1 and HIV 2 infection in Urban and rural areas in TN. Int. J. of STD & AIDS 1998; 9: 98 -103 TN Objective: Find prevalence and risk factors. Objective: Setting: Centers in metropolitan city & municipality. Setting: Subjects: Individuals in Tamil nadu. Subjects: Sampling Procedure: “ Health camps were organized in 5 urban and 5 rural centers to cover entire state graphically” “ Every third person screened, in the active reproductive age group, were recruited as a subject. At each camp the inclusion of subjects continued until 200 persons were recruited”

Sex differences in the use of asthma drugs: Cross-sectional study. BMJ 1998; 317: 1434 -7 Objective : To assess the use of asthma drugs. Design : Crosssectional study. Setting: Six general practices in East Anglia. Subjects : Adults aged 20 -54 with Asthma Sampling method “identify cases with asthma received drugs one year before – through database from each participating practices. The sample was stratified into three categories of severity corresponding the prescribed drugs Bronchodilator alone (mild) 38% Steroids (moderate) 57% Nebulizer treatment (severe) 5% Use SRS to select subject in each practice based on proportion of use of each type of drug within the practice

Genital ulcer disease and acquisition of HIV infection. Indian J Med Microbiol 1992; 10(4): 265 -269 Objective : To find out the association of HIV infection with Objective : genital ulcer disease. Setting : Dept. of STD, GGH, Chennai. : Subjects : Individuals attending the STD dept. Subjects Sampling procedure ‘ Blood samples from first 20 patients were taken for analysis once a week for 40 weeks’.

Prevalence of series eye disease and visual impairment in a north London population: Population based, cross sectional study. BMJ 1998; 316: 1643 -48. Objective: To estimate eye disorders and of visual impairment Design: Cross-sectional survey. Setting : General Practices in metropolitan in England. Subjects: aged 65 or older & registered

Sampling Procedure 17 general practice group Random sampling 7 were selected People age 65 or older were registered with the general practices. Total 750 -850 in each Gen Pract Use SRS to select eligible people in each practice One third in each practices were selected to form survey sample

A die is rolled to decide which one of the six volunteers will get a new , experimental vaccine A. Simple Random sampling B. Stratified random sampling C. Cluster sampling D. Systematic random sampling

A sample of students in a school is chosen as follows: Two students are selected from each batch by picking roll number at random from the attendance registers A. Simple Random sampling B. Stratified random sampling C. Cluster sampling D. Systematic random sampling

A target population for a telephonic survey is picked by selecting 10 pages from a total of 100 pages from a telephone directory by using a table of random numbers. In each of the selected pages, all listed persons are called for Interview A. Simple Random sampling B. Stratified random sampling C. Cluster sampling D. Systematic random sampling

The number 35 is a two-digit random number generated by a calculator. A sample of two wheelers in a state is selected by picking all those vehicles have registration numbers ending with 35 A. B. C. D. Simple Random sampling Stratified random sampling Cluster sampling Systematic random sampling

Example • A medical student in a city in South Africa conducted a survey to measure the prevalence of HIV in his village. He used simple random sampling to select the subjects. At the end of his study, he was able to estimate the prevalence in the general population of the village. However, he was not able to calculate the prevalence of HIV in some subgroups such as homosexual due to the absence of this subgroup from his sample. So, to guarantee the presence of such rare group, what kind of sampling should he have used? A. Systematic random sample. B. Cluster sample. C. Multistage-staged sample. D. Stratified random sample. E. None of the above.

Example A post-graduate trainee of family medicine was assigned a project to evaluate the effect of teachers’ smoking on students’ behavior. He presented the following scenario as an explanation of his method of subjects’ selection: “Out of 400 schools in Riyadh 30 schools were selected randomly and then all subjects (teachers) in each selected school will be included in the study” The type of sampling method is: A. Multi-staged sample B. Cluster sample C. Simple random sample D. Stratified random sample E. None of the above

Example Stratified random sample: A. Make use of random number tables B. Is one type of non-random sample C. Divide the population into groups or clusters according to characteristic of interest D. Take all units in some clusters E. Increase precision